Talk:Magnetic field/Archive 1

$\epsilon ,\mu$ instead of $\epsilon _{0},\mu _{0}$?

It's been a while since I've done this stuff, and I don't have my textbook here to verify, but shouldn't we be using $\epsilon ,\mu$ instead of $\epsilon _{0},\mu _{0}$? Or we can use H and D fields instead... am I correct?

Yes, you're correct. Using ε and μ would only be correct for linear media, using H and D would be more general. I fixed it by saying that the equations are only for free space -- generalities can stay at Maxwell's equations I think. -- Tim Starling 06:14 Apr 1, 2003 (UTC)

To Stephen: either magnetic field can be called "B" accurately, or we move some or all of this page to magnetic flux density. I don't like this "really it's H but we'll just call it B" business. It's too confusing. -- Tim Starling 08:49 11 Jun 2003 (UTC)

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Tim: Too bad, life (and the English language) is confusing. =) The point is, that people are not entirely consistent in their terminology, and an encyclopedia should describe this. (In most cases, μ=1 so B=H and the point is moot. It's only when you're talking about both at once that you need two different names. In this case, Jackson goes by the historical names of magnetic field for H and magnetic induction for B. Purcell writes:

Even some modern writers who treat B as the primary field feel obliged to call it the magnetic induction because the name magnetic field was historically preempted by H. This seems clumsy and pedantic. If you go into the laboratory and ask a physicist what causes the pion trajectories in his bubble chamber to curve, he'll probably answer "magnetic field," not "magnetic induction." You will seldom hear a geophysicist refer to the earth's magnetic induction, or an astrophysicist talk about the magnetic induction of the galaxy. We propose to keep on calling B the magnetic field. As for H, although other names have been invented for it, we shall call it "the field H" or even "the magnetic field H".

And this is just Purcell's take. As you say, Griffiths calls H the auxiliary field, and Jackson (the god of electromagnetism) uses the historical names only when he has to distinguish B and H.

In most cases mu=1 so B=H - this is completely wrong. What most cases? Give references. There is no such situation in real world, because B = mu_0 * mu_r * H, where B - flux density (magnetic induction) in (T), mu_0 - permeability of free space 4*pi*10^-7 (H/m), mu_r - relative permeability (referred to the mu_0) of a given medium (dimensionless), H - magnetic field (A/m). Even if mu_r = 1 then B = mu_0 * H and still B is not equal H. Calling B a magnetic field is just plain wrong and this is caused mostly by shortened notation used commonly in physics. EVERYWHERE in international electrotechnical standards (the whole series IEC:60404) the only correct notation is that H is magnetic field and B is flux density (magnetic induction). Moreover, there is also J which is magnetic polarisation. H is a completely different quantity to B - similarly we could say that since resitance = 1 then voltage is synonymous with current, which is obviously not. I am going to change the whole article soon. If someone is interested please talk to me on my discussion page, because it gets too much text here. --Zureks 15:25, 26 March 2007 (UTC)

mu=1? That is incorrect. mu is most often (for non-ferromagnetic materials) much closer to mu_0 or 4 x pi x E-7 H/m ! What is this mu=1 idea? ... I just realized that someone is probably confusing mu_r with mu! He may have read that mu_r is close to 1 for non-ferromagnetic materials -- which is indeed correct. ... I just read the remarks by Zureks above. Zureks is correct and even if mu_r=1, that in no way makes B=H. (I should have read the remarks by Zureks first.) -Emfieldtheory 09:28, 6 June 2007 (UTC)

Sure mu can equal one, when you use units such that mu_0 is also one. I don't have Jackson in front of me, but I'm pretty confident that's the usage intended. --Starwed 07:56, 7 June 2007 (UTC)

Yep! That is correct. I stand corrected. Thank you. mu can be close to 1.0 for many materials (except ferromagnetic ones -- which are way different by many orders of magnitude) when the units for mu_0 are chosen for that result. I naturally assumed SI units for permeability (mu_0= 4 x pi x E-7 H/m) before thinking about it more carefully. Jackson was probably doing as you state. I never read Jackson, but he, being a physicist (assuming that he is a physicist or his doctorate is in physics), probably has an inclination towards dealing with equations where all of the constants have their value exactly equal to 1. Many physicists tend towards this approach (no offense to the many physicists here). But this approach is very misleading for permeability since all materials differ slightly from having the exact same value for mu (pick any value -- 1.00000000 or something else). Even given mu_0=1, the only material that will exactly have mu=1 is the same material that has mu=mu_0 and that is free space -- itself an often disputed concept! This is hardly the general case! I would argue that Jackson is not doing his readers any favors by misleading them into thinking that all materials have a value of mu exactly equal to 1.0000 (where mu=mu_0), or even generally close to 1.0 (since the ferros are way different). Further, as Zureks pointed out above, even when mu=1.000000 for some single material in the universe (given the proper units), that in no way makes B=H! Writers who assume that will get into difficulty when dealing with the practical interaction of EM fields with materials. -Emfieldtheory 23:07, 7 June 2007 (UTC)

- Steven G. Johnson

At no point does Purcell say that B is formally, technically, or more accurately called magnetic induction. We are not bound by historical nomenclature, and the historical terms are not a priori "correct". We no longer refer to refractive index as "refrangibility" or to Uranus as "George's star". Common usage is what goes in dictionaries, historical usage is for the history books. This is my point: if B is magnetic field in common usage, then that definition is as "correct" as any other. But if, as you claim, B is "more accurately" called magnetic induction, it would be inappropriate to write an entire article referring to B as the magnetic field. The current situation is confusing in that we claim that the entire article is inaccurate. A student learning the material wishes to hold accurate information in their head, therefore every time they see "magnetic field" on this page, they will be distracted by a little mental note telling them that this usage is not to be trusted. -- Tim Starling 00:14 12 Jun 2003 (UTC)

Tim, people aren't consistent in their usage, and that sucks, but both usages need to be reported; describing usage is not the same thing as describing "correctness." On the one hand, the term magnetic induction is a historical one for B (a fact that would arguably be worth mentioning by itself), and it remains in present day usage when people want to disambiguate B and H (e.g. in Jackson, one of the most respected advanced electromagnetism texts, but also in 2003 physics journal articles, as a quick literature search will tell you). On the other hand, many many people (including physicists and Jackson himself) call B the magnetic field, especially when μ=1. - Steven G. Johnson

Not to put too fine a point on this, but if this Jackson (renown physicist?) says that mu is usually or closely =1 for most materials, then he is somehow very confused or he more likely may have a typo in his book and really intended mu_r! -Emfieldtheory 09:28, 6 June 2007 (UTC)

The article looks good now. Thanks. -- Tim Starling 01:04 12 Jun 2003 (UTC)

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"...the magnetic field is the field produced by a magnet." Straightforward enough, and there is a nice handy link to magnet. However, in the magnet article, I'm told that a "magnet is an object that has a magnetic field". That's not useful! That's just frustrating in a very tired and cliche manner. Could someone make one of these articles more primitive than the other? Suggestion: Make it clear to a non-physicist like me why an electron does not count as a magnet (or why the force field associated with an electron is not a magnetic field, if you prefer that point of view). (Okay, so an electron only has one pole. But having two poles can't be part of the definition of "magnet", else the article on magnetic monopole makes no sense at all and someone should fix that.)

It's certainly not clear to me why an electron does not count as a magnet. Steven may well disagree -- he has some funny ideas about classical limits and pseudovectors. But an electron has two poles. It can be modelled as a very small current loop. It even has angular momentum.

Pfftbt. I agree that an electron is a magnet; it has a magnetic moment, after all. But it's not a classical magnet, since its moment is not a vector (and various other quantum funniness). (I don't know what you mean by the electron having "only one pole", though; it's a quantum dipole, after all.) —Steven G. Johnson

Speak of the Devil...  :) -- Tim Starling 00:20, Dec 18, 2003 (UTC)

Note also that, as soon we have things like μ and ε (as in the Wikipedia Maxwell's equations), one is talking about a macroscopically averaged field, as opposed to the rapidly-varying microscopic field generated by individual particles. Sophisticated textbooks like Jackson are careful to distinguish the two (Jackson even goes so far as to use different symbols—lower-case letters—for the microscopic fields). —Steven G. Johnson 05:07, 18 Dec 2003 (UTC)

A magnetic force is that force caused by moving charges. Whenever I say that, of course, someone has to add "or spin", which may be true but I happen to think it's pretty irrelevant at your level. -- Tim Starling 22:24, Dec 17, 2003 (UTC)

(Or by a changing electric field—this was Maxwell's big contribution, after all, and leads to wave propagation in vacuum.) Anyway, the historical understanding of the magnetic field came first from the Lorentz force law, and only later was an independent "physical existence" attributed to the field in its own right, and this is a reasonable pedagogical practice as well. (Freshman physics courses typically talk about the effects of magnetic fields before describing how they are generated, which is more complicated.) —Steven G. Johnson 00:13, 18 Dec 2003 (UTC)

Good point about the changing electric fields. -- Tim Starling 00:20, Dec 18, 2003 (UTC)

To Steven:

Just a note to your comment about μ generally equaling 1. For a lot of the work that is done by Geophysicists (and maybe others), we cannot assume that. At least for me, I make a concerted effort not to exchange B and H, at least while writing. I would suggest that we all try to do the same. It gets really hairy when measuring "magnetic field decays" when they are really "changes in magnetic field flux with time."

However, no big deal. It all comes out in the wash anyway and you all make good points. Andykass 18:56, 21 March 2007 (UTC)

velocity with respect to what ?

In the equation

$\mathbf {F} =q\mathbf {v} \times \mathbf {B}$

what frame of reference is v measured with respect to? If any inertial frame will do, then v can take on arbitrary values, which would change F and therefore the acceleration applied to the charged particle, which seems absurd. Is v measured with respect to the magnetic field flux lines? Is so, what does that really mean?

If an answer to this question is added to the article, perhaps the article on the Lorentz force should be updated to also include the answer or to point to this article. MichaelMcGuffin 21:36, 30 Aug 2004 (UTC)

Any inertial frame will do. When you change inertial frames of reference, of course, not only v but also B and E will transform ... and yes, the force will transform, too, according to relativity. (This is in contrast to the original conception of electromagnetism in Maxwell's equations, which did indeed postulate a "preferred" inertial frame, that of the ether.) Indeed, you can transform to a frame of reference where v is zero, and thus the magnetic force is zero...but in this frame of reference, there will generally be a non-zero electric-field force. (A famous thought-experiment along these lines shows how, in relativity, electric and magnetic fields are two aspects of the same thing.) —Steven G. Johnson 02:14, Aug 31, 2004 (UTC)

But the current in a wire does not depend on the reference frame. It (and therefore the magnetic field) is uniquely determined by the relative velocity of the electrons and ions in the wire (which is unrelated to the velocity v in the Lorentz force). Also, the resultant electric field of the wire is obviously zero. So the definition of the Lorentz force is indeed ambiguous unless one specifies what v is referred to. I would think that this should be the center of mass of the current system producing the magnetic field, i.e. approximately the frame where the ions in the wire are at rest (see also my website http://www.physicsmyths.org.uk/#lorforce in this respect).--Thomas

Of course the current in a wire depends on the reference frame—it's electrons moving! These issues were resolved in physics in the early 20th century, and the resolution is part of the foundation of all of modern physics. I can explain in great detail if anyone asks, but I warn you the answer is not short. -- SCZenz 16:58, 5 November 2005 (UTC)

No, the total current is the sum of the currents due to the negative and positive charges and thus independent of the reference frame (if you are comoving with the electrons you are then moving relatively to the positive charges, which results in the same current). -- Thomas

Current is not a concept limited to wires. What of the current due to a single charged particle, or many charged particles, with no balancing charges? There the current must depend on the reference frame. In fact, in electrodynamics, under Lorentz transformations, current and charge transform into each other as part of the same four-vector. See, for example, J. David Jackson's Classical Electrodynamics. -- SCZenz 17:27, 6 November 2005 (UTC)

Obviously, the concept of a current is not limited to wires (in general not even to charges). The question is whether these 'bare' currents (consisting only of unbalanced charges) produce any magnetic field. But I think this question may go too far for this article. Fact is that the article uses the example of a current in a wire as an illustration, and in this case the current (and hence the magnetic field strength) does not depend on the reference frame. The velocity v in the Lorentz force requires therefore a physical definition. --Thomas

You're simply wrong. The mathematics of proving it in the specific case of a current loop would be very hard, but relativity is fundamental to electrodynamics; velocities, magnetic fields, and currents all transform in a way that keeps the equation correct in any frame. In absolute generality. To argue this further, you would need to know electrodynamics in some detail; I've cited a book above, which is the graduate text for almost every university in the U.S. (and likely abroad, although I don't know for sure). If after reading it you still disagree, I can help get you in touch with Professor Jackson. -- SCZenz 18:01, 6 November 2005 (UTC)

To clarify, here's an expanded version of the equation in the presence of an electric field:

$\mathbf {F} =q\mathbf {v} \times \mathbf {B} +q\mathbf {E}$

There is only one reference frame in which there is no electric field, the one where the wire was stationary, and it is in this frame that F=qvxB holds. In other frames, the velocity transforms, and the B field transforms into an E field, but if you use the equation above you still get the same force. Does that help? -- SCZenz 18:10, 6 November 2005 (UTC)

So you are suggesting then also that v in F=qvxB (which is the formula given in the article for the Lorentz force) refers to the stationary wire? -- Thomas

In this example, if you leave off the qE, yes it refers to the stationary wire. If you leave in the qE, it could refer to anything; the real point is that in the frame with the stationary wire, E=0, whereas in the others it doesn't. -- SCZenz 06:25, 8 November 2005 (UTC)

Well, this should answer then the original question of this topic. I have allowed myself therefore to add a corresponding statement to this effect in the 'Definitions' section of the article.--Thomas

Yea, J (just like F) changes with a Lorentz transformation, but the dependence is only second order in v_t/c (where v_t is velocity of transformation) for a charge-neutral wire. So for practical purposes, B, E, and v depend on reference frame but J and F don't. Walk first, run later.Petwil 05:20, 8 September 2006 (UTC)

In a frame of reference in which v is equal to zero, the Lorentz force will be equal to zero. In a frame of reference in which v is not equal to zero, the Lorentz force will not be equal to zero. Not even relativity can explain how a particle could have acceleration in one frame of reference but zero acceleration in another frame of reference. (58.69.250.10 16:24, 21 February 2007 (UTC))

I have looked, but I can not see that the problem identified has been resolved in the article. Since you have introduced relativity into the definition, you need to carefully specify reference frames. This problem still needs to be addressed. 72.84.71.56 20:49, 3 July 2007 (UTC)

First mention of the thought experiment

Thanks, I see now that a sketch of a thought experiment has been added to the article. Something still confuses me though. In the thought experiment, call the first observer A (i.e. the observer that is "stationary") and the second observer B (i.e. the observer moving with the lines of charge). The current description points out that, from A's point of view, B's clock ticks more slowly, thus A perceives the net force F_A between the lines of charge as weaker, i.e. F_A < F_B. This weakening corresponds to the magnetic field that A perceives, attracting the moving lines of charge and opposing the repulsive electric force. However, couldn't we also change our perspective to that of B, and say that from B's perspective, A's clock ticks more slowly, thus we should expect F_B < F_A ? Surely there's something basic about special relativity that I don't understand. We can't have both F_A < F_B and F_B < F_A. MichaelMcGuffin 18:01, 8 Dec 2004 (UTC)

Stop thinking about the thought experiment, talk of special relativity and the twins

Isn't that the classic "twin paradox" of special relativity? I do not know how to resolve that paradox (I hear that general relativity is necessary) but both inertial observers see the other's clock as ticking more slowly than their own. How can that be? However, the two lines of charge are moving along only with observer B. You can think of B and the two lines of charge are stationary and *all* that B observes is the electrostatic repulsion of the lines of charge. Since observer A is moving relative to B and the parallel lines of charge, that observer will not see it the same as B. r b-j 18:15, 8 Dec 2004 (UTC)

(General relativity is not required to understand the twin paradox. There are various ways to show conclusively what the observed result would be, but one of the simplest is to imagine keeping the twins in constant communication by having them send radio pulses of their respective clocks towards one another. At the end of the trip, they compare their cumulative "clock" counts, and you can see that they both agree that the stationary one is older. French (Special Relativity) has a simple discussion of this. —Steven G. Johnson 21:29, Dec 8, 2004 (UTC))

It's funny, because while the "moving" twin is at a constant velocity, there is no sense that he is moving and the other is stationary. How do they view each other's clock during that period? It's only that the twin that goes to the far away planet and returns younger relative to his brother, is experiencing acceleration over the stationary twin, that you can differentiate them. I didn't think that SR had anything to say about acceleration (other than the normal Lorentz transformation in SR) whereas GR has a lot to say about acceleration (and gravitation). Anyway, my 28 year old "Elementary Modern Physics" textbook says literally that the paradox is explained by use of GR (without explaining it). Steven, could you translate that French explanation and put it in the English version of Special relativity? r b-j 22:19, 8 Dec 2004 (UTC)

Let me clear up two confusions. First, you're right that the fact that one observer has to accelerate at some point is the key difference between them — one observer does not remain in a single inertial frame of reference. However, you don't need general relativity to explain what happens, because you can make the acceleration itself a negligible fraction of the trip (and even with acceleration, you can still use special relativity as long as you describe the acceleration from the rest frame...you only need GR if you want to make the laws of physics have the same form in the accelerated frames). Second, A. P. French is the name of the author (a former MIT professor who wrote many physics textbooks in the 60's); the explanation itself is in English. Many other modern textbooks on special relativity contain a similar explanation (e.g. Basic Concepts in Relativity by Resnick and Halliday). Further, French (1968) writes:

One last remark. It has been argued by some writers that an explanation of the twin paradox must involve the use of general relativity. The basis of this view is that the phenomena in an accelerated reference frame (including the behavior of a clock attached to such a frame) are regarded in general relativity as being indistinguishable, over a limited region of space, from the phenomenon in a frame immersed in a gravitational field. This has been interpreted as meaning that it is impossible to talk about the behavior of accelerated clocks without using general relativity. Certainly the initial formulation of special relativity, although it leads to explicit statements about the rates of clocks moving at constant velocities, does not contain any obvious generalizations about accelerated clocks. And, as Bondi has remarked, not all accelerated clocks behave the same way. The clock consisting of a human pulse, for example, will certainly stop altogether if exposed to an acceleration of 1000g — in fact, a mere 100g would probably be lethal — whereas a nuclear clock can stand an acceleration of 10¹⁶g without exhibiting any change of rate. Nevertheless, for any clock that is not damaged by the acceleration, the effects of a trip can be calculated without bringing in the notions of equivalent gravitational fields. Special relativity is quite adequate to the job of predicting the time lost. It had better be, for (as Bondi has facetiously put it), "it is obvious that no theory denying the observability of acceleration could survive a car trip on a bumpy road." And special relativity has amply proved itself to be a more durable theory than this.

When I first took a course in special relativity, some years ago, I distinctly remember my professor saying that the notion that general relativity was required to describe the twin paradox had been disproved years ago. —Steven G. Johnson 22:54, Dec 8, 2004 (UTC)

that must have been some time ago. anyway i'm looking at http://www.sysmatrix.net/~kavs/kjs/addend4.html as well as twin paradox here on wiki. i understand this stuff a lot less than signal processing and FFTs. not sure if you would say the same :-) r b-j 04:51, 9 Dec 2004 (UTC)

A lot of the trouble here is that the accelerated twin is assumed to have set up a bunch of clocks synchronized within his own reference frame. They are synchronized by exchanging light signals with his clock (and/or each other). When he suddenly changes velocity he finds that these clocks are way out of synch, the difference being proportional to their (signed) distance from him. The "paradox" always results from comparing one clock with a set that are all synchronized within an inertial frame. The "traveling" twin cannot compare a "stationary" clock with his; he compares it with a sequence of clocks he has synchronized beforehand (but after he was in motion); comparisons are done between clocks instantaneously in justaposition. General relativity is not needed for the analysis. Pdn 13:47, 28 July 2005 (UTC)

You've got it all right, I think. But it is actually quite a common mistake to make among non-GR-specialist physicists. -- SCZenz 15:44, 28 July 2005 (UTC)

now, back to the thought experiment, which is messed up in its current form

This twin paradox stuff is interesting, but it doesn't seem to address my original question. In the thought experiment I was asking about, neither observer ever accelerates or changes direction, so there is never any change of "simultaneity planes" as illustrated in the twin paradox article. Each one observes a net force, F_A and F_B, between the lines of charge, according to their frame of reference. Each observer's clock ticks more slowly from the other's point of view. If we want to conclude that F_A < F_B, and not F_B < F_A, I think there's some missing reasoning or logic that should be added to the explanation of the thought experiment. Or, at least, could someone add a reference to a textbook or academic paper/article that explains the thought experiment in more detail? Thanks. MichaelMcGuffin 18:50, 9 Dec 2004 (UTC)

For reference, here is the thought experiment in its current form, which I believe is wrong: "A thought experiment one can do to show this is with two identical infinite and parallel lines of charge having no motion relative to each other but moving together relative to an observer. Another observer is moving alongside the two lines of charge (at the same velocity) and observes only electrostatic repulsive force and acceleration. The first or "stationary" observer seeing the two lines (and second observer) moving past with some known velocity also observes that the "moving" observer's clock is ticking more slowly (due to time dilation) and thus observes the repulsive acceleration of the lines more slowly than that which the "moving" observer sees. The reduction of repulsive acceleration can be thought of as an attractive force, in a classical physics context, that reduces the electrostatic repulsive force and also that is increasing with increasing velocity. This pseudo-force is precisely the same as the electromagnetic force in a classical context."GangofOne 07:59, 28 July 2005 (UTC)

The problems: First it says "lines of charge having no motion relative to each other", but then you say they experience "repulsive force and acceleration", so they ARE moving relative to each other? Second, an infinite line of CHARGE against another infinite line of charge will feel and infinite force, but it also has an infinite mass, so who knows what the acceleration will be. The force will be infinite for either observer. You say below a = F / m = (1/(4*pi*epsilon_0)*2*lambda^2/R)/rho , if this is a force; but it is force /(mass/lenght), so it's acceleration / length, whatever that is. Jumping down a few paragraphs....GangofOne 07:59, 28 July 2005 (UTC)

this following is a quantitative expression of that thought experiment. i think the twin paradox is applicable. in addition i do not see any of this "F_A < F_B, and F_B < F_A" conclusion that you have brought up. think about perceived acceleration in a direction that is perpendicular to the lines and on the same plane for both observers. i do not think you get a_A < a_B, and a_B < a_A. i think you only get a_A < a_B . the observers are not qualitatively in the same situation. both can observe the other as moving and themselves as stationary, but both do not observe the lines of charge in the same way because one is moving relative to the lines of charge and the other is not. r b-j 21:45, 9 Dec 2004 (UTC)

The classical electromagnetic effect is perfectly consistent with the lone electrostatic effect but with special relativity taken into consideration. The simplest hypothetical experiment would be two identical parallel infinite lines of charge (with charge per unit length of $\lambda \$ and some non-zero mass per unit length of $\rho \$ separated by some distance $R\$. If the lineal mass density is small enough that gravitational forces can be neglected in comparison to the electrostatic forces, the static non-relativistic repulsive (outward) acceleration (at the instance of time that the lines of charge are separated by distance $R\$) for each infinite parallel line of charge would be:

$a={\frac {F}{m}}={\frac {{\frac {1}{4\pi \epsilon _{0}}}{\frac {2\lambda ^{2}}{R}}}{\rho }}$

If the lines of charge are moving together past the observer at some velocity, $v\$, the non-relativistic electrostatic force would appear to be unchanged and that would be the acceleration an observer traveling along with the lines of charge would observe.

Now, if special relativity is considered, the in-motion observer's clock would be ticking at a relative *rate* (ticks per unit time or 1/time) of ${\sqrt {1-v^{2}/c^{2}}}$ from the point-of-view of the stationary observer because of time dilation. Since acceleration is proportional to (1/time)², the at-rest observer would observe an acceleration scaled by the square of that rate, or by ${1-v^{2}/c^{2}}\$, compared to what the moving observer sees. Then the observed outward acceleration of the two infinite lines as viewed by the stationary observer would be:

$a=\left(1-v^{2}/c^{2}\right){\frac {{\frac {1}{4\pi \epsilon _{0}}}{\frac {2\lambda ^{2}}{R}}}{\rho }}$

or

$a={\frac {F}{m}}={\frac {{\frac {1}{4\pi \epsilon _{0}}}{\frac {2\lambda ^{2}}{R}}-{\frac {v^{2}}{c^{2}}}{\frac {1}{4\pi \epsilon _{0}}}{\frac {2\lambda ^{2}}{R}}}{\rho }}={\frac {F_{e}-F_{m}}{\rho }}$

The first term in the numerator, $F_{e}\$, is the electrostatic force (per unit length) outward and is reduced by the second term, $F_{m}\$, which with a little manipulation, can be shown to be the classical magnetic force between two lines of charge (or conductors).

jumping to here. The above shows you have an understanding of what's wrong, but missed it. The '2 lines of charge' is different than '2 current carrying conductors' (overall charge is 0). What your analysis ends up with is the result for 2 current carrying conductors.GangofOne 07:59, 28 July 2005 (UTC)

The electric current, $i_{0}\$, in each conductor is

$i_{0}=v\lambda \$

and ${\frac {1}{\epsilon _{0}c^{2}}}$ is the magnetic permeability

$\mu _{0}={\frac {1}{\epsilon _{0}c^{2}}}$

because $c^{2}={\frac {1}{\mu _{0}\epsilon _{0}}}$

so you get for the 2^nd force term:

$F_{m}={\frac {v^{2}}{c^{2}}}{\frac {1}{4\pi \epsilon _{0}}}{\frac {2\lambda ^{2}}{R}}={\frac {\mu _{0}}{4\pi }}{\frac {2i_{0}^{2}}{R}}$

which is precisely what the classical E&M textbooks say is the magnetic force (per unit length) between two parallel conductors, separated by $R\$, with identical current $i_{0}\$.

Thought experiment needs to be reworded and analysis to fit. I leave it you, since I see you are competent. GangofOne 07:59, 28 July 2005 (UTC)

i'm still not clear as to what to fix without bringing in the quantative analysis. (is that what you want me to do?) even if there is outward acceleration between the two lines of charge, there is an instant of time where the relative velocity is zero (therefore not moving relative to each other). it is only this instant of time that i was referring to in the thought experiment.

two infinite lines of charge do exert an infinite force on each other, but the force per unit length is finite and if the mass per unit length is also finite, then the outward acceleration is determinable. no?

let's be specific about what needs to be fixed. i'm happy if it is fixed. r b-j 03:26, 1 August 2005 (UTC)

I have a number of comments and unclarities, maybe some are my own inadequacy of understanding. I will continue anyway. What you say directly above about the instanteaous acceleration, if it is infintesially short moment, what relevance does the speed of clock ticks? That would only apply in a finite interval of time. Anyway, my original idea was that these infinite lines of charge as an example would be better as an example as two parallel conductors, which I think your analysis is really referring to. But then the next question is , does this examplify that which it is supposed to be an example? I'm still thinking about this. But consider this: let's say we have a long but finite pair of lineal charges, just to work around the red herring of the the infinites involved. Assume the charged wires are contrained to only move away from each other, not arbitrarily freely. A force meter is put betweem them and reads some value. (The force is related to the acceleration it WOULD experience if free.) So another observer flies by in a differnt frame of reference and reads the same number on the meter. So, where's the relativity come in? GangofOne 05:26, 1 August 2005 (UTC)

i dunno how Lorentz transformation of special relativity would deal with the numerical force meter but i do know that, assuming the motion is in the x direction, Lorentz transformation does not change the perspective of distance in the y or z directions but does change how one observer views the other's flow of time and that the lengths in the x direction is changed. when the two lines are infinitely long, then they remain infinitely long after the application of length contraction.

it's just a thought experiement, not a real experiment. in a real experiment, to measure acceleration just by looking at position, we would need snapshots at at least 3 instances of time. in the thought experiment, we know there is this concept of instantaneous acceleration and we are asking what it would be at a single instance of time.

the issue about charge neutral conductors vs. these lines of charge can be dealt with by just thinking about it a little. it does not negate the physics of the thought experiment at all. the charge neutral conductors have a net magnetic field, but no net electrostatic field. the lines of charge have both electrostatic field and electromagnetic field for the "stationary" observer that observes the lines of charge moving past him/her. the "moving" observer that is moving alongside the two lines of charge observes no electromagnetic effect. it is simply electrostatic for him/her. i don't want to do this thought experiment with charge neutral conductors, but i can still use the results of current in conductors as a basis for determining the classical magnetic field. r b-j 05:07, 2 August 2005 (UTC)

ugly math symbols

I really don't like the ugly $\mathbf {B}$ in the text. Why not B for vector, or B for scalar. Much cleaner. dave 04:04, 6 Jan 2005 (UTC)

personally, i think it's cleaner if precisely the same symbol (except possibly smaller) that is used in the math equations are used in the text. whether it's $\mathbf {E}$ or $E\$. i think it's particularly cleaner if the Tex math is used for greek and exponents and subscripts and other special symbols than the kludge that many use. $x^{y}\$ vs. x^y . r b-j 17:36, 6 Jan 2005 (UTC)

Your point still has some validity, but don't cheat. Do it right—in text it should be x^y with italic symbols. A serif font would make it look better; I don't know if there's an acceptable way to do that in Wikipedia articles. The disparity in size often makes the Tex math look weird when written inline (the bottom of your E letters descending below the line is real ugly). Gene Nygaard 18:48, 6 Jan 2005 (UTC)

Depends on your screen resolution. I turn on "always render PNG" and it looks fine for me. Remember that you aren't the only person who views it. - Omegatron 02:41, Apr 26, 2005 (UTC)

I gotta add my 2 bucks. The current B and H look pretty bad. And as a programmer, anything that "depends on screen resolution" is broken. It should work the same for all resolutions. Precisely the same symbol is a good idea, but the text is pretty broken right now. Maybe the wiki redering needs to be enhanced, but something really ought to be done.

According to my corrections instead of all this mumbo jumbo with all these letters and stuff, why dont you just say R=B+C?

moving with respect to what?

"moving electric charges (electric currents) that e"

One thing I guess I never learned. Because of relativity, don't we need to specify what the particles are moving relative to? Do they not see each others magnetic field if they are not moving relative to each other? I guess they would behave as if they were only electrostatically repelling or attracting each other? Oh man, now I have confused myself... - Omegatron 23:41, Apr 25, 2005 (UTC)

This is why the presence of a magnetic field depends upon your frame of reference. Consider a charged particle moving at a constant velocity (i.e. in an inertial frame). If I am in an inertial frame of reference where the particle is moving with respect to me, I see a magnetic field. If I am in the same inertial frame as the particle, so that it is at rest with respect to me, I see no magnetic field. In general, when you change frames of reference, magnetic and electric fields get mixed up (together, they form a rank-2 tensor). —Steven G. Johnson 02:04, Apr 26, 2005 (UTC)

'O', the bottom line is that magnetic effects are a result of special relativity. That is, if you start with Coulomb's Law and then impose Lorentz invariance (or is it covariance?), you get magnetic effects. It turns out that there is an analog to magnetism in gravity - so called gravito-magnetism. I think it is also called 'frame-dragging'.Alfred Centauri 12:39, 2 September 2005 (UTC)

field line flow? field shells in open space?

I've added a little item about the orientation markers vs actual field flow. I've been unable to find anything that says if the magnetic field lines actually move or if they are simply static lines through space. (The arrow is just a reference to mark field orientation, as far as I've been able to determine.)

They don't move. In fact, they don't even exist, see below. -- Tim Starling 12:32, Jun 24, 2005 (UTC)

I'm not a professional physicist by any means, but I've also never determined if the field actually exists as separate concentrated lines/shells as iron filings demonstrate, or if the lines form only as a RESULT of the iron filings being there, building up into thicker lines as more iron filings enter the field. Is a magnetic field in empty space "ridged" as the filings suggest, or is a field in open space simply an even undifferentiated gradient from strong to weak? DMahalko 09:31, 24 Jun 2005 (UTC)

Field lines are just diagrammatic. The number drawn in any given diagram is arbitrary, the field is smooth, not ridged. Lines are just one way to show the direction and magnitude of a vector field at every point on a plane. Iron filings tend to mimic the shape of diagrammatic field lines, because adjacent lines of iron filings tend to repel each other, and because grains that are in contact tend to line up end-to-end with unlike poles touching. -- Tim Starling 12:32, Jun 24, 2005 (UTC)

This particular explanation needs to be included in the main text. It also should delve cautiously into more fundamentally what the field may consist of (e.g. alignment/coherence of virtual photons or e/p pairs from the vacuum, conceptual vortex mechanisms versus vacuum "permeability" changes leading to repulsion/attraction, etc (never liked the descriptions using compression of field lines/rubber bands for attraction). (Dfwrunner 20:54, 8 June 2007 (UTC))

Rotating magnetic field

I do not think that long quotes on Tesla's philosophy are appropriate for this article. -- SCZenz 18:13, 27 July 2005 (UTC)

I agree. I'm not sure if anything beyond the first paragraph in that section is appropriate for this article. Salsb 18:19, 27 July 2005 (UTC)

Ok, I'm paring that stuff down now... -- SCZenz 18:27, 27 July 2005 (UTC)

The people should be in the section. JDR 18:30, 27 July 2005 (UTC)

Why? The discussion strikes me as a historical interlude about an engineering application. Shouldn't it be in say an article about the history of motors as opposed to a basic article on magnetic fields? Salsb 18:37, 27 July 2005 (UTC)

It should be with the topic. The RMF concept is redirected here, so the history should be with that (as it is the history of the RMF). JDR 18:49, 27 July 2005 (UTC)

Yeah, people really aren't appropriate here. This article is about the concept of the Magnetic field, in great generality. My objection to your additions, Reddi, is that you are going into great detail on an issue you care about in particular, when no other sub-topic of magnetic field has such detail. A separate article really is more appropriate. -- SCZenz 18:41, 27 July 2005 (UTC)

SCZenz, people were in the see also section before. A separate article (which would be ideal) has been redirected here over and over again (lately by Salsb, WMC; earlier by Starling). JDR 18:49, 27 July 2005 (UTC)

People are appropriate for the see also section, not for the main article. As for the redirects, I think perhaps the issue is that the history of rotating magnetic fields, and the engineering applications, should be in separate places. In particular, I rather suspect that electrical motors and power plants have their own extensive articles already. But a separate article that brings it all together, if it's important to you to organize it like that, wouldn't be the end of the world to me. -- SCZenz 18:56, 27 July 2005 (UTC)

I removed the history except the two main, Ferriari and Tesla.

As for the redirects, the concept of "rotating magnetic field" is redirected here, and the engineering applications and it's history should have (in the least) a summary here.

A separate article on the RMF should exist. JDR

There is a place where this would fit in nicely: Electric_motors#AC_motors. As you point out, this is an important engineering principle, and your text seems to be part of the history of motors. Salsb 18:54, 27 July 2005 (UTC)

The concept redirects here. It wasn't even mentioned before, which it should have been, and it should have a brief summary, in the least. JDR 19:09, 27 July 2005 (UTC) (eg., The concept redirects here. The history of the concept should be at the article where the concept is.)

Since there is minimal history in this article, I disagree, I would include it in a nice history of engineering article but its not too important Salsb 19:28, 27 July 2005 (UTC)

The one other objection I have to this section, is the inclusion of the Earth's magnetic field from dynamo theory. This is about convection and rotation in fluids creating a magnetic field not about a rotating magnetic field. So if it should be placed in this article, which I am not sure it should be, it shouldn't be in this section Salsb 19:28, 27 July 2005 (UTC)

The Earth is one big dynamo (core rotor; atmosphere stator), directly related to rotating magnetic fields. JDR 19:41, 27 July 2005 (UTC)

As written it does not follow well, since the earth does not have a rotating magnetic field. There are articles on the Earth's magnetic field, on dynamos and on the dynamo theory, so I don't think there needs to be an additional discussion here, as opposed to a see also. Salsb 19:57, 27 July 2005 (UTC)

Salsb, you have to understand that you are talking to someone who thinks that the Earth's magnetic field is rotating because "it goes from south to north. THIS movement is the rotation of the field. It's rotating back and forth ... from the south pole to the north and back again. That's why compasses work." (see Talk:Rotating magnetic field.) —Steven G. Johnson 02:38, August 5, 2005 (UTC)

Stevie ... contrary to your negative implication via the link ... the inner core and outer core are rotating (akin to a rotor and stator) conducting (north-south) the magnetic field of the earth ... "THIS movement is the rotation of the field" and this action does make a compass work. JDR

Rotating magnetic field proposal

To find a way out of the impasse thus far, I propose that we have Reddi put his material for rotating magnetic fields into rotating magnetic fields, in place of the redirect. The concept isn't important enough for the space taken up in magnetic field, but it is true that a rotating magnetic field is a concept, independent of its applications, and that it could be useful. It might end up being a longer article than I would have written, but I don't think of that as a realy problem. But we certainly need a consensus somehow... thoughts? -- SCZenz 20:00, 27 July 2005 (UTC)

A rotating magnetic field in of itself is not special, its useful though its applications. I suggest that this text be added to the Motors article under AC motors, since there is a small history section there already which could be expanded. Salsb 20:05, 27 July 2005 (UTC)

What I'd consider even better, if Reddi would take the text on rotating magnetic fields and expand it into an article on the history of electric motors, that would be very cool indeed. Although admittedly a fair amount of work. Salsb 20:09, 27 July 2005 (UTC)

That sounds interesting ... I have been aquiring much of Edison's patents and Tesla's patents (as well as others). Alexanderson (sp?) built huge machines ...and this would include the early work in electrostatic machines. I'll kick this history of electric motors around in my head abit. Sincerely, JDR 18:19, 8 November 2005 (UTC)

I think the Magnetic Field article as it stands now is OK We'll keep a short section on rotating fields, and leave rotating magnetic field as a redirect. Sound ok? -- SCZenz 23:18, 27 July 2005 (UTC)

More velocity relative to what

I just reverted the edit made assigning v a specific reference frame in F = qvxB, because it was not correct. I then made an edit that I hope clarifies the situation. Here's a fuller explanation, for reference.

F = qv x B is always the correct force due to the magnetic field in any reference frame. However, the magnetic field can turn into an electric field as you change reference frames, so this equation will not remain constant for a system that produces a B field with moving charges (i.e. a current loop). However F = q(E + v x B) does remain constant in all reference frames; i.e. the total electromagnetic force can be defined unambiguously. F = qv x B is only the correct electromagnetic force when E = 0. In the case of a current loop, this occurs in the frame where the loop itself isn't moving.

However, the first part of the definition section doesn't refer to any example; it's a general example for force on a particle due to a B field. It doesn't say where the B field is from, so it is the correct equation for the force due to the B field in whatever frame you choose—you just have to pick the particle velocity and B field for the same reference frame. Hope that helps. -- SCZenz 21:12, 8 November 2005 (UTC)

I don't agree that the addition I made by referring v to the rest frame of the wire was incorrect. Given that F=qvxB in the article it was correct (I thought you agreed with this above). The total electromagnetic force is not written out here, so it should not be referred to either. As it is now, it is only counter-intuitive and in fact inconsistent (note also in this context my further comment under Talk:Lorentz force#Should the Lorentz Force Include the Electric Field?).--Thomas

The article states that the force due to the magnetic field is qvxB, which is correct in any reference frame. It's just not the same force in every reference frame, because you don't have the same magnetic field in every reference frame. -- SCZenz 19:58, 10 November 2005 (UTC)

How should the magnetic field depend on the reference frame if it is produced by the current in a wire? Assuming the wire is overall electrically neutral, the electric field is zero (in all reference frames) and the total current (and hence the magnetic field) is independent of the reference frame as well, as it depends only on the relative drift velocity of the ions and electrons in the wire (which has nothing to do with the test charge velocity v).--Thomas

Charge and current transform into each other under Lorentz transformations. Thus the magnetic field and electric field produced from them change under Lorentz transformations. A mathematical discussion of this is at an advanced undergraduate or graduate level, and non-trivial, so if you want a detailed proof I would do far better to refer you to a textbook than to try to reproduce the explanation myself. I recommend reading J. D. Jackson's Classical Electrodynamics, chapter 11, particularly section 11.9. I believe Griffiths' electromagnetism textbook also has a discussion; both texts are in the reference section of the Magnetic field article itself. -- SCZenz 19:13, 11 November 2005 (UTC)

Consider this heuristic, handwaving argument. You say: "Assuming the wire is overall electrically neutral, the electric field is zero (in all reference frames)...", but is it? If the e- are moving w.r.t. the wire (the positive charges), then there is a relativistic length contraction, and the charge per length of the e- is no longer the same as the charge per length of the positive charges, so there is a "net charge" per length, (or , better stated, something that acts like a charge, that can cause forces, etc). It "is" the magnetic field. The magnetic field is a relativistic effect. (And that's why the E and B are mixed up together, and mutually change, depending on the motions of the charges and point of space. (This could be better expressed, but maybe it's helpful. Continue your questions, maybe we can generate some explanations suitable for the article.) GangofOne 20:17, 11 November 2005 (UTC)

To continue, you say: "and the total current (and hence the magnetic field) is independent of the reference frame as well," No the current depends on the ref. frame. If I am static with the wire and "see" the e- move, I "see" one value for the current. If I move with the e- so it is the wire that moves, I "see" the opposite value for the current. If I split the difference, and move half the speed, so that the wire is moving one way and the e- the other, I see no current. So the current is NOT reference frame independent.

The idea is that from any inertial frame of reference, current, E, B, v, ALL change, but is such a way that F=qE +qvxB is still true. GangofOne 20:39, 11 November 2005 (UTC)

I am afraid what you are saying above is incorrect in several respects:

First of all, you seem to forget that electrons and ions are oppositely charged, so if you change the rest frame from one to the other, the velocity changes direction but also the charge, i.e. the current does not change sign (contrary to what you stated above).

Secondly, it would be quite a funny wire if the charge density of the ions would become different from that of the electrons depending on the reference frame: this would mean that charge neutrality would not be fulfilled anymore and hence corresponding electric force fields would be set up along the wire in addition to the electric field that you propose to be created perpendicular to it. So overall you would have a net force depending on the reference frame, which is physically not acceptable.

Thirdly, one should bear in mind that a magnetic fields doesn't do any work on a charged particle as the associated force is always perpendicular to the velocity. This property should obviously not depend on the reference frame. However, the proposed relativistic 'charging' of the wire however should always create an electric field directed towards to or away from it, i.e. it is only perpendicular to the velocity if the charge velocity is parallel to the wire. In all other cases, the resultant field would do work on the charge and change its kinetic energy. Again this is physically not acceptable.

For clarification, just consider the case of a charged particle in the magnetic field of a wire from a kinematical point of view: in the rest frame of the wire the orbit of the particle is a circle around the corresponding field line (assuming the velocity v to be perpendicular to the magnetic field and the field as homogeneous i.e. the Larmor radius as sufficiently small). Now if you view this scenario from a different inertial reference frame moving with velocity U, the latter velocity will simply be superposed to the Larmor circle which the charge traces out in the wire's frame i.e. we will have a Cycloid motion, which is however just the result of the superposed linear velocity but not of an electric field. --Thomas

You're right that GangofOne made an error in the bit about moving along with the electrons above. Ignoring relativity, you'd be right that the current wouldn't change with reference frame. However, because the electrons are moving at a different rate than the protons, they are affected differently by Lorentz transformations. Thus current does transform into charge (a fact which, even if we explain it poorly, is cited in every sufficiently advanced physics textbook on the subject).

Your second argument that, when the wire becomes charged, there is an electric field along the wire is rubbish; a charged wire has an electric field that points radially outward, as is solved in elementary E&M textbooks (see, e.g., Halliday, Resnick, and Krane's Physics, Volume 2, section 29-5). This removes the new, unexplained force and the phantom work you were concerned about.

A suggestion: if you want to keep trying to understand what's going on, that's great—the charged wire obscures the physics principles a bit, which makes it interesting. But you're not going to succeed in overturning the learned consensus of physicists on an issue that's been settled for over half a century, whether you win an argument with a lowly grad student like me on Wikipedia or not. -- SCZenz 18:49, 12 November 2005 (UTC)

I would agree that Wikipedia is probably not the right place to overturn learned consensus, but on the other hand, the contributors should also have some responsibility regarding the factual correctness of the articles. In this sense I think the points I mentioned are at least worth considering here.

I could actually go much further and discuss the Lorentz transformation in the first place, but I think this would go too far off topic here (for anyone interested, see my web page http://www.physicsmyths.org.uk/lorentz.htm ).

In any case, I don't agree that my argument connected with the charge invariance is rubbish: if the charge densities of the negative and positive charges are different in the wire, charge invariance requires that there is a corresponding surplus charge external to the wire, or in other other words, the negative and positive charges are merely distributed over different lengths, with the total charge being identical and unchanged. Now this may not make a significant difference if the wire is much longer than the distance to the wire, but consider the opposite case where the distance d is much larger than the length of the wire: in this case, the electric field is basically that of a point charge and does not depend on the charge density of the wire i.e. a different Lorentz contraction for the electron and ion distribution would not result in a net charge (there would only be a second order effect decreasing like 1/d^4 and which could therefore be made arbitrarily small compared to the magnetic field (which goes like 1/d^2 for the short wire)). So in this case the Lorentz contraction would not yield the required electrostatic force when changing reference frames.

Another point that I find very questionable in corresponding derivations is the fact that reference frame of the moving charge (i.e. the one where the v in F=qvxB is zero) is apparently being treated as an inertial frame when in fact the particle is accelerated due to the Lorentz force in the wire's frame (if you treat for instance the earth as an inertial reference frame and assume that the sun rotates around it, you would obviously arrive at vastly incorrect results regarding the force between the two). So there is actually no additional electrostatic force required in the frame of the moving charge as this frame is not inertial but itself accelerated by the force on the charge in the wire's frame (an exact definition of 'wire's frame' is still missing as well by the way, not only here but also in some textbooks that I checked out). --Thomas

Basically, what you're point out is that treating a current loop in the context of relativistic electrodynamics is complex, and you have to be very careful if you care about all the details. But nobody does care--there are far more interesting tests of relativity and electrodynamics. That's why textbooks don't discuss it. -- SCZenz 19:22, 15 November 2005 (UTC)

Suggestion to merge articles

I strongly disagree with the suggestion to merge this article with magnetic flux density. These are two different, though related, concepts. For starters, the two have different units of measures (dimensional decompositions). Magnetic field is amps per meter, magnetic flux density is webers per square meter. -- Metacomet 15:06, 31 January 2006 (UTC)

The article magnetic field discusses in detail both fields B and H. Therefore, there is no reason to have a separate article discussing B. (The units of B and H are indeed different. But the units of B from "magnetic field density" and of B from the article "magnetic field" are the same, and this is exactly the same quantity). Yevgeny Kats 17:13, 31 January 2006 (UTC)

In my opinion, there should be an overview article that discusses both B and H, including high-level definitions, differences between the two, and the relationship between them. Then there should be two separate, more detailed articles, one article on each of the two fields. For historical reasons, and because of the way electromagnetics is often taught in introductory courses, there is a lot of confusion between B and H. It would be a shame if WP were to reinforce the confusion, instead of trying to clarify the distinction and explain where it comes from. Again, these ideas are simply my opinion. -- Metacomet 17:28, 31 January 2006 (UTC)

As a suggestion, the three articles might be called:

• Magnetic field (overview) to give high-level overview
• Magnetic field intensity to give detailed discussion of H
• Magnetic flux density to give detailed discussion of B

-- Metacomet 17:32, 31 January 2006 (UTC)

I think it's not possible to discuss H separately from B. It is possible, however, to discuss B without discussing H. Therefore, I'd suggest to divide it to

• "Magnetic field", which will discuss only B.
• "Magnetic fields in matter", which will discuss B and H in matter.

Each article will include a major link to the other.

Currenly we have some random division of the content between the articles "magnetic field density" and "magnetic field"

Yevgeny Kats 18:47, 31 January 2006 (UTC)

I disagree. I prefer the approach that I suggested above. You can easily discuss either field by itself, as long as you have a definition that does not involve the other, which is quite easy to do. I don't really want to get into a huge argument about it though. You are entitled to your opinion, and I am entitled to mine. -- Metacomet 19:56, 31 January 2006 (UTC)

I think we may put the whole discussion about B and H in the same "magnectic field" article, but we should create a separate magnetic flux density article, with some description, and pointing to the magnectic field article... There (here) we can explain B as being an macroscopic effect of atomic phenomena... But I strongly disagree that "it's the same thing", or that the same "magnetic field" name applies to both, that's an absurd. At least this doesn't happen in the books I've read, or in my university.

In the electric field and electric displacement field case, the two articles exist without problem. The only problem is some confusion about what this "macroscopic thing" means... I may try to rewrite some of the four pages! Is there anybody who believe that the current versions are untouchable!? -- NIC1138 03:19, 20 April 2006 (UTC)

The question is not what you prefer, or what I prefer, but what is actually used by professionals and by educators. A little dose of reality here: the name "magnetic field" is used for both B and H. See any recent professional literature, or a respected textbook such as Jackson. IIRC, Griffiths uses "magnetic field" for B and "auxiliary field" for H. Other textbooks insist on the historical usage of "magnetic induction" for B and "magnetic field" for H. Living languages are sometimes ambiguous...learn to deal with it. (As for B and H having different units, that's a totally artificial consequence of SI units.) Which is not to say that B and H are the same thing, but you are doing readers a disservice if you oversimplify the terminology situation or proscribe certain common usages as "wrong". I would suggest a single "Magnetic field" article that describes both B and H, with the focus on B (a more intuitive concept since it appears in the Lorentz force), and sub-articles on specific topics such as magnetization of matter, etc. —Steven G. Johnson 02:33, 21 April 2006 (UTC)

I don't know how physicists teach the concept of magnetic field but for me B is the flux density and H is the magnetic field and I was quite shocked to read the article. How do you teach hysteresis and saturation without having the two. All the books I know about motor design (ie applied electromagnetism) separates these two because we need them. Ckoechli 15:40, 8 September 2006 (UTC)

You still talk about H when relevant, it's just that in physics, B is considered more fundamental and thus is normally what when means when one says "the magnetic field." Griffiths offers the quote below. --Starwed 20:55, 30 January 2007 (UTC)

Many authors call H, not B, the "magnetic field." Then they have to invent a new word for B: the "flux density," or magnetic "induction" (an absurd choice, since that term already has at least two other meanings in electrodynamics). Anyway, B is indisputably the fundamental quantity, so I shall continue to call it the "magnetic field," as everyone does in the spoken language. H has no sensible name: just call it "H".

— David J. Griffiths, Introduction to Electrodynamics

Question of validity - biot savart law

$\mathbf {B} ={\frac {\mu _{0}}{4\pi }}{\frac {q}{r^{2}}}\mathbf {\hat {r}} \times \mathbf {v}$

is this equation right, or should r hat and v be switched (in the cross product). Cause i just had a physics HW problem that contradicted. Still doing the HW, so don't have time to check up on anything. User:Fresheneesz

The Biot-Savart Law is usually applied in differential forms, like in the following two expressions:

$\mathbf {dB} ={\frac {\mu _{0}}{4\pi }}{\frac {dq}{r^{2}}}\mathbf {v} \times \mathbf {\hat {r}}$

$\mathbf {dB} ={\frac {\mu _{0}}{4\pi }}{\frac {i}{r^{2}}}\mathbf {ds} \times \mathbf {\hat {r}}$

This law is important in studying magnetic fields. May somebody please add more detail about that in the article? Thanks.
- Alanmak 23:35, 12 February 2006 (UTC)

Yes, I agree with you. I am not a wikipedia user myself so I am not going to do any kind of correction or whatever in this article, but a friend of mine called me and asked me to explain some magnetics because she was trying to get some general idea first using this article before starting serious studies usin textbooks. When she showed me, I could immediately understood the source of her confusion. This article is too focused in relativity and simply ignore the basics like Gauss' Law and Biot-Savart Law. They have very significant practical and historical value, the second Maxell Equation is the Gauss Law, not that formula derivated from the Lorentz Transformation. By the way, the Gauss Law, in its both "shapes" have more practical value than the Lorentz transformation. If I wasn't an engineer I wouldn't understand more than a half of information in this article. This article is in an Encyclopedia and should not be just a badly-done gathering of formulas. Who ever wrote this article, if you think you are cool showing far too advanced formulas and definitions, then you are very wrong. No wonder why wikipedia is not respected in serious academic environments. —The preceding unsigned comment was added by 222.150.226.168 (talk) 14:21, 13 April 2007 (UTC).

About the picture at the beginning of the article

This picture looks nice. But there are a few things that could be improved:

1. Magnetic field lines should form closed loops.
2. It is a widely accepted convention to use "B" instead of "M" as the symbol for magnetic field.
3. As the positive and negative ends of the electric wire has already been indicated, it is not necessary to specify that the current is "DC". It would be better to use "I", which is the common symbol for electric current.

Would anybody like to modify that picture for a little bit?----

I think the current (and the mag field) should be shown in the opposite directions. Its easier for me to think CW rotation than CCW.--Light current 14:49, 10 April 2006 (UTC)

The picture looks ok to me. The current flow is fine. In physics/engineering, there are two types of current flow: conventional and actual. The diagram is merely being very explict and indicating conventional current flow (+ to -). For an introductory type of explaination, being brain-dead and explicit is good. And I think the magnetic field orientation is correct, but I'd have to check and my books are in storage. Summary: don't touch anything yet, untill we're sure. —The preceding unsigned comment was added by 69.109.242.191 (talk • contribs) 12:32, 11 April 2006 (UTC)

For an easy mnemonic that doesn't require checking your reference books, see Right hand rule. --Blainster 23:05, 25 April 2006 (UTC)

Yes, this picture is really well designed to be easy to check with the right hand rule. Whoever drew it was clearly thinking ahead. I'd vote that we keep it as is. --- Markspace 18:37, 4 May 2006 (UTC)

Im not saying its wrong, Im saying it would look better to me if the picture was turned around thats all. BTW can you please sign and date your posts by typing 4 tildes ~~~~. THanks--Light current 19:55, 11 April 2006 (UTC)

I think this picture is actually quite confusing: it seems to imply that the ends of the rod are charged - and thus that density of charge plays a role in magnetism, while only the density of current actually matters. _R_ 23:19, 4 July 2006 (UTC)

I think the picture is fine. In fact, it helps explain why parallel wires with like currents attract each other. In the "Symbols & Terminology" section, there appears this sentence, which I don't like: "While like charges repel and unlike ones attract, the opposite holds for currents: if the current in one of the two parallel wires is reversed, the two will repel." It's misleading to suggest "the opposite" of some principle holds for currents. What holds for everything is that opposites attract. The two wires attract because they present opposite magnetic polarities to each other, which becomes obvious if you stare at that swell picture for awhile. The arrows pointing down in the picture would be pointing up in an identical wire right next to it, since the magnetic field lines form a circle.Charlie Raeihle 21:53, 12 July 2006 (UTC)

I may be mad but I would take the plus and minus signs to indicate the ends were connected to positive and negative sources respectively and since electrons are negative the current would flow from negative to positive. I suggest changing to the +/-ve notation commonly used in physics to give a sense of the potential at each end of the wire, that will be more intuitive for readers I feel in respect to what way the electrons are moving. Apart from that its fine.

Iron filings pic.

I suggest that the picture does not show the magnetic lines of force due to an 'isolated' magnet. What it shows is the magnetic lines of force with a lot of iron filings scattered in the magnetic field. The picture is therfore misleading in that if you plotted the field lined using one tiny isolated bar of metal, the pattern you would get would not be the same as that shown! Comments? --Light current 18:20, 12 April 2006 (UTC)

I agree it is confusing and i do not like it, i also cannot speak english good.

Electric and magnetic fields- whats the difference?

If the presence of a dielectric (E >1) can distort an electric field, does the presecnce of a ferromagnetic material (U>1) distort a magnetic field from a magnet. If so, what do iron filings do to the magnetic filed lines when spread around a bar magnet? 8-?--Light current 00:12, 4 May 2006 (UTC)

Yes. The field lines are nearly perpendicular to the surface of a high permeability material. Madhu 14:36, 10 August 2006 (UTC)

So the iron filings actually distort the magnetic field?--Light current 00:08, 11 August 2006 (UTC)

Here's an image of distorted field lines. It's not great, but it's the first one I could find quickly. Of course, iron filings are usually light enough to be shifted by the field of a typical bar magnet, so each affects the other. If the iron filings were not permitted to move (or the field strength was not sufficient to move them), the field lines would follow the filing, rather than the other way around. Think about the field lines within an iron core transformer. Without the core, the field lines would be all over the place :-( Madhu 04:29, 11 August 2006 (UTC)

Right hand rule

um...this is the left hand rule, no? reverse thumb vector...Gatoatigrado 03:32, 6 June 2006 (UTC)

No that picture is of the right hand rule. For magnetic fied, if the current flows in the direction of your thumb, the magnatic field goes in a circular path in the direction of your fingers. You need to make a kind of thumbs-up sign with your right hand for that. The left hand rule is motion of charged particles. --H2g2bob 16:21, 6 June 2006 (UTC)

Can anything block magnetic fields?

I know that many objects are not magnetic (i.e. wood) but magnetic fields still go through them. For example when you place a metal object behind a thin piece of wood and place an attracting magnet on the other side, the force pulling them together is the same as it would if there was nothing in between them(given they were the same distance appart). So the magnetic field goes through these things, is there anything that magnetic fields do not pass through? So basically an easy way to understand would be: if there was a strong magnet in the center and you surrounded it behind a wall of substance X which then makes it so nothing outside the wall would feel any pull from the magnet inside. Is there any such substance? Thanks ~Matt Email, Demostheness@hotmail.com

See http://en.wikipedia.org/wiki/Permeability_%28electromagnetism%29 and mumetal.--Light current 11:32, 5 August 2006 (UTC)

A superconductor (read Meissner effect) will block a magnetic field up to a limit depending on the material the superconductor is made from and its temperature. Conductors will dampen changes in the magnetic field flowing through them as the changes induce a current which in turn induces a magnetic field which perfectly opposes the applied field change. This is very short lived as the currents induced die away due to resistance in the material and so stop blocking the field. Its still worth knowing about becuase it leads to Inductance and a few effects to do with fluctuating magnetic fields CaptinJohn 11:15, 13 March 2007 (UTC)

Intuitive explanation of B

Hello. I came to this page hoping for an intuitive explanation of the measure B of an electic field, but I can't find one. I have searched the web for several hours and I still can't find one.

The measure E of an electric field make sense to me, the amount of force in the direction of E, per unit of charge of a test charge placed in the field. However B is a bit of a mystery.

Why didn't physicists define B as being in the direction of the force as well - something like force in the direction of B per unit charge per unit velocity. It seems a bit ugly to me to have the force of an electric field with E, but the force of the magnetic field is at right angles to B. I'm sure there is a deep reason for it, but I don't see it. It would be helpful, on this page, to have an intuitive explanation of exactly what B is in a physical sense, and why it is at right angles to the velocity of the test charge and the force on the test charge. Can anyone please enlighten me? Nicolharper 16:33, 9 August 2006 (UTC)

The difference is that electric charges move in the direction of E and magnetic domains line up in the direction of B. I believe magnetic field lines were theorized based in orientation of other magnets or iron filings within a B field. Michael Faraday, James Clerk Maxwell, and others observed and formalized the relationship between moving charges and magnetic fields. It wasn't planned, it was discovered long after magnetism was observed. I guess it would possible to redefine B in the direction of a moving charge, but then it would be at right angles with intuitive notions of field lines based on simple experiments with a compass or iron filings. Madhu 14:32, 10 August 2006 (UTC)

Thanks. Much appreciated. It would be good if this could be explained in the article. Maybe I'll do it if I find time. Nicolharper 15:38, 10 August 2006 (UTC)

What is all this about pressure??

I noticed this bit in the section about energy density : << For example, a magnetic field B of one tesla has an energy density about 398 kilojoules per cubic metre, and of 10 teslas, about 40 megajoules per cubic metre.

This is the same as the pressure produced by magnetic field, since pressure and energy density are essentially the same physical quantities and thus have the same units. Thus, a magnetic field of 1 tesla produces a pressure of 398 kPa (about 4 atmospheres), and 10 T about 40 Mpa (~400 atm). >>

Does anyone understand what this means about pressure, as a physics PhD student i just dont get what its on about. Pressure on what? Physical pressure? what does it mean? A magnetic field on its own does not exert pressure it only exerts pressure on a magnetic substance inside the magnetic field and then the force is proportional to the field gradient, not field strength.

Any comments.

This was supposed to be force (or pressure) on ferromagnetic materials as described in slightly greater detail in the electromagnet article. The old section included a complete, but short derivation. Since then, it has been edited to the point where it no longer appears to make sense. I'm not completely sure why it was whittled down, but you are welcome to improve it. Madhu 23:02, 12 September 2006 (UTC)

Magnetic Field's

The diagram showing the magnet and iron filings is not acuate for when you use an electromagnet http://www.ndt-ed.org/EducationResources/CommunityCollege/MagParticle/Graphics/coil1.gif Also magnetic feilds can be alternating by using an electromagnet and alternating current insted of direct current Does anyone know much about the effects of AC magnetic feild's? Im esspecally intrested in verry high frequencies Alan2here 15:15, 1 October 2006 (UTC)

I Know that alternating magnetic fields are very difficult to generate at high frequencies. This is because to alternate : I Know that alternating magnetic fields are very difficult to generate at high frequencies. This is because to alternate the field requires you to dump all the energy in that field. If you look at the above numbers (I'm not sure they are correct but I have no reason to doubt them) then to make a 1000cc (a 10cm cube) volume field of 1T oscillate at 1kHz would need a 400kW of power to be generated and dumped. The problem you have is that it would also need a lot of very thin wire wound very tightly to actually generate the field. The wire would melt very easily if not cooled and what is difficult to do. I ran a 1T water cooled magnet in DC (direct field) mode when I did my masters and it took about 5 minutes to get it up to 1 T because if you went any faster it burned out. So with our cooling system (which was huge) we could have had a 1T field oscillate at 0.833mHz (one cycle per 20mins). On that basis Id say it is the cooling system that limits suck work.

I should note here that the magnet I used was NOT superconducting. It you use a superconducting magnet that power is dumped in the power supply rather than the coils so its easier to cool but I think you still have the same problem of needing ever bigger cooling systems to run even small, low frequency fields. CaptinJohn 11:31, 13 March 2007 (UTC)

major error in lead

The lead stated:

In physics, a magnetic field is that part of the electromagnetic field that exists when there is a changing electric field. A changing electric field can be caused by the movement of an electrically charged object, as in an electric current; or a combination of the orbit of an electron around an atom and the spin of electrons themselves, as in a permanent magnet.

That was just completely wrong. A constant electric current, for example, does not create a varying electric field, but it does create a magnetic field. There are two physically distinct mechanisms for creating a magnetic field, which are expressed by two separate terms in Maxwell's equations. I've fixed the error.--24.52.254.62 04:54, 2 November 2006 (UTC)

Although I've fixed that error in the lead, the whole rest of the article is in a horrible state. The explanation section is extremely poorly written, and has bizarre, mispelled sentence fragments floating around in it. The article is also not written so as to be intelligible to the general reader. I've added a cleanup tag.--24.52.254.62 05:05, 2 November 2006 (UTC)

Still somewhat of an error in "a magnetic field is that part of the electromagnetic field that exerts a force on a moving charge." Particles with spin can have intrinsic magnetic moments, and thus interact with a magnetic field. A point particle with spin isn't quite the same as a moving charge. Glancing through the article I see that the explanation section needs serious work. (There seems to be some confusion between the electric field and the electromagnetic field. Also, it implies that the electromagnetic field has a non-relativistic portion?) --Starwed 07:50, 2 December 2006 (UTC)

Clean Up Is Required

I Think A Clen Up Of This Article Should Be Ordered. Meanwhile, can anyone suggest other articles??? —Preceding unsigned comment added by 89.241.123.153 (talk • contribs)

Yeah, it could probably do with a bit of a review. Meanwhile..., other articles for what? --h2g2bob 19:58, 21 November 2006 (UTC)

Large error in explanation

Note on the following presented text in the main article:

"A thought experiment one can do to show this is with two identical infinite and parallel lines of charge having no motion relative to each other but moving together relative to an observer. Another observer is moving alongside the two lines of charge (at the same velocity) and observes only electrostatic repulsive force and acceleration. The first or "stationary" observer seeing the two lines (and second observer) moving past with some known velocity also observes that the "moving" observer's clock is ticking more slowly (due to time dilation) and thus observes the repulsive acceleration of the lines more slowly than that which the "moving" observer sees. The reduction of repulsive acceleration can be thought of as an attractive force, in a classical physics context, that reduces the electrostatic repulsive force and also that is increasing with increasing velocity. This pseudo-force is precisely the same as the electromagnetic force in a classical context."

This explanation is incorrect. In the first place the "reduction of repulsive acceleration" as a "reduction of the electrostatic repulsive force" violates the requirement that lorentz force must be conserved in all inertial frames. Also additional problems arise from the implied direct relation between force and acceleration. The proper explanation is to first insist on charge conservation in all frames, then insist on the fundamental correctness of coulomb interaction in all frames. Then under the transformation of inertial reference frames, notice that the force also changes even though charge and coulombic interaction is invariant. Then and only then can a force every bit as real as that suffered by two neigbhoring charges be surmised to force the invariance of coulomb interaction. Just my small contribution if anyone is interested.

                                        The shadow

WTF does "B" stand for anyway?

What does it stand for, seriously? I know it's the Magnetic Flux Density or Magnetic Field Strength, but I have no idea what word it's actually supposed to stand for, if any. You know the way "v" is the initial letter of "velocity" and the way "c" is the inital letter of "capacitance"? Well, WTF does "B" mean? It's driving me mad, I can't find its meaning anywhere! (Of course, I don't actually care, as long as I understand the actual physics, but still I like to know what it means...) Perhaps it stands for "Bloody Victorians and their crap notation." Stuart Morrow

It doesn't stand for anything im afraid. Its like s for distance CaptinJohn 11:05, 13 March 2007 (UTC)

I think there is, at least, an explanation for why the letter B is the convention. At the very least, I'v heard such an explanation, but I can neither remember it nor vouch for it's veracity. --Starwed 21:34, 21 March 2007 (UTC)

the s for distance is an abbrevation for "spatium" (latin).

Extension to theory of relativity section

To me, this section seems like it could be unclear or misleading.

Einstein explained in 1905 that a magnetic field is the relativistic part of an electric field.

This makes no sense as written. If the magnetic field is the "relativistic part", what is the nonrelativistic part of an electric field? I would prefer to say that both are components of an electromagnetic field.

It's true that the magnetic force between two moving charges can be deduced from their interaction in one particles reference frame and special relativity. That's an entirely different matter than the magnetic field being "part" of the electric field.

One of the products of these transformations is the part of the electric field which only acts on moving charges — and we call it the "magnetic field".

Again, this isn't how the issue is normally presented. The author of this section seems to be using the phrase "electric field" to refer to what is more commonly called the Electromagnetic field. Even if this is valid terminology in some literature, it isn't what's used elsewhere on wikipedia and should definitely be avoided.

The quantum-mechanical motion of electrons in atoms produces the magnetic fields of permanent ferromagnets. Spinning charged particles also have magnetic moment.

This phrasing makes it seem like the particles are always physically spinning on some axis, which of course isn't necessarily the case. I would also say that the phrase "quantum-mechanical motion" should link to the article on Spin (physics), rather than the word spinning.

A magnetic field is a vector field: it associates with every point in space a (pseudo) vector that may vary through time. The direction of the field is the equilibrium direction of a magnetic dipole (like a compass needle) placed in the field.

Currently this is simply a one liner; it doesn't seem to belong in this section. Perhaps a broader description of how the magnetic field behaves under transformations should go here?

We use the symbol ${\vec {B}}$ for the magnetic field and for the sake of mathematical simplicity (one symbol instead of seven).

I'm probably missing something here, but what are the seven symbols referred to? I know a previous version of this section discussed writing the magnetic field as combinations of the electric field and velocity; is this an orphaned ref. to that? Also, the text following this statement is just a general discussion of the meaning behind the magnetic field vector, which is needed somewhere in the article, but probably in a more general section.

My thoughts are as follows:

• Details of the relativistic transformation of the electric field into the magnetic are not needed in this article; they belong at Electromagnetism and related pages.
• The section should be renamed, and be devoted to briefly explaining the role of the magnetic field in "advanced" theories like relativity and QED.
• Some of the content in this section belongs in a more general dicussion of the properties of the magnetic field; conversely, the entire introduction to the properties section is actually about special relativity. It would be nice if some dicussion could happen on this talk page about exactly how the article should be laid out!

--Starwed 12:04, 23 February 2007 (UTC)

thanks to anon 132.236.59.30 for fixing spurious duplication from me.

it must have been a spurious "paste", but i do not know how it happened nor how i didn't see it afterward. r b-j 06:30, 10 April 2007 (UTC)

Relativity and the Magnetic Field

This quote is taken from the main article,

"Einstein explained in 1905 that a magnetic field is the relativistic part of an electric field".

The main article then goes on to say that the magnetic field arises as a by-product of the Lorentz transformations.

However, the Lorentz transformations as applied to electric and magnetic fields already include the inter relationships determined by Maxwell's equations. The magnetic field therefore already exists independently of relativity or Lorentz transformations. We cannot therefore state that magnetism is a relativistic effect of the electric field under a Lorentz transformation.

It would be more correct to state that Einstein's Theory of Relativity effects the magnetic field relativistically, but that the magnetic field as affected relativistically doesn't differ in nature from the classical magnetic field.

If we were to suggest that the classical magnetic field was merely an effect of coordinate frame transformation, this would be tantamount to suggesting that the magnetic field is only fictititious.

The magnetic field is clearly a different concept altogether from the electric field. The electric field measures force per unit electric charge. The magnetic field, whatever it is, doesn't even have the same dimensions. (58.10.102.2 15:12, 29 April 2007 (UTC))

The E and B fields have the same units relativistically speaking. They only appear to have different units because a factor of 'c' has been taken out of the time unit and placed into the electric field unit. Measuring time as a distance means qE and qB have units of momentum per meter. Alternately, if distance is measured as a time, qE and qB have units of energy per meter (AKA force). Alfred Centauri 18:35, 29 April 2007 (UTC)

I still dislike how this is presented in the article. Clearly the magnetic field and the electric field are inter-related, and it's reasonable to think of them as two aspects of the same thing, but I'd really like to see a source for the electric field being considered the more fundamental. And if I don't see a specific source for the claim that Einstein said that "a magnetic field is the relativistic part of an electric field." I'm going to remove it from the article. --Starwed 07:04, 30 April 2007 (UTC)

Defining the magnetic field is actually a very tricky business. The mathematical definition is given by the Biot-Savart law but this doesn't assist any as regards giving a physical picture for the layman. Maxwell seemed to have been in the process of giving a picture of the magnetic field as lines of force acting along the angular momentum vector of a sea of molecular vortices that are aligned solenoidally along their angular momentum axes. However, this explanation has been disregarded by mainstream modern science. Since then, all definitions of the magnetic field, whether classical or relativistic have been purely mathematical.

Interestingly, the Lorentz force first appeared in Maxwell's original paper regarding molecular vortices and it appeared again as one of the original eight 'Maxwell's equations' in his famous paper 'A Dynamical theory of the Electromagnetic Field' 1865. The Lorentz force is actually the solution to Faraday's law of electromagnetic induction. However, in 1884, Oliver Heaviside reformatted Maxwell's equations and he presented a version of Faraday's law in partial time derivative format. This partial time derivative version of Faraday's law eliminates the convective component of the solution ie. E = vXB. The E = vXB component was once again introduced to physics when Heaviside's versions of Maxwell's equations were subjected to the Lorentz transformation. The Lorentz transformation had the effect of restoring the convective component that Heaviside had removed as well as introducing the relativistic factors.

This seems to have given rise to the misconception that the E = vXB, nowadays referred to as the Lorentz force, is purely a relativistic phenomenon. In fact the relativistic factors are relativistic, but the core formula goes back to Maxwell and it exists quite independently of Einstein's theories of relativity. David Tombe 30th April 2007 (210.86.146.100 07:53, 30 April 2007 (UTC))

The Simplification of the Article

Unfortunately magnetism is not a simple subject. It is considerably more complex than either gravity or electrostatics. There are therefore no half measures. As far as the layman is concerned, the magnetic field is a force field that exists around a bar magnet or an electric circuit and which aligns iron filings into a solenoidal pattern. A changing magnetic field induces an electric current in a wire. There is no point in making it more complicated than that for the layman.

For the student of physics, there is alot of hard work ahead. Alot of the hard grind was done in the nineteenth century by Ampère, Weber, Faraday, and Maxwell to name only a few. Our present day textbooks on electromagnetism lay out all the laws as established by these nineteenth century masters.

Einstein's theories of relativity came about in the twentieth century after electromagnetism had already obtained its final form. Relativity is a specialized topic of which the effects only become noticeable at very high speeds approaching the speed of light.

I can't therefore see why it has been felt necessary to cloud an already complicated topic with relativity, especially when most of the readers will be laymen. All matters relating to Einstein's theories of relativity should be kept to a special section further down. There is absolutely no need to mention relativity in the definitions when all those definitions and laws were established before Einstein was born.

The article should begin with a very simple overview of magnetism for the layman. It should proceed with an historical evolution of its dicovery and formulation going back to lodestones in Asia Minor, leading to Gilbert, and then to Oersted, Ampère, Faraday, Maxwell, Weber etc.

The various laws such as,

(1) Ampère's law (2) Faraday's law (3) Maxwell's Equations (4) The Biot-Savart law (5) The Lorentz Force

etc. should then be dealt with in separate sections further down.

Dr. Nelson White, Cambridge 28th April 2007 (61.7.165.234 13:57, 28 April 2007 (UTC))

I agree. I actually said two months ago that whoever wrote this article is just showing off that they have done a course on Einstein's Theories of Relativity. (58.8.1.227 15:49, 28 April 2007 (UTC))

I agree with most of this as well. There's no need to bring relativity into it straight off the bat, especially since there is a separate article on the Electromagnetic field. However, I do think that the introduction shouldn't be simplified to the point of being incorrect; defining it as "a force field that surrounds electric current circuits", for instance, is inaccurate and misleading. Define it correctly, and then offer up more everday examples. --Starwed 07:19, 30 April 2007 (UTC)

I first added the "technical" tag ("This article may be too technical for a general audience..."), because someone had got as far as complaining on the help desk about the article. Within minutes, someone made this edit [1]. I felt it was a little unfortunate, because (a) it didn't reduce the technical nature enough (b) it removed material which was built on in the article (c) it removed tags. But it would seem ungrateful to revert the edit, so I tried to put back what was most obviously deleted, in context.

I guess it might be useful to share my thoughts on the article and the process in general... I think the word "simplification" needs to be used carefully. It doesn't necessarily mean that articles should have technical content removed. Rather, the article can be structured to give people what they need at the level they need it. This is often an entirely different skill than being an expert in a subject, but I hope experts will appreciate the value of this. Above all, Wikipedia is written for a general audience: defences like "this is basic stuff, in any college textbook" don't work for a technical introduction.

It's worth commenting on the lead section since few people know what the Wikipedia style guide says. The lead section should be removable from the article without any actual information going missing; it should be a summary, drawing on the rest of the article. So this is the ideal place for a simple overview. However, it may be that the subject needs a rather longer overview, which could be placed as the first actual section in the article.

Also, I feel the article has too great an emphasis on physics, and far too little on the technology. These are not incompatible. People will often come to this article because they have heard that "(some technology) works with magnetic fields". Take a look at maglev for instance, which tells us that a Maglev train is a form of rail transport that works using magnetic levitation, and that Magnetic levitation is a method by which an object is suspended above another using magnetic fields. Would a layman be any the wiser after coming here? I think not. I'd like to see the "Applications" section expanded beyond a few bullet points (it looks as if it was grudgingly allowed). I'd like to see the lead section: explain magnetic fields without physics terms; talk about where magnetic fields are found naturally and how they are made artificially; give a few key applications of magnetic fields in the everyday world, and perhaps one or two more exotic applications like maglev (exotic unless you use Shanghai airport). Then, still in the lead section, and signposted by a few words like "In physics", a very general overview of the topics of discussion under physics.

If relativity complicates matters beyond classical physics, that should be mentioned, but not by replacing the classical discussion. After all, the articles on Newton's law have not been scrapped in favour of a relativity-modified form of the laws of motion. There is room in this article for a reasonable separation if that's how things are (and I honestly don't know, because I don't understand the article in its present form). Notinasnaid 07:48, 30 April 2007 (UTC)

Your point about Newton's laws is absolutely correct. When we are studying Newton, we don't need to keep labouring the fact that Einstein made amendments that come into effect when we approach the speed of light. Likewise with the magnetic field. But there is added confusion as regards the magnetic field because when Heaviside's equations are treated relativistically, the vXB component of the Lorentz force appears. This has led to the claims that the magnetic field is a relativistic effect. In actual fact, the Lorentz transformations are only restoring the convective component to Maxwell's equations, that was removed by Heaviside in 1884. The Lorentz transformations as applied to electric and magnetic fields do two things. (1) They introduce the relativistic factors, and (2) they restore the convective vXB component. But the convective component was there anyway in Maxwell's original equations independently of relativity and so it cannot be claimed that the magnetic field is the relativistic component of the electric field.

As such, any article on the magnetic field should leave all references to relativity to a special section. David Tombe 30th April 2007 (210.86.146.100 08:41, 30 April 2007 (UTC))

Reference to general relativity should be in the article beause special relativity is the very reason why magnetic fields actually exist. So it should be noted in the lead section that on the fundamental levem, magnetic field is only a relativistic manifestation of more fundamental electric field to help reader to not have common misconcepcions about magentic field. Thank you. --83.131.65.112 11:28, 30 April 2007 (UTC)

You are quite wrong. The Lorentz transformations only expose what is already inside Maxwell's equations and they add a convective term vXB that was already in one of Maxwell's equations before Heaviside removed it in 1884. Check equation (D) in Maxwell's paper 'A Dynamical Theory of the Electromagnetic field' 1865. Magnetism was around long before relativity was ever thought of. There are too many people who think that it is cool to show off that they know about relativity and they want to dominate an article about the magnetic field with relativistic effects that only occur as we approach the speed of light. (58.10.103.126 13:45, 30 April 2007 (UTC))

58.10.103.126, it should be at least mentioned that entire electrodynamics (not QED of course) can be derived from Coulomb's law and special relativity. Sometimes people have common misconcepcion that special relativity is consequence of Maxwell's equations just because they were discovered before. That's why it's worth to say that magnetic field is only a relativistic manifestation of more fundamental electric field. Thank you. --83.131.5.63 14:52, 30 April 2007 (UTC)

You're quite wrong. Relativity adds effects to electromagnetism but it doesn't create it. The Lorentz force and the Biot-Savart law are both present within Maxwell's original equations of 1864. All that the Lorentz transformation does is adds a relativistic factor which becomes noticeable if we travel close to the speed of light. You're assertion that the whole of electrodynamics can be derived from Coulomb's law and special relativity is totally wrong. Try deriving the whole of electrodynamics using only Coulomb's law and special relativity but without using Maxwell's equations and see how well you get on.

You seem to think that we have to dwell on this relativistic amendment. (58.10.103.126 15:40, 30 April 2007 (UTC))

I agree with the suggestions above that this article should focus on a qualitative description of the magnetic field and its applications and leave the quantitative material to one or more of the electromagnetic / relativity articles, e.g., four-potential, vector potential, EM field tensor, etc.). The key to doing this such that future editors won't be so tempted to simply add the quantitative 'stuff' back is to make mention (but only a mention) of the relativistic aspects in a separate section with a prominent link to the main article that the summary is taken from. This approach seems to work well in other articles. In other words, the subject of 'magnetic field' is so broad that this article should be primarily composed of summaries from other main articles with pointers to those articles for the benefit of those desiring more detail. Alfred Centauri 12:53, 30 April 2007 (UTC)

To 58:10:103:126: Consider the following quote from the textbook "Basic Concepts in Relativity and Early Quantum Theory" by Resnick & Halliday:

"In fact, starting only with Coulomb's law and the invariance of charge, we can derive (see Ref. 7) all of electromagnetism from relativiy theory - the exact opposite of the historical development of these subjects."

Ref 7 is "Electricity and Magnetism" by Edward M. Purcell. Alfred Centauri 23:02, 30 April 2007 (UTC)

Whoever made that quote seems to have forgotten that the relativity has to be applied to Maxwell's equations first in order to give it any meaning in the context of electromagnetism. The relativity itself cannot then claim credit for the relationships that were already inherent in Maxwell's equations. You cannot link up relativity directly with Coulomb's law and expect the Biot-Savart law and the Lorentz force to fall out. That quote is obviously a high handed quote and should not be taken seriously. (210.86.146.70 08:54, 1 May 2007 (UTC))

Maxwell's equations (and therefore entire electrodynamics) can be derived from Coulomb's law and special realtivity (assuming the invariance of charge). It is only historical incidence that Maxwell's equations were discovered before special relativity. It is also wrong to think that special relativity is due to laws of electrodynamics, quite opposite - if special relativity wouldn't be true (and if Galilean transformations would be true), there would be only electric fields. Thank you. --83.131.93.54 10:26, 1 May 2007 (UTC)

You are totally overlooking the fact that when relativity is applied to electromagnetism, the first step is to apply it to Maxwell's equations. I can't therefore see how it can then be inferred that Maxwell's equations are a product of relativity. If you believe in what you are saying, can we have a citation that demonstrates how Maxwell's equations are obtained from Coulomb's law and relativity? (58.10.102.198 12:18, 1 May 2007 (UTC))

On the contrary, beginning with just the Lorentz transformation (with c being understood as an invariant speed), it is straightforward to show that potential energy must be in the form of a four-vector. Deriving the four-force resulting from this four-potential yields a force law identical in form to the Lorentz force. The dynamics of the force fields also follow. Thus, as had been said above, assuming only Coulomb's law (in the 'rest' frame) and the invariance of charge, SRT is all that is needed to not only to see that a velocity dependent force must exist , but also to derive the resulting dynamics. See "Electricity and Magnetism" by Edward M. Purcell and [2] Alfred Centauri 13:22, 1 May 2007 (UTC)

What potential energy are you talking about? You begin with a Lorentz transformation and then suddenly you are talking about a potential energy. Where did this potential energy suddenly come from? It came from Heaviside's versions of Maxwell's equations. I've seen the derivation myself. Maxwell's equations are converted into a potential energy format using both the magnetic vector potential and the electrostatic potential. The Lorentz force comes out of Maxwell's equations and not out of relativity. There is no point in deluding yourself that relativity alone can produce the Lorentz force in conjunction with Coulomb's law.(58.10.102.198 13:38, 1 May 2007 (UTC))

But, Maxwell's equations are the ones that necessarily come from Coulomb's law, STR and invariance of charge. --83.131.1.164 15:44, 1 May 2007 (UTC)

83.131.1.164, you forgot about Faraday's law and Ampère's law which are the core equations in Maxwell's equations. Ampère's law and Faraday's law are most certainly not the product of relativity. You are getting confused with the fact that the Lorentz transformations are applied to Ampère's law and Faraday's law in four vector form and the Lorentz force falls out. How could Ampère's law regarding a current in a wire producing a magnetic field around it possibly be a consequence of relativity? That current in the wire has an absolute interaction with the surrounding magnetic field that it generates. Now see my reply below to Alfred Centauri for the rest.

You really aren't paying close enough attention to what I wrote. Please note that I wrote about a potential energy. In my comments above, I'm stating that a potential energy must be a four vector to be consistent with the SRT. That result does not come from Heaviside or Maxwell. Then, as should have been clear from my comments, the force associated with this potential must have a certain form and that form necessarily involves a velocity dependent part. None of the preceding involves any appeal to electromagnetism.

The Lorentz transformation alone requires that a force and its associated potential be of a certain form if they are to be covariant under the transformation. Thus, if all we know is that there is an inverse square law force that can be repulsive or attractive - call it whatever you want, the 'X' force - then, by the SRT, that force will necessarily obey a force law of the form of the Lorentz force. Further, the dynamics of the force fields associated with the 'X' force will necessarily obey laws of the form of Maxwell's equations. Alfred Centauri 15:16, 1 May 2007 (UTC)

I'm paying attention alright. First of all, your linked reference didn't cover the issue in question, but it doesn't matter because I've done all this anyhow. To get the vXB component from the Lorentz transformation, we need to apply it to the Heaviside partial time derivative versions of Maxwell's equations. What you have said above is total nonsense. Show me a citation. You are talking about a potential energy without specifying what that potential energy is. And you think that I don't know that it has to be the four vector potential energy associated with Maxwell's equations ie. the one that involves the electrostatic potential energy and also the magnetic vector potential A. It is ludicrous to suggest that the the vXB component of the Lorentz force comes about simply from any four vector potential energy that is consistent with SRT.

When the Lorentz transformation acts on the Maxwellian four vector potential, in respect of generating the vXB component, it is not doing anything that a simple Galilean transformation couldn't do. It is merely adding the convective component unto a partial time derivative and making it a total time derivative. That vXB term was already in Maxwell's equations before Heaviside took it away. In other words, the Lorentz transformation is merely adding on the velocity dependent term that the Galilean transformation could also add on. The vXB term is merely the difference between a partial time derivative and a total time derivative

If you are so confident that the magnetic field is only a relativistic effect, then can you please explain to me the role of relativity in paramagnetic attraction and diamagnetic repulsion. Paramagnetic attraction as you know is when a magnet picks up non-magnetized pieces of metal. Let's see you explain that relativistically. (58.10.103.214 16:19, 1 May 2007 (UTC))

The linked referenced most certainly does cover the issue in question and the fact that you dismiss it outright with an "it doesn't matter" speaks volumes.

Further, why would I need to specify the potential? A non-relativistic potential energy is simply an energy valued function of space. A relativistic potential energy is simply four energy valued functions of spacetime where the four functions are components of a four-vector. What more needs to be said???. If you had bothered to read the section in the linked textbook entitled "Forces from Potential Momentum", you would have seen an equation that has the exact form of the Lorentz force law but expressed in terms of an unspecified relativistic potential.

So please, let me suggest that you come down off of your high horse and address what you believe to be incorrect about that equation. Alfred Centauri 01:09, 2 May 2007 (UTC)

I saw the equation that you are talking about (15.12). That equation does indeed have an identical form to the Lorentz force which also happens to be equation (D) of the original eight Maxwell's equations in Maxwell's paper 'A Dynamical Theory of the Electromagnetic Field'(1865). See part III at [3]. But tell me what has that equation got to do with Einstein's theory of relativity? I can't see your point. That equation falls straight out of classical hydrodynamics yet you are trying to tell me that it is somehow a product of relativity.

I will now give you a web link that shows the Lorentz transformation producing that same equation (15.12) but with relativistic gamma factors added. The main point is that in order to do do, it has to act upon the Heaviside partial time derivative versions of Maxwell's equations, and in doing so it merely restores the convective vXB term that Heaviside removed from Maxwell's original equation(D). This is the way that the relativists do it, and you can see the result at equation (19). See the web link [4]

You have been trying to tell me that the Lorentz transformation can act on the Coulomb force alone and still produce the results at equation (19). I challenge you to show me how. Let me see you producing the Lorentz force using only the Lorentz transformation and Coulomb's law.

Your reference was supplied on the basis that it was going to show just that, but it didn't. It merely stated the Lorentz force as being a fact when the condition curl A = B holds. This is Maxwell's second equation and it is a hydrodynamical vortex equation. Whoever that contributor was who noted that B is an axial vector should perhaps take note of this fact as it might provide some clues as to what the magnetic field actually is.

Meanwhile until such times as you can produce a citation which demonstrates that the Lorentz transformations can produce the Lorentz force directly from Coulomb's law, then we can no longer maintain this myth that the magnetic field is the relativistic part of the electric field.

If you really believe that a magnetic field is the relativistic part of an electric field, can you then consider iron filings sprinkled on a sheet of paper over a bar magnet. Consider the solenoidal lines of force that become exposed and then tell me what reference frame I would have to go into for this pattern to convert into a radially divergent electric field pattern. (210.86.146.250 05:29, 2 May 2007 (UTC))

Anonymous said: "You have been trying to tell me that the Lorentz transformation can act on the Coulomb force alone and still produce the results at equation (19)". I hope your kidding because that's not what I've been saying all along. The idea here is to find the answer to the question "Knowing only the Coulomb force and the STR (and the fact that they are incompatible), how must the Coulomb force be modified to be relativistically covariant?". To find the answer to this question, one needs to know what a relativistic force field must 'look' like.

Right off the bat it is clear that the potential associated with the force cannot be a scalar but must instead be a four-vector. This implies that the 'gradient' (partial deriviative) of this four-vector potential will be a rank 2 tensor field on space time. The four-force will then be given by contracting the field tensor with the four-velocity.

Then, it is clear that this tensor field must be anti-symmetric since the four-force must be orthogonal to the four-velocity. This anti-symmetry is assured by taking the difference of the 'gradient' with its transpose. Thus, the 'gradient' operation on the four-potential will 'look' similar to a curl operation as the components of the tensor will consist of differences of partial derivatives.

Now, when this anti-symmetric field tensor and the four-velocity are contracted, the resulting four-force has a spatial part that is in the form of a Lorentz force law. This must be true for a force field in STR so, the Coulomb force must look this way to covariant. So, now we know that the Coulomb force must have a velocity dependent part in order to relativistically covariant. That is, knowing only Coulomb's force law and the STR, we deduce that there must be a magnetic field (part) and an associated magnetic force.

Further, the dynamics of the tensor field are constrained by STR and, when these tensor equations are written in '3 + 1' form, we get equations of the form of the Maxwell equations. Alfred Centauri 13:13, 2 May 2007 (UTC)

I'll now translate what you have just said into plain English.

The Coulomb force is not relativistically covariant but Maxwell's equations are.

That's it in a nutshell. I've never before seen such an illogical chain of total and utter nonsense as you have written above. You have presumed to work backwards to Maxwell's equations because of Einstein's theories of relativity. There wasn't a single grain of sense in anything that you said.

Maxwell himself deduced the Lorentz force from three dimensional hydrodynamics. You can see how he did it between equations (54) and (77) in his paper 'On Physical Lines of Force' 1861. It can't therefore be deduced from relativity also. What you are doing is taking a known result and then pretending to derive it using a language that nobody could possibly understand.

There is nothing to beat the benefit of hindsight, and what you have said above is totally unacceptable because it is totally incomprehensible.

At any rate we can prove the point far easier without even resorting to maths. You say that a magnetic field is the relativistic part of an electric field. OK then, tell me which frame of reference I need to go to in order to view solenoidal magnetic field lines around a bar magnet as radial electric field lines? (58.10.103.145 14:49, 2 May 2007 (UTC))

You need to cut back on the personal insults. I'm sorry if you don't understand what Alfred stated, but it's actually a pretty common line of argument in physics texts. For example, section 12.1.A in Jackson states that: "The general requirement that γL be Lorentz invariant allows us to determine the Lagrangian for a relativistic charged particle in external electromagnetic fields, provided we know something about the Lagrangian for nonrelativistic motion in static fields." The form of the Lagrangian is then deduced using similar arguments as above, although "Verification that [this] does indeed lead to the Lorentz force equation will be left as an exercise for the reader." --Starwed 22:16, 2 May 2007 (UTC)

Well Starwed, I'll leave you to do the excercise. Let me know when you have it completed. (210.86.146.200 04:41, 3 May 2007 (UTC))

Just to make a small point, I have to disagree with Anonymous' statement that "...It can't therefore be deduced from relativity also." Just because Maxwell could derive his equations well before relativity doesn't mean that starting from a different starting point (which may or may not include relativity) you can't get to the same conclusions. Certainly in classical mechanics and quantum theory there are multiple pictures and formalisms which give the same results. Both Newton's Laws and the Lagrangian will give you, say, the same equations of motion for planets going around a star (or for charged particles in a field I suppose; in the classical regime only, that is). And in quantum mechanics, there are a handful of formalisms (the Schroedinger Eqn and the Heisenburg Eqn come to mind). So, just because there exists a method X of getting to a result doesn't mean that method Y is invalid.

As to explaining complicated magnetic fields in terms of electrostatic-like fields, it seems to me that any such exercise would be too complicated to be meaningful. In some sense, for instance, a bar magnet's magnetic field is a result of all the magnetic fields of its constituent atoms and molecules. The fields of each of these are caused by effects which can be fudged classically (orbital angular momentum) and those which can't (spin). I would think you could fudge the former, but working with the latter would probably involve relativistic quantum theory, with which I am unfamiliar. But at the same time, it seems to me that according to someone sitting on a charged particle (with all its uncertainty in position and momentum) would only see a radial field (even if the rest of the universe seemed to be doing rather wacky things). Of course, the transformation from the rest frame of any given particle to a frame at rest with respect to the bar magnet as a whole would be horrendously complicated, if not impossible to write down. And it would only deal with one particle at a time. And of course, this has all the status of a thought experiment, and isn't rigorous. But I think it gets the idea across. DAG 23:20, 2 May 2007 (UTC)

Anonymous: your nutshell summary indicates to me that (at least) you didn't comprehend what I said. But, simply because you didn't comprehend it doesn't imply that it's utter nonsense. But don't take my word for it (OK, I know that you won't). Consult any advanced text on the STR written in the language of tensors to see what you've haven't seen yet.

You said "You say that a magnetic field is the relativistic part of an electric field." In fact, I have been arguing that the electromagnetic field equations can be derived from the STR and Coulomb's law (and invariance of charge) alone. Clearly, you disagree with this, however, you keep coming back to this example of a bar magnet as if it has a bearing on my arguments above. Why don't you see that it doesn't?

It (should be) clear to anyone with a reasonable grasp of the STR that it is not possible in general to find a frame of reference in which the the magnetic field vanishes everywhere. Consider the very simple case of a two charges moving parallel with different speeds. In what frame of reference does the magnetic field vanish everywhere for this most simple case? So why exactly is it that you keep bringing your example up?

Even better, please try to explain to me what relevance you believe your example has to my assertion that the STR (alone) requires that any force has a velocity dependent part?

Finally, if you didn't believe what I said earlier then your won't believe this either. In the context of the STR, all components of force depend on velocity. The 3-force we see coming from the gradient of a 3-potential is in fact a velocity dependent force that is orthogonal to the motion... the 'motion' through time that is. Enjoy! Alfred Centauri 02:35, 3 May 2007 (UTC)

No. What you said in your previous letter is what is known as 'Defensive Rubbish'. It is a strategy used when somebody is cornered in an argument. The strategy is to talk such absolute total and utter nonsense that nobody could possibly understand it. It then allows you to claim that the fault lies with that person for not understanding it. Stage two is to refer them to a big thick text book. And of course you will also have your allies such as Starwed backing you up and claiming that he understands it totally and without any difficulty at all.

The fact is that your assertion that a magnetic field is the relativistic part of the electric field is totally ludicrous. Even if what you said in your passage above happened to contain any truth at all, at the very most all that you would be saying is that in order for a force to be covariant under a linear transformation, it needs to have a velocity dependent term. This is so even with an ordinary Galilean transformation. A Galilean transformation can easily show that the vXB term is merely the convective component of the total time derivative of Faraday's law.

At the very most, you merely pointed out that the vXB term is commensurate with a linear transformation. You added in relativity as an extra without any justification whatsoever. All the relativity does is adds extra terms which we know as the 'Lorentz Factor' or the 'Gamma factor'. You slipped relativity in under a huge smokebomb of tensor field theory language .

Take the curl of vXB. You get -(v.grad)B. That's the convective component of a total time derivative. Add it to the partial time derivative and you've got Faraday's law in total time derivative format. Heaviside took the convective component away. A linear transformation puts it back again. All the relativity is totally superfluous and your incomprehensible passage, which Starwed fully understood, did not in any way link Coulomb's law to relativity.

Some other guy questioned the idea that if vXB can be derived hydrodynamically, why can it not also be derived from relativity. The answer is that three dimensional classical hydrodynamics is totally incompatible with relativity. They can't therefore both lead to the same result. At any rate, we still have to see how relativity can derive the vXB term. (210.86.146.200 05:06, 3 May 2007 (UTC))

This argument could be brought to a swift end if we had a reliable citation showing the mathematical link between Coulomb's law and Einstein's theory of relativity. From what I can see, the argument has centered on the link between the Lorentz Force and covariance. (58.136.112.127 06:52, 3 May 2007 (UTC))

To 58:136:112:127: There is no swift end to this argument. Anonymous is an anti-relativity troll from USENET and frankly, I've been feeding it a bit too much. Note that it doesn't provide any logical justification of its claims and pronounces all evidence contrary to its claims as nonsense, rubbish, superfluous, incomprensible, etc. Note I and others here have provided links and citations but anonymous has yet to do so. But, since you asked, here's another: [5]. And finally, here is an excerpt from the preface to the original edition of the textbook "Electromagnetics" by R. S. Elliot [6]:

This alternative retains the scope of the senior-graduate sequence but begins with a study of special relativity. With this as a basis, it is possible to develop all of electromagnetic theory from a single experimental postulate founded on Coulomb's law. An enriched understanding of magnetism results, and the Biot-Savart law is a consequence rather than a postulate. The Lorentz force law is seen to be a transformation of Coulomb's law occasioned by the relativistic interpretation of force. Upon accepting the Lorentz force law as fundamental, one is able to derive Faraday's emf law and Maxwell's equations as additional consequences. This procedure provides the further satisfaction of demonstrating that the fields contained in the Lorentz force law and in Maxwell's equations are one and the same, a conclusion not possible in the conventional development of the subject.

Alfred Centauri 13:15, 3 May 2007 (UTC)

The Definition of the Magnetic field

That definition of the B field in the main article only applies in special situations. I can imagine situations in which there is a B field but no E field. I think that we all need to take a closer look at the meaning of that E term. If that E term is causing the B field, then we need to know more about it. Is it a Coulomb force or is it a Lorentz force? Until we know, we may have to delete it. There is no point in trying to define the undefinable. (58.10.103.126 18:10, 30 April 2007 (UTC))

There should be no need to look too hard: just look at the references. Wikipedia editors should never have to make difficult calls like this; the original authors we cite have done that. Notinasnaid 18:13, 30 April 2007 (UTC)

What is the page number and the section number, and which reference are you referring to? (210.86.146.70 07:32, 1 May 2007 (UTC))

Yes, the 'definition' isn't one at all. Instead, the 'definition' section appears to be giving the B of a moving point charge. The (implicit) definition, according to a college textbook that I have is this:

"Given a test charge with velocity v, the magnetic force on the particle is given by F = qv X B".

Alfred Centauri 00:46, 1 May 2007 (UTC)

Even F = qv X B is not a definition of the magnetic field. That equation is merely one of the solutions to Faraday's law. It describes one particular effect of a magnetic field ie. that a charged particle moving at right angles to a magnetic field experiences a force that is at right angles to both its motion and the magnetic field. There are other aspects of the magnetic field not catered for by that formula. A stationary charged particle experiences a force in a changing magnetic field. That is the other part of Faraday's law. Then there is also the direct effect that magnetic field lines have on magnetic poles. In that capacity, the field lines are acting like lines of force. They pull along their axes and they push each other laterally. When two like poles repel the magnetic field lines spread outwards from each other. When two unlike poles attract, the magnetic field lines cross over directly between the two unlike poles.

There are many strands to the magnetic field. I have as yet to see a single definition. (210.86.146.70 07:32, 1 May 2007 (UTC))

There is no major problem here. Frequently editors tie themselves in knots trying to synthesise meaning from contradictory sources: what is the definition when these sources disagree? The job of an encyclopedia editor is not to try and synthesise a definition, but if there is contradiction, report it (with sources). Notinasnaid 09:02, 1 May 2007 (UTC)

For reference, the intro used to use the definition: A magnetic field is that part of the electromagnetic field that exerts a force on a moving charge. I think that's preferable to the current intro, and doesn't contain any gross inaccuracies. (There are subtleties with spin, which I think are important enough to mention in the intro.) It basically delegates a lot to the electromagnetic field article, which I think is a Good Thing.

A stationary charged particle experiences a force in a changing magnetic field.

Right, because a changing magnetic field produces an electric field, and electric fields act on stationary charges. --Starwed 09:38, 1 May 2007 (UTC)

I think that is way too technical by itself. How about

A magnetic field is a field which has particular influences, originally named because it is found around a magnet, and the original influence known was the attraction of some metallic objects. Magnetic fields have now been found to occur naturally without magnets, as in Earth's magnetic field, and to be produced by an electric current.

In technology, magnetic fields have many applications, from compasses and refrigerator magnets, through electric motors and electromagnets to the linear particle accelerator (which can be used in medical treatment) and the maglev train (a train "levitated" by magnetism).

In physics, more formally, a magnetic field is that part of the electromagnetic field that exerts a force on a moving charge. This article deals mostly with the physics of magnetic fields.

Notinasnaid 10:03, 1 May 2007 (UTC)

I took some of your ideas, and tweaked it a bit:

"A magnetic field is a physical force field that acts on moving charges, electric currents, and other objects which are susceptible to its effects. The existence of the magnetic field was first discovered in the existence of effects of certain naturally occurring rocks which exerted forces on similar rocks and on some metals such as iron, which came to be known as magnets. Later, magnets revealed the existence of the Earth's magnetic field and led to the invention of the compass. It wasn't until the 19th century, however, that physicists first began to understand and quantify the effects of the magnetic field. In particular, the magnetic field was shown to also affect and be created by currents, and to have a strong and important relationship to the electric field."

"Magnetic fields have many applications in modern technology. These applications include compasses, refrigerator magnets, electric motors, electromagnets, maglev trains, magnetic resonance imaging (MRI), and particle accelerators of various designs. Magnetic fields play keys roles in many areas of science, particularly physics."

"In the SI unit system, the magnetic field has units of Tesla (T), where one Tesla is equal to one kilogram per second per Coulomb. As the Tesla is a large unit in practice, another common unit is the Gauss (G), which is used in the CGS system of units, where 10000 G is equal to one Tesla."

Let me know what you think. I tried to give a bit of historical perspective, which I also used to introduce some of the key effects of the MF. I reworded your applications section a bit, and added a short bit on units (maybe a lot of people come here for that, I don't know). DAG 21:11, 1 May 2007 (UTC)

Starwed, you agreed that a stationary charged particle experiences a force in a changing magnetic field. You then presumed to know the reason why and proceeded to restate the original fact using different words. You said that it is because a changing magnetic field produces an electric field, and electric fields act on stationary charges.

Well we know that an electric field is defined as a force per unit charge and so it obviously acts on stationary charges. You have effectively said that a stationary charged particle expereiences a force in a changing magnetic field because a changing magnetic field produces a force on a charged particle, and you have presumed to have given us all extra information that wasn't already in the originator's statement. You have agreed with a statement and then re-worded it in order to appear wiser than the person making the statement. (58.10.102.198 12:29, 1 May 2007 (UTC))

Introduction

Somebody put in a very novel but clumsy definition of the magnetic field as being an axis of all the possible directions that a force would act if a charged particle were to move perpendicularly to a magnetic field.

Magnetic field lines are demonstrated to first day high school pupils by sprinkling iron filings on a sheet of paper over a bar magnet. When unlike poles are attracting, the magnetic field lines are acting like lines of force directly connecting the two unlike poles. That is about as basic a concept as we will ever get of a magnetic field line. It is a line of force. More precisely it is a line of tension.

You don't try to give an intuitive description of a line of force in terms of some specialized aspect of it, in this case the F = qvXB effect which is only one aspect of the magnetic field. That equation bears no relation to the force produced on a stationary charge by a changing magnetic field, or to paramagnetic attraction, or to diamagnetic repulsion, or to either ferromagnetic or electromagnetic attraction or repulsion.

Until such times as we agree on what a magnetic line of force actually is, then we will merely have to accept that it exists and describe it as it would be described to a high school physics student. (58.10.102.198 12:43, 1 May 2007 (UTC))

Any comments on my proposed opening (previous section, in italics)? Notinasnaid 12:48, 1 May 2007 (UTC)

OK. let's go over your proposal point for point.

A magnetic field is a field which has particular influences, originally named because it is found around a magnet,

This line involves repitition of both the words 'field' and 'magnet'. In the current introduction, it states something to the extent that a magnetic field is a force field that is detected by its effects. Why would you want to replace that?

and the original influence known was the attraction of some metallic objects.

OK, so you have mentioned paramagnetism and assumed that it was the first effect known to man. I'm not so sure about that. Anyhow, the effects of a magnetic field are (1) paramagnetic attraction, (2) diamgnetic repulsion, (3) electromagnetic induction which splits into the force acting on a moving charge at right angles to a magnetic field, and a force acting on a stationary charge in a changing magnetic field, (4) ferromagnetic and electromagnetic attraction and repulsion, (5) force on a moving charge that is not tied up with electromagnetic induction. The present introduction lists three of the important effects. What is wrong with it the way it is?

Magnetic fields have now been found to occur naturally without magnets, as in Earth's magnetic field,

Did the first magnets not occur naturally?

and to be produced by an electric current.

This would be implied in the existing introduction.

In technology, magnetic fields have many applications, from compasses and refrigerator magnets, through electric motors and electromagnets to the linear particle accelerator (which can be used in medical treatment) and the maglev train (a train "levitated" by magnetism). In physics, more formally, a magnetic field is that part of the electromagnetic field that exerts a force on a moving charge. This article deals mostly with the physics of magnetic fields.

That is material for a special section on applications. That is not introduction material.

Why not leave the introduction as it is. It is short, concise and covers the main points. (58.10.102.198 13:11, 1 May 2007 (UTC))

Thank you for your detailed reply. I see we are really debating something much more fundamental to Wikipedia, so I will start a new section, below. Notinasnaid 02:15, 2 May 2007 (UTC)

Too technical for a general audience

When I added the Wikipedia tag for "Too technical for a general audience" tag to the article, it led to a lot of very good discussion about definitions, which should continue. However, I feel it has largely avoided the real significance of this tag. At issue is not just whether the article is accurate (though this is vital), but whether it is accessible.

I'd recommend the linked Wikipedia:Make technical articles accessible in full, part of the Wikipedia Manual of Style, but I will also quote some of the key points.

• "Articles in Wikipedia should be accessible to the widest possible audience. For most articles, this means accessible to a general audience."
• "Consider the types of readers that may encounter a technical article...The general public, with no technical background... it should be clearly established what field of study the concept belongs to, and if it has any practical applications. "
• "Put the most accessible parts of the article up front. It's perfectly fine for later sections to be highly technical, if necessary. Those who are not interested in details will simply stop reading at some point. "
• "Add a concrete example"
• "Use jargon and acronyms judiciously"
• "Use analogies"
• "Do not 'dumb-down' the article in order to make it more accessible. Accessibility is intended to be an improvement to the article for the benefit of the less-knowledgeable readers (who may be the largest audience), without reducing the value to more technical readers."

I contend that the article fails most of this test, except avoiding dumbing down, by any measure. At the moment it approaches the subject purely as an exercise in (largely theoretical) physics, except for a small and underdeveloped "applications" subsection of "See also", some mention of compass needles (though they are never put in context), and a good (but technical) discussion of electric motors in "Rotating magnetic fields". The article does not even use the word "electromagnet".

I contend that to make this article accessible, it needs more material on applications, such as a complete subsection discussing applications in a non-technical way, probably first in the article after the lead sections (as this is likely to be the most accessible part). The technical aspects of these applications can later be referred to in context (as in the electric motors) section.

Above all, the lead section needs to be rewritten. At the moment it is

In physics, a magnetic field is a force field that surrounds electric current circuits. A magnetic field can also be found in the vicinity of ferromagnetic materials such as iron. The existence of a magnetic field is ascertained by its effects. The most important of these effects are (1) Force on a moving electrically charged particle, (2) Force on a stationary charged particle when the magnetic field is changing, (3) Mutual force acting between two objects or electric current circuits that are surrounded by a magnetic field.

I realise technical details are under discussion, and this is more accessible to a "general technical audience" at about the level of first year college science course than it used to be. But words like "ferromagnetic" are an obstacle, and that's still about the simplest sentence.

I contend that it is perfectly possible to write an article that the average child of age 10 or more can take away some enlightenment about magnetic fields from. Enlightenment such as "magnetic fields are what you get around magnets" and "magnetic fields make a compass work". Maybe younger; I don't know at what age magnets are introduced to a typical curriculum.

I have therefore proposed (elsewhere) a form of words which begins by defining a magnetic field in terms of the its most familiar everyday form, continues to list a handful of everyday applications (not an exhaustive list), and then moves on to provide a strictly accurate definition in terms of physics. Recall that the lead section should say nothing not repeated and expanded later in the article. I proposed earlier in this post that the first section following be an expanded applications discussion. Then the rest of the current article.

Before getting bogged down in a discussion of the form of words, I would like to open the debate on the general principle: How can we make this article more accessible? What do people think of the general framework proposed? Does anyone contend that the article would be fatally damaged by providing an opening that could be understood by a 10 year old?

Comments please. Notinasnaid 02:58, 2 May 2007 (UTC)

While I agree to some extent, the simple fact is that not all articles on Wikipedia can be accessible to a general audience, nor should they be. However, this article should be, IMHO. More technical articles related to this subject can be written and linked to from this article. Do you agree or disagree with this approach, Notinasnaid? Alfred Centauri 03:23, 2 May 2007 (UTC)

I think the biggest problem with the article vis-a-vis a general audience has to do with Notinasnaid's point #3 (that is, with putting less technical things up front). The first thing (after the intro) a reader sees is basically an equation. Probably there should be a section or two on less technical or less mathematic material (similar perhaps to the Properties section half-way down the article). I'm not saying take out the technical material (though a good rewrite seems in order), but move it to the end, after more discussing the magnetic field more generally. And then, ease into it. DAG 03:35, 2 May 2007 (UTC)

Good point. Are you ready to start the editing? Alfred Centauri 03:42, 2 May 2007 (UTC)

Yes. We have to get the equations away from the first few sections. More emphasis needs to be placed on describing the pattern of a magnetic field and discussing all the observed effects. I can count (1) attraction between unlike poles (field lines connect directly) (2) repulsion between like poles (field lines spread outwards). (those first two effects are electromagnetism and ferromagnetism). Then there is (3) the alignment of a bar magnet in a magnetic field. (4) attraction of certain non-magnetized materials (paramagnetism) (5) Weak repulsion of other non-magnetized materials (diamgnetism). (6) force on a charged particle that is moving at right angles to a magnetic field (7) force on a stationary charged particle in a changing magnetic field.

Then we need to start doing sections on the mathematical formulations of these effects.

(a)Ampère's law (closed current loop causes magnetic field) (b)Biot-Savart law (defintion of B field commensurate with Ampère's law) (c)Faraday's law of electromagnetic induction (covered by aspects (6) and (7))

and finally how these equations come together into Maxwell's equations. (210.86.146.250 05:42, 2 May 2007 (UTC))

A naive question

Does all of the definition and mathematics in here apply purely to the magnetic field, or is any of it related to the electromagnetic field? Notinasnaid 19:34, 2 May 2007 (UTC)

Lorentz force on wire segment

I had to blink at this formula. The information is correct, I'm only nitpicking on the display. The formula is:

$F=Il\times B\,$

Which is correct. However, directly after the forumla, the section goes on to label each variable within the formula with:

F = forces, measured in newtons

I = current in wire, measured in amperes

B = magnetic field, measured in teslas

$\times$ = vector cross-product

l = length of wire, measured in metres

This text (and this effect should replicate above) is in Arial. The capital I ("eye") and lowercase l ("el") appear exactly the same (pixel-perfect for me) in both IE and Firefox. The letters are also not in order, so some knowledge (which, hopefully, could be picked up in the article) is needed to decipher which variable is being explained.

Also, it seems a twee odd (and certainly doesn't help) that the variables are not labelled in the same order that they appear in the formula. They appear to be in no real order at all...

The text immediately below contains similar problems when discussing vectors with current and the segment. To clear it up, some possible solutions:

• Rearrange the variable explanations to match up with appearance in the formula.
• Could the formula be modified to use a capital L as opposed to a lowercase one? Anything wrong with this / would it be confused with other common uses? (such as L for rotational momentum?)
• Make the variable explanation monospace. This doesn't correct the paragraph afterwards discussing vectors, however.
• Is there an HTML entity for a cursive lowercase L?

I might "be bold" in a few days, but if anyone has any objections, now's the time to let the world know... ;-) (Ack, forgot to sign... these bots are fast!) Deathanatos 04:21, 3 May 2007 (UTC)

Ah hah! There is a unicode script L, which might also help: It's &#8467; and displays as ℓ. Kinda small... would it work? (It appears to be the character my physics equation sheet uses) Deathanatos 05:19, 3 May 2007 (UTC)

But of course the HTML entity doesn't display in IE (at least for me in IE6)... I'm such a spoiled FireFox user... Deathanatos 05:21, 3 May 2007 (UTC)

Electromagnetic Induction

The force that acts on a moving charged particle in a magnetic field is a component aspect of electromagnetic induction. It was not incorrect to have mentioned it in the introduction. However it is a specialized aspect of the magnetic field and it has now been side referenced. An introduction to an article entitled Magnetic Field should only give an overview of the general picture of the magnetic field. The general picture is that of solenoidal field lines in conjunction with the fact that like poles repel and unlike poles attract. (201.53.10.180 16:20, 14 May 2007 (UTC))

Cleanup of this page

I think the best approach to cleanup this article would be to move the discussion of B and H fields to the end of the article.

Lines of Force

I can't see what the problem was with the term 'Lines of Force'. The term 'Lines of Force' was good enough for Faraday. These lines of force pull magnets together and they push magnets apart. It seems to me rather clumsy to replace the term 'Lines of Force' with 'Lines of Alignment of the needle of a compass' as if to suggest that the alignment of a compass needle has got nothing to do with force. Whoever made that amendment seems to have forgotten that the torque that causes the alignment of a compass needle has got a force component to it. That force comes from the magnetic field lines. Magnetic field lines are 'Lines of Force' without any shadow of doubt about it. (81.129.175.154 09:16, 17 June 2007 (UTC))

This change was probably made because forces that magnetic fields exert do not have direction of $\mathbf {B}$ but direction of $\mathbf {v} \times \mathbf {B}$. --83.131.87.100 11:58, 18 June 2007 (UTC)

When two magnets are attracted together, the direction of the magnetic force is exactly along the magnetic field lines. That means that magnetic force is exactly in the direction of $\mathbf {B}$. You are getting confused with the force on a moving charged particle which is at right angles to $\mathbf {B}$ (81.129.175.154 19:56, 18 June 2007 (UTC))

Incorrect. When you place a magnet in uniform magnetic field, then THERE IS NO NET FORCE on it. (There is torque instead. And the direction of the torque DOES NOT coincide with the direction of the magnetic field either, but is perpendicular to it instead).

You are correct in saying that a magnetic field vector is an axial vector field.You are further correct in saying that a charged particle moving in a magnetic field will experience a force that is at right angles to the magnetic field. However you seem to be wilfully blind to the fact that two magnets pull together and that the force in this situation is directed exactly along the magnetic field lines. Magnetic force has got more aspects to it than just the

If you place two magnets parallel to each other, the net force each is experiencing is directed TOWARD another magnet (it is either attraction or repulsion - depending on poles' orientation). As you can see, the force is again directed NOT along magnetic field lines (which are parallel to magnets in this situation). So, magnetic field lines are NOT lines of force as you erroneousely claim. Why did you claim what you don't know? Can you please revert back your INCORRECT reverts? Sincerely Enormousdude 20:14, 20 June 2007 (UTC)

Place the north pole of a bar magnet near to the south pole of another bar magnet. The magnetic field lines will cross directly between these two poles. The two poles will pull together in the direction of these field lines. Your mention of there being no net force in a uniform magnetic field is actually a separate phenomenon that applies to the force on unmagnetized materials in an inhomogeneous magnetic field. It comes under the study of diamagnetism and paramagnetism.

You cited another scenario in which a bar magnet will align in a magnetic field. Yes indeed a torque is involved in this scenario but every torque has a force, and the forces in this scenario are in the direction of the magnetic field lines, even if the torque is perpendicular. Torque and force are related to each other through a vector cross product.(81.129.175.154 12:21, 21 June 2007 (UTC))

Incorrect again. Looks like you never took e/m class. To begin with, there are NO magnetic poles. Neither inside a bar magnet, nor anywhere else. It would be enough to point to the second Maxwell's equation (Gauss's law for magnetism) which shows that you are dead wrong about magnetic poles and stop discussion right there. But it seems that you are not familiar with those equations.

To explain this to you in more obvious terms, take a disk-like Nd magnet (say, like a quarter in shape). Tell then, where is its north pole and where is its south pole if the magnet happens to be very thin (say, like a quarter)? And what happens when two such magnets are at some distance from each other (say, a few diameters away)? Magnets still strongly attract or repel each other depending on orientation, but where are the poles? Another example - a circular current loop. Where is its north pole and where is its south pole? Place two loops at some distance from each other - and again similar to disk magnets they would attract or repel (plus mutual torques, of course) - yet there are NO POLES! What then attracts to what?

Take a ball Nd magnet. Where are its poles? Finally, take a bar magnet and break it into two halves. Do you know that you will NOT get two separate poles as you probably expect - instead, you will get two bar magnets with two poles each!. Where are then two SEPARATE poles? And where did NEW poles came from?

What do you mean by saying "Your mention of there being no net force in a uniform magnetic field is actually a separate phenomenon that applies to the force on unmagnetized materials in an inhomogeneous magnetic field. It comes under the study of diamagnetism and paramagnetism..." ? This is nonsense. Permanent magnet in uniform magnetic field has nothing to do with unmagnetized materials (permanent magnet IS magnetized by definition) nor with paramegnetism nor diamegnetism. Look up any e/m textbook. Paramagnetizm is a phenomenon of realignment of atomic magnetic moments in external magnetic field (just as a current loop is experiencing torque in external field, atomic magnetic moments do the same). Diamagnetism is inducing magnetic moments by external magnetic field in a substance atoms of which have zero own magnetic moments. Then according to Lenz law induced moments are directed opposite to the source field - thus resulting in net force on the diamagnetic directed opposite to the gradient of magnetic field (=repulsion from stronger field regions). One example of perfect diamagnetic is a superconductor.

As you can see, a permanent magnet in uniform magnetic field has nothing to do with paramagnetizm, diamagnetizm or behaviour of nonmagnetized materials.

You know, not only permanent magnets and current loops have magnetic field, but also some so called elementary particles do. For example, electron has magnetic field - and thus magnetic moment, proton has magnetic field, neutron, etc. So, two electrons or neutrons interact with each other in a similar way two bar magnets do (if to neglect quantum effects here). But where are poles in an electron? In a neutron? Electron is considered elementary particle - meaning it has no internal structure. So, if it had poles then the two poles must sit right in the same place - and thus must cancel completely each other out resulting in zero net force AND in zero net torque on an electron in external magnetic field. But this is NOT the case. Electron in external magnetic field does experience both torque (which results in its precession and in different magnetic potential energy depending on its orientation) and does experience net force (which resulted in sorting of spin up and spin down Ag atoms in historic Stern-Gerlah experiment).

So, where are those imaginary magnetic poles you like so much?

And if there are no poles, then what force (on poles) you are talking about? If there is no force (on non existing poles) - then when you claim that magnetic field represent lines of force - then lines of WHICH force are you talking about?

Sincerely, Enormousdude 19:45, 22 June 2007 (UTC)

I'm talking about the force that pulls two magnets together. It's directed along the $\mathbf {B}$ lines. (86.145.135.204 16:59, 23 June 2007 (UTC))

It is NOT. Place two magnets parallel to each other. Say, place two 1" long bar magnets at 2" distance from each other in parallel say by north poles up. The magnetic field of each one in the location of another magnet is directed DOWN then. Yet the force left magnet is experiencing is directed to the LEFT, and the right one - to the RIGHT (not UP as you claim).

Please, also address the questions of my reply to you above - about magnetic poles of thin disk-like magnet, magnetic poles of a circular loop of current and magnetic poles of say electron. Also, explain me why second Maxwell equation (Gauss law for magnetic field) states that density of magnetic poles is zero?

Sincerely, Enormousdude 20:45, 23 June 2007 (UTC)

Enormousdude, you are in a state of denial. Magnetic force is more than just $\mathbf {v} \times \mathbf {B}$. There is another aspect of magnetic force that acts in the direction of magnetic field lines, and it is not the $\mathbf {v} \times \mathbf {B}$ force. This other aspect of magnetic force can cause a change in kinetic energy as can be witnessed when two bar magnets are accelerated together, whereas the $\mathbf {v} \times \mathbf {B}$ force never changes the kinetic energy of a charged particle. You have overlooked this other aspect of magnetism and now you are trying to deny that it exists. You are denying the most basic aspect of magnetism. You are denying Faraday's lines of force that pull two magnets together. You are deliberately turning a blind eye to this most basic of scenarios and trying to divert attention away to alternative scenarios. Every child knows that two magnets pull together, and every high school pupil knows that the force of attraction is directed along the magnetic field lines.(86.145.135.204 22:16, 23 June 2007 (UTC))

Wow, what a bunch of nonsense! Did you ever take physics class? Magnetic force is indeed MORE that $\mathbf {v} \times \mathbf {B}$ - it is actually $q\mathbf {v} \times \mathbf {B}$. Thare are NO "aspects" of magnetic field which "act" in the direction of magnetic field lines. Do I have to explain you how (and why) magnets attract to each other? Or you can read it in e/m textbook yourself, saving mutual waste of time? A permanent magnet consists of a bunch of atomic magnetic moments (magnetic dipoles). Energy of a magnetic moment μ in the external magnetic field B (of, say, another permanent magnet nearby) is equal to: U = -(μB). Force the dipole μ is experiencing in this magnetic field B can be expressed via gradient of potential energy (by definition of work): F = -grad U = grad (μB). You may see that the force is NOT directed along magnetic field lines but along the GRADIENT of magnetic field. On the axis of a cylindrical permanent magnet magnetized along its axis gradient is directed along the axis of the magnet - that is why two cylindrical permanent magnets PLACED COAXIALLY attract or repel along their axis. Non-coaxial arrangement resilts in a force between them NOT directed along either axis or magnetic field line direction, BUT always along the direction of gradient of magnetic field. The same result is obtained if to consider a permanent magnet as a loop of surface current (similar to a solenoid) and integrate Lorentz force its current elements are experiencing in the magnetic field of another magnet.

So, why do you keep insisting on the existence of 2 century old incorrect concept of "Faraday's lines of force" stretching between poles of a magnet - while here are NO magnetic monopoles, and while magnetic field lines are NOT lines of force?

How to explain you that there are no magnetic poles (which is evident from both definition of magnetic field and from second Maxwell's equation)? Consider thin disk-like magnet magnetized in axial direction. Very thin - like a quarter. Where is its north pole and where is its south pole? How close they are to each other if the magnet is really very thin? Or consider a single loop of current. Say, 10 A current is circulating in a 3 cm diameter circular wire. This loop behaves in external magnetic field the same way a permanent magnet in the shape of disk does. Answer please, where is north pole and where is south pole in this loop?

Also consider usual cylindrical bar magnet magnetized along its axis. Let's say, magnet is oriented up-down, with the north pole up. What is the direction of the magnetic field directly above the north pole? Obviousely up. What is the direction of the magnetic field directly BELOW north pole (=inside the magnet)? If the north pole is a monopole, then the answer is obvious - B is directed down (=from north monopole on top of magnet to the south monopole on the bottom of the bar magnet). However, if you make a small hole in the actual magnet directly under its north pole and insert a magnetic probe into the hole, you find that actual magnetic field is directed in the OPPOSITE direction: it is directed not down but UP!

Thus there are no magnetic monopoles, and claiming that magnetic field is a force field directed from north pole to south pole is incorrect.

Because you can't answer any of my questions above, I just safely assume that you don't know the answer to any of them simply because you are ignorant about electromagnetism as well as about physics in general. Why do you edit the article then?

So, don't correct what you PERSONALLY don't understand or don't know. Leave it to physicists. If you want to understand what magnetic field is and how two permanent magnets interact, take a physics class - then things may become a little more clear to you.

Sincerely, Enormousdude 20:11, 27 June 2007 (UTC)

There are no magnetic forces in direction of magnetic field, all of those forces are perpendicular to direction of magnetic field, so not even any net force can be in direction of magnetic field. There is one thing about magnetic field that deserves more attention than it usually does: vector of magnetic field is axial vector. This means that plane perpendicular to it's direction is one with direct physical meaning, and not it's direction itself. --83.131.92.177 17:24, 23 June 2007 (UTC)

You are correct in saying that a magnetic field vector is an axial vector field. You are also correct in saying that a moving charged particle in a magnetic field experiences a force that is at right angles to the magnetic field. That is one aspect of magnetism. But you seem to be keen to overlook another aspect of magnetism. You seem to want to turn a blind eye to the fact that two magnets pull together, and that the force involved is exactly in the direction of the magnetic field lines. (86.145.135.204 20:22, 23 June 2007 (UTC))

Incorrect. See my reply with explanations (on various levels) of how permanent magnets actually interact, and some questions to you (about magnetic poles of a disk-like magnet, a loop, an electron, anout magnetic field direction inside permanent magnet, etc) which will help you to understand that the force is NOT directed along magnetic field lines, (but along the gradient of magnetic field instead). Enormousdude 20:20, 27 June 2007 (UTC)

Should we remove the line "Another intuitive way to view \mathbf{B} is as a bundle of lines of force that pull two unlike magnetic poles together" from the definition section. I am no expert on magnetism so I can't tell from this discussion what to do, and whether it is correct or not. Nicolharper 23:49, 27 June 2007 (UTC)

Why would you want to deny the most fundamental aspect of magnetism? Magnets do pull together. Every child knows that. Whoever worded that line about "a bundle of lines of force" might have worded it better, but from what I can see it is absolutely correct in principle. What about re-wording it to ---- Ah wait a minute! I see now. He was specifically talking about the definition of $\mathbf {B}$ which is the magnetic field vector $\mathbf {H}$ multiplied by the magnetic permeability. Yes, $\mathbf {B}$ is a weighted version of $\mathbf {H}$ and so it is effectively a bundle of $\mathbf {H}$ lines. Quite frankly, I would just leave it in. (81.158.161.160 11:41, 28 June 2007 (UTC))

Origins of the Magnetic Field

I removed the section that claims that the magnetic field is an electric field as viewed by an observer in a moving reference frame. When I look at magnetic field lines around a bar magnet, I cannot imagine which rest frame I would need to be in in order for these field lines to become electric field lines. (81.158.161.160 20:26, 27 June 2007 (UTC))

Read any physics textbook - there is no magnetic field in the co-moving with charge frame (and don't forget that electrons have not only electric charge which creates electric field but also spin which is quantum mechanical motion - so electric field of electron is already in some motion). Moving electric field is what magnetic field is (to be more accurate - RELATIVISTIC component of moving electric field). Enormousdude 19:30, 28 June 2007 (UTC)

If the supposed fact that a magnetic field is the relativistic component of an electric field is well documented in the physics literature, that doesn't mean that this fact needs to be added to the introductory paragraph in the magnetic field article. There have already been complaints that the article is too technical for the average reader. So why the insistence on adding this obscure and higly controversial piece of relativity into the introduction? (81.158.161.160 12:20, 28 June 2007 (UTC))

Hold on, the only reason magnetic field exists is special relativity (Loretz transformations). Not many people understand that (apparently including you, by the way). There is NO magnetic field in classic (Galilean) transformation of Coulomb force from co-moving with the source electric charge to non-moving reference frame of observer. None. Nada. Zero. So, if you remove it then a reader will be lost as to understand the origin of magnetic field. (Is this your intention - to promote personal ignorance to Wikipedia readers?) There are plenty of phenomena in nature which are difficult for "average reader" to understand because they require proper education of the reader. For instance, understanding of origin of conservation laws require knowledge of mathematical symmetries, of least action principle and of Emmy Noether theorem. So, should we simply state that conservation laws are just the way nature works, or should we point to their origin? If a Wikipedia project is to accurately explain things and phenomena (as encyclopedias suppose to do), then we should. Sincerely, Enormousdude 19:30, 28 June 2007 (UTC)

Enormousdude, Maxwell was able to explain the magnetic field before relativity was ever thought of. The vXB force was in Maxwell's fourth equation. We don't need a Lorentz transformation to get the vXB force. Besides that, no amount of relativity can explain the other magnetic force that acts along the magnetic field lines. Magnetism was well understood in terms of Ampère's law and Faraday's law, well before Einstein or Lorentz came on the scenes. A magnetic field occurs around a closed electric circuit. It has got absolutely nothing to do with the Lorentz transformation. (81.158.161.160 20:56, 28 June 2007 (UTC))

Um, sorry, no. Care to provide a reference for the idea that a magnetic field has nothing to do with Lorentz transformation, cuz I got plenty of sources that say otherwise. I think you're misunderstanding Maxwell's equations a bit; the vXB comes from the Lorentz force law. Maxwell's equations do a lot, but they say nothing about the force on charged particles due to those fields. However, prior to Einstein, the Lorentz force law was based only on observation. You cannot discuss magnetic fields without a discussion of how the magnetic force naturally comes out of the Lorentz transformation of the Coulomb force, with a vector field crossed into the velocity exactly identical to the magnetic field described by Maxwell's equations. Special relativity basically says why a magnetic field has to exist given an electric field. There is no force along the field lines, as ED has already explained above; the attraction between to bar magnets is due to a non-uniform magnetic field. If you're really interested, I highly recommend Jackson's "Introduction to Electrodynamics" for an exhaustive explanation of EM phenomena. Unless you've taken university courses in E/M then most of what you know of electromagnetism is likely a simplified analogy to avoid heavy math that leads to faulty understanding when taken too far. So either provide a reference for some of these claims (forces along magnetic field lines) or else this falls into the WP:OR especially when we can cite physics textbooks that state otherwise. --FyzixFighter 05:05, 29 June 2007 (UTC)

No reference is needed to show that a magnetic force exists along magnetic field lines. First form high school pupils learn that with iron filings. Look at the field lines joining two attracting magnets. The attractive force is along those lines. You are in denial of this most basic fact because you know that this aspect of magnetism definitely cannot be explained by the Lorentz transformation. (81.158.161.160 10:30, 29 June 2007 (UTC))

Revision to intro

Sorry for the double post, but I just decided to be bold and changed the intro - the old intro was somewhat misleading and simplified to the point of absurdity (let's keep it "as simple as possible, but not more so"). It also already threw enough technical jargon around (axial vector, solenoidal) so the non-technical argument for not including SR in the intro doesn't hold water. I tried to model it after the the intro over at electric field. I think (or rather I hope) that I've avoided some of this "lines of force" disagreement by getting down to what the field describes, specifically in terms of the Lorentz force law. I also tried to address the "lines" question by using Faraday's original formulation (magnetic dipoles align themselves along these lines), since this is how most readers have been introduced to the concept, but leaving the more detailed explanation for later in the article. Also, certainly the full derivation of the magnetic field with SR does not belong in the intro, but it must be mentioned succinctly in the intro as this is a fundamental concept and is addressed later in the article. --FyzixFighter 06:42, 29 June 2007 (UTC)

New Edits

FyzixFighter, Regarding your points above, your wording in the introduction is better in some respects. You have said 'According to relativity----'. That is a better way of introducing that point. As regards Lines of Force, Faraday introduced the term, and so likewise I have added in that Faraday called the magnetic field 'Lines of Force'.

Check out equation (D) of Maxwell's original eight equations. Equation (D) is the Lorentz force if ever there was a Lorentz force. Lorentz only reintroduced the vXB component after Heaviside removed it in 1884.

I would agree with you that I see no need to specify that B is an axial vector field. I actually removed that yesterday, but somebody restored it.

Also, very importantly, vXB is not the entire picture of magnetism.The attractive force that acts in the direction along magnetic field lines, does not arise from vXB. Neither does the magnetic force that is involved in diamagnetism or paramagnetism. There seems to be too much attention focused exclusively on the vXB force in the definition and introduction. I tried to neutralise that a bit.

On another point, you said that there are no references to say that magnetism can be explained without the Lorentz transformation. What about if I were to mention Maxwell's equations?

On another point, try and see if you can fit solenoidal field lines around a point source. Ampère's law tells us that we need a closed circuit. (81.158.161.160 09:53, 29 June 2007 (UTC))

You're joking right - you're misreading Ampere's law - a moving point source is a current that is a delta-function - there is no require closed circuit in Ampere's law (except the closed loop around the surface of integration when it's presented in integral form, which has nothing to do with the current circuit). Everyone knows any moving electric charge (no closed circuit) has a magnetic field associated with it. That's basic physics. That's why accelerated charges (like in a wiggler) radiate electromagnetic radiation. I don't need a closed loop to create a magnetic field. You're vastly misunderstanding what Faraday meant by lines of force and perpetuating bad physics. Faraday's analogy of "tension" and "repulsion" is a nice intuitive way to understand what happens, but when you get down to the actual math and physical descriptions/equations, it no longer becomes valid. Most scientist today will tell you that - Faraday is nice for intuition, but bad for actual physics. Iron filings aren't pushed along the "lines of force" like electrons/protons are along electric "lines of force", they line themselves up parallel to them, and a bar magnet cannot exert a force on itself, so when calculating the force of one bar magnet on the other you have to ignore the bar magnets own field. And yes, it is possible to explain the attraction of two magnets (I saw this derived in a plasma physics course - can't find my book at the moment, working on it...), diamagnetism, and paramagnetism with vXB (and hence Lorentz transformation) - in fact, check out diamagnetism where it talks about vXB producing that effect. So vXB is the entire picture, but when dealing with non-uniform magnetic fields, and with electric fields also, can produce some cool results.

Secondly, Maxwell's equations are laws based on observation. Of course they're not going to bring up the Lorentz transformation. But the Lorentz transformation says why the constants are the way they are, and why a magnetic field should exist in the first place. Maybe you misunderstood me, I asked for references that state magnetism can be explained (not quantified as Maxwell's equations do) without SR.

As to the PDF reference for vXB in Maxwell's equations, I'll get back to you on it as it requires translating Maxwell to modern math (I'm constantly amazed at Maxwell's achievements without the modern notation of multivariable calculus). To sum up....reverting since your intro has glaring mistakes. --FyzixFighter 15:20, 29 June 2007 (UTC)

Well I'll be interested in seeing your conclusions when you've studied Maxwell's equation (D). The dx/dt terms are clearly velocity. The magnetic permeability is in there too and that converts the H into a B. The H is clearly present in the right context. There is actually a glossary of terms at the end of that section in his paper. The other terms in equation (D) are Gauss's law and the component of the Lorentz force that is written as the partial time derivative of the magnetic vector potential A. There is no doubt that Maxwell got there before Lorentz.

Equation (D) applies to moving conductors. It is the Lorentz force if ever there was a Lorentz force. Andre Waser has already transcribed it into modern format on that other link that I gave you.

Now regarding whether or not Maxwell gave an explanation for magnetism, the answer is that he clearly did. It is well described in his 1861 paper 'On Physical Lines of Force'.

You seem to be under the impression that the tension in the lines of force can be explained by the vXB force. In Maxwell's theory, it is explained by Gauss's law. It can't possibly be explained by the vXB force because the vXB force never changes the kinetic energy of a body. The solution to vXB is a circle or a helix. Yet when two magnets pull together, there is a change in kinetic energy and hence an irrotational force must be involved. This would agree with Maxwell's idea that the tension agrees with Gauss's law. This tension does not act on electric charge. It acts on magnetic dipoles. It can create a torque and align a compass needle and it can pull two magnets together.

At any rate, how could the vXB force possibly be in the same direction as B itself?

Finally, if an electric current circuit is not closed, then there will be no Ampère's law. The entire derivation of Ampère's law depends on the fact that the current circuit is closed.

I would have to strongly take issue with the idea that magnetic force ends with vXB. The Lorentz force (misnomer) has got two other components asides from vXB.

Think it all through very carefully. The picture that is coming over is one of denial. It would very much appear that you are in denial of one particular aspect of magnetism because you can't explain it in terms of relativity. You can't explain the tension in magnetic field lines in terms of realtivity and hence you are trying to brush this phenomenon under the carpet.(81.158.161.160 16:53, 29 June 2007 (UTC))

Well one of us is misunderstanding Ampere's Law. I don't see anywhere in it that it implies a closed current circuit. There is a closed loop over which H is integrated, and the only current Ampere's deals with is the total current flowing through the surface circumscribed by that closed line integral. The Biot-Savart law (a solution to Ampere's law) does a much better job of showing how any moving charge produces a magnetic field. As to how vXB explains how two magnetic, reduce a bar magnet/magnetic dipole to it's minimum representation, a circular loop of current. Now two of these loops, oriented to be in the same plane and rotating in the same direction are like two bar magnets oriented the same way (so they should be repulsed). Alright, now when calculating the force on one current loop (A), I only have to consider the magnetic field produced by the other loop (B), which field is normal to the plane of the loops (all the internal forces of the loop on itself cancel out). The near edge of the first loop (A) sees a stronger field than the far edge, so it feels a stronger force and a force opposite the direction of the far edge. When the two current loops rotate in the same direction, the net force on A is always away from B, and towards B when they rotate in the same direction. Voila, I just explained the attraction between two magnetic dipoles just using vXB. The idea that a magnetic field cannot change the kinetic energy of a charge is only true (as I understand it) if the field is uniform. There are only two terms in the Lorentz force law, qE and qvxB, so what is the other term that describes this "other" B force?

And Maxwell's stress tensor is totally derived from the electromagnetic (Lorentz) force law and the Maxwell's equations (the modern notation ones) - see pages 260-261 in Jackson (3rd ed).

Also, in the interest of full disclosure, I've posted a request over on WP:PHYSICS to get some other input here to help build a consensus. --FyzixFighter 18:16, 29 June 2007 (UTC)

The three terms in the Lorentz force are exactly as in equation (D) of Maxwell's 1865 paper, and also equation (77) of his 1861 paper. They are vXB, the Coulomb force, and $-{\frac {\partial \mathbf {A} }{\partial t}}$. (where A is magnetic vector potential)

It is absolutely impossible for the vXB force to act along the B line and hence you have not, as you seem to believe, explained the force between two magnets in terms of vXB. vXB must be perpendicular to B. But at least, unlike the others, you have admitted that two magnets do pull together along the B lines. There is absolutely no argument against that very plain fact. It doesn't matter whether or not the B field has to be inhomgeneous. The fact is, two magnets snap together and increase their kinetic energy, as a result of a force that acts along the B lines. Maxwell studied this problem and concluded that this tension force must be irrotational and obey Gauss's law. It cannot be the vXB force.

Next, you cannot derive Ampère's circuital law unless you assume a closed circuit in the derivation.

Relativity cannot explain the irrotational aspect of magnetic force that acts along the B lines and neither can relativity explain the $-{\frac {\partial \mathbf {A} }{\partial t}}$ aspect of electromagnetic induction.

Relativity claims to explain the vXB aspect of magnetism, despite the fact that Maxwell explained it long before Einstein was born.

It has however crossed my mind that an accelerating charged particle could create EM radiation by invoking the $-{\frac {\partial \mathbf {A} }{\partial t}}$ aspect of EM induction. However I don't think that this is a suitable basis for defining the magnetic field. It's a specialized aspect of magnetism.

The basic definition ought to be in line with Biot-Savart, and that necessarily involves closed current circuits as it is a solution to Ampère's law.(81.158.161.160 20:01, 29 June 2007 (UTC))

No, no, and no. The magnetic field lines from (B) at the position of the dipole (A) are normal to the plane of (A), and therefore perpendicular to the direction of the force, which is in-plane (remember, when calculating the net force on (A), you must ignore the magnetic field produced by (A)). The grad-A term in Maxwell's original list is for magnetic charge (mass), ie magnetic monopoles, which have never been observed, hence every textbook having the force law as F=q(E+vxB). You still have not said where in Ampere's law a closed current circuit is implied. Every explanation I've seen, including the one on wiki (Ampère's Circuital law), do not include that caveat - the "circuit" of "circuital" refers to the closed line integral for H. Again the Maxwell's stress tensor is found by combining F=q(E+vxB) with Gauss' law and Ampere-Maxwell law. There is no magnetic force effect that falls outside of the correct application of qvXB.

However, I refuse to argue further with you on this point until others get involved. You have shown yourself to be completely unwilling to believe reliable sources like basic physics textbooks. As this appears to be an intractable issue between us, I'm requesting an RFC and then we'll see if we can build a consensus. I will make one more edit/revert (my 3rd in this 24hours), but I will continue to fight this inclusion of bad basic physics in this article, especially in the intro. --FyzixFighter 20:34, 29 June 2007 (UTC)

References

I've found two web linked references that show that Maxwell had the Lorentz force long before Lorentz. First of all look at page 6 of the pdf file of this web link. It is Maxwell's original 1865 paper 'A Dynamical theory of the Electromagnetic Field'. Equation (D) on page 484 (page 6 of the pdf file) is the fourth of Maxwell's original eight equations. It is the Lorentz force. If we take its curl, we get Faraday's law. In the Heaviside versions of 1884, Faraday's law is preferred, but the vXB term has been dropped. Lorentz reintroduced it with his transformations. Here is the link,

http://www.zpenergy.com/downloads/Maxwell_1864_3.pdf

Also, I found another link which exposes this same fact. See,

• Waser, André, "Original Maxwell Equations"

(81.158.161.160 10:43, 29 June 2007 (UTC))

Maxwell's Equations

I'll give you all an example of how ridiculous this is getting. Somebody decided to mention Maxwell's equations in the introduction. No harm in that. They then stated that Maxwell's equations demonstrate the relationship between magnetic fields, electric fields, and electric charge. They ommitted electric current.

Electric current was added in by somebody else (me), but it was immediately deleted again. Ampère's law is one of Maxwell's equations. It gives the relationship between magnetic field and electric current. Yet somebody is totally determined to mask the involvement of electric current in Maxwell's equations. Why? (81.158.161.160 20:20, 29 June 2007 (UTC))

No, stop reading too much into others actions. An electric current is a specialized form of a moving charge. Really, we should say Maxwell related magnetic fields, electric fields, and charge densities, since the divergence of the current density is the negative of the time derivative of the charge density. That's why I removed it, not because of some supposed conspiracy. --FyzixFighter 20:45, 29 June 2007 (UTC)

FyzixFighter, Equation (D) of Maxwell's original eight equations is unequivocally the Lorentz force. The Lorentz force, even in modern textbooks contains a magnetic vector potential term. If we take the curl of the magnetic vector potential term in the Lorentz force, we get the partial time derivative version of Faraday's law.

You are in denial of quite a number of indisputable facts. That was one of them.

There are three separate componets of force in the Lorentz force equation. You are masking this fact by insisting on using the term E as an umbrella term for the Coulomb force and the magnetic vector potential term combined.

You are also in denial of the fact that since the vXB force must by definition be perpendicular to B, then whatever the force is that acts parallel to B cannot be the vXB force. And that parallel force does exist. At least you acknowledge that it exists, where others have tried to deny it.

The magnetic force that acts parallel to magnetic field lines is the most fundamental example of magnetism. It pulls two magnets together and it converts potential energy into kinetic energy. Maxwell recognized it and recognized that it must be an irrotational force. Faraday recognized it and hence referred to magnetic field lines as 'Lines of Force'. That force is not the vXB force.

As for Ampère's law, the derivation of it necessarily begins with closed loops of electric current even if the final result can be applied to fragments of the overall picture. And it is fragments that you wish to concentrate on.

You clearly don't want anybody to see the overall picture of magnetism. The overall picture of magnetism cannot be explained by relativity and hence you wish to mask out the bits which are not convenient for relativity. You would prefer that we don't think in terms of electric current circuits and solenoidal lines of force pulling magnets together. You would prefer a partially eclipsed picture of the part of a magnet field that is associated with single moving charged particles. You actively moved the term electric current from the bit on Maxwell's equations after I had inserted it, even though it stands out clearly as one of the key quantities. It was inconvenient for relativity and so you were trying to hide it.

You are insisting, despite modern and ancient evidence to the contrary, that magnetic force exclusively comes under the jurisdiction of vXB. This is because you think that you can link vXB with relativity, despite the fact that Maxwell derived vXB before Einstein was born.

This is all about trying to conceal the wider picture of the magnetic field in the name of serving relativity and trying to make the readers think that magnetism depends entirely on relativity for its cause. (81.158.161.160 08:10, 30 June 2007 (UTC))

This whole article and subsequent discussion completely misses the point of what people want when they look up 'magnetism' in Wikipedia. It also seems that none of the contributors have read recent text books on the subject. The first thing is to separate magnetic fields in free space from those in materials. In free space magnet fields are defined in terms of forces on currents. Unfortunately, since there appear to be no magnetic monopoles, the simplest experimental magnet is a dipole, with correspondingly complicated forces. However the magnetic field can still be defined quite simply to give the correct forces. A separate effect is the induction of electric fields by changing magnetic fields. Experimentally this is caused by the same field as causes forces on currents so we only need one field in free space. It is of no moment whether we call it B or H or measure it in tesla or amps/metre. (Units of measurement are a complete red-herring and of no consequence.) A similar situation arises with gravity where the inertial and gravitational masses are the same, and similarly if the two effects of magnetic field were different it would contradict special relativity, but this connection should be in a later article. The need to use both B and H only arises in magnetic materials where it is useful to separate the currents into macroscopic transport currents and local atomic currents or electron spins. B is defined as the average of the local magnetic field (or flux density) on an atomic scale averaged over a volume of many atoms. The magnetisation M is defined as the magnetic dipole density per unit volume and these are the only two vectors we need. However Maxwell's equations in materials can be made to look more elegant by defining a new and rather abstract vector H=B/muo -M. This is not new, Lorentz did all this at the turn of the last century, but it is taking a long time to filter into undergraduate courses. If I can find time I will rewrite this article, but for the moment everyone should realise that to discuss B and H in materials without mentioning the magnetisation is a nonsense, while in free space there is no distinction between them.

Even in free space, we have to multiply H by the magnetic permeability of free space to get B. I don't see how you can say that they are the same thing in free space. (81.158.161.160 20:37, 30 June 2007 (UTC))

14:32, 30 June 2007 (UTC)=amc

@81.158.161.160: Please WP:AGF. This is not a conspiracy to cover up anything. This is an attempt to correctly describe the magnetic field based on reliable sources. Perhaps that is the only way to deal with this as both of us are pulling from our own understanding. So find a reference that says that the "tension" force cannot be traced back to vxB. I've got references that says it can be explained by vxB, Jackson pg 260-261 and Griffith pg 351-354. The idea of currents is not inconvenient for relativity, in fact it's essentials to most derivations of magnetism via SR (see Griffith pg 522-525, who is referencing Purcell's "Electricity and Magnetism" in that section). The most general case is a moving charge - that's what a current is (be it a line, surface, or volume current), that's what bar magnets/magnetic dipoles are (loops of moving charges). That's why I changed the first sentence to moving charges, because that is the overall grouping of which currents and bar magnets are a subset.

@81.107.40.58: I agree, the distinction between H and B should be treated earlier. This used to be in the introduction, however, it was relegated to later as someone thought it was too technical. --FyzixFighter 17:49, 30 June 2007 (UTC)

Refusing to view the Overall Picture

To 67.166.103.28, nobody is disputing the vXB force so there is no point in me looking up a textbook to verify it. The issue here is that you are in denial of the fact that the Lorentz force contains two other terms apart from vXB.

Actually, that 67.166.103.28 was me. The problem is that every physics textbook says that F=q(E+vxB). The third term in the force law as written by Maxwell, m*grad-Omega, is for the force felt by magnetic charges. Back then they didn't know that magnetic monopoles don't exist (or rather have never been observed). Magnetic charge, as a mathematical construct and as Maxwell understood it, is the gradient of the magnetization (M); this is called the "Gilbert" model. In fact the force on a magnetic dipole is grad(m.B). But that's a force on a magnetic dipole. However, if we treat the magnetic dipoles as what they physically are, ie loops of current (the "Ampere" model), then this force on a magnetic dipole/magnetic charge can be absorbed into vxB. That is the overall, real world physics picture, not the intuitive, useful but slightly wrong when looked at up close, non-quantitative picture of magnetic charge and Faraday's lines of force. The force that a B exerts on moving electric charges is always vXB. But don't believe me, let me pull up some references/reliable sources:

"In fact, the magnetic force on a charge Q, moving with velocity V in a magnetic field B, is F_mag=Q(vxB)" -Griffith, "Introduction to Electrodynamics"

Got a reference that says the B field exerts a parallel,non-vxB force on electric charges? --FyzixFighter 17:16, 30 June 2007 (UTC)

FyzixFighter, I don't know which equation you are looking at. I am looking at equation (D) on page 484 of Maxwell's 1865 paper 'A Dynamical Theory of the Electromagnetic Field'. It is on page 6 of the pdf link. It is the fourth of the original eight Maxwell's equations. This is the Lorentz force. I don't know what equation you are talking about.

The Lorentz force has got three components. It has got a curl component vXB. Then there is a (partial)dA/dt component, where A is the magnetic vector potential. Finally there is a Gauss's law component. This is confirmed in any modern texbook.

You have completely overlooked the fact that the attractive tension in the lines of force cannot possibly be given by vXB because vXB has to be perpendicular to B. The attractive tension converts potential energy into kinetic energy. It is therefore most likely to derive from the Gauss's law component of the Lorentz force. Hence it cannot be explained by relativity and this is why you want to brush it under the carpet.

You are quite wrong to insist that vXB is the only magnetic force and you are refusing to accept that by the definition of vector cross product, it cannot possibly act along the field lines. Why would I need a reference to show that a vector cross product cannot be parallel to any of the vectors in the product? Besides that, it has got no associated potential energy function to account for the change from potential energy to kinetic energy.

It also seems that you are in denial of the fact that the Lorentz force appears in Maxwell's papers at all even though you can see it before your very eyes. (81.158.161.160 20:35, 30 June 2007 (UTC))

No, I'm not in denial - please (for the umpteenth time) assume good faith. It's not that I'm refusing to accept anything accept vXB, but all the reliable sources I check say that this is true. That's how we do things on wikipedia. I'm asking (again) for a reference that says that there is a magnetic force that cannot be traced to vXB.

As to what I'm looking at, I'm actually looking at Waser's analysis of those pages, namely equation 1.11. Equation (D) from Maxwell's papers is not exactly the Lorentz force law - where's the "F" for force in it, or at least d2x/dt2? Equation (D) is actually a combination of the potential equation for a electric field in the non-static case (the -dA/dt-grad.phi) - if you take the curl of it, you get Ampere's law, ie the electric field induced by a time-varying magnetic field. Waser calls the other part (vxH) of it Faraday's force law - though I'm not familiar with that phrase, I would imagine that this could possibly be a form of the Lorentz force law, attributing the magnetic force to an induced electric field, which then exerts a force on the particle. Waser actually lists Maxwell's force equation in eq 1.11 - that's what I was looking at.

One of the problems is that we seem to be talking past each other. You're talking about the forces felt by the lines themselves, whereas I'm talking about the forces felt by particle at the point of the particle. In that case, the tension in the field lines of course isn't going to be vxB because there is no v, there is no particle to feel a force there. However, the field lines are not physical entities, which is what Faraday got wrong - ie there are not these invisible lines out there. The lines are graphical representations of the field, nothing more. They're a good intuitive image useful for grasping what qualitatively happens, but say nothing quantitative about the force. If so, what is the equation for the force on a particle that is parallel to B (and what's the ref)?

And after looking more at the bar magnet/magnetic dipole issue, it appears that I was wrong. It's not the magnetic field/force that causes the magnets/dipole to come together. The magnetic force just redirects the forces already acting on the dipole. It's whatever force is holding the loop of current together that causes the dipoles to move towards one another, in the case of the bar magnet, it's the internal electric fields that do this. If the electric field holding the dipoles together were suddenly switched off as soon as the current loops felt the magnetic field, the electric charges that made up the dipoles would begin orbiting the other magnet, and their kinetic energies would not change. Therefore it's the combination of both forces, the magnetic and the electric (or whatever other force is holding the dipole together) that causes the two to attract, but it's that other force that does the work, not the magnetic force. Momentum is transferred from the fields to the bar magnet, but it's the internal electric fields that do the work.

The problem here is not my refusal, it's your refusal to accept information from reliable sources, ie university-level physics textbooks. I've provided at least two (Griffith and Jackson). --FyzixFighter 22:16, 30 June 2007 (UTC)

No sir. You have just demonstrated above that you haven't got a clue how to explain the magnetic force of attraction. I have directed you to a reliable source where you can find it all explained perfectly. That reliable source is Maxwell's original papers. But you have demonstrated that you cannot understand what is written in these papers and you have dismissed alot of the contents as fictitious. You are still trying to deny that equation (D) (1865) and equation (77) 1861 are the Lorentz force. You are even trying to deny that a modern textbook uses (partial)dA/dt as a Lorentz force component. There is no need to refer me to reliable sources. No reliable source will explicitly state that magnetic attraction is caused by the vXB force. Magnetic attraction is dealt with as a first day topic for high school pupils. It is then swept under the carpet and never dealt with again. In later years electromagnetic induction is taught and the vXB force is introduced, but magnetic attraction is never mentioned again. Magnetic attraction and repulsion are inconvenient for things like the electromagnetic field tensor because they contradict the idea that magnetism is a relativistic effect of the electric field. I notice that the censors have come down on your side despite the fact that I was the one that was referring to reliable traditional sources. I would suggest that you all have alot to learn about magnetism. (81.158.161.160 11:08, 1 July 2007 (UTC))

Electromagnetic Induction

There are two kinds of magnetic force involved in EM induction. There is the vXB force that occurs when a charged particle moves in a magnetic field. Then there is one of the forces that you are denying. There is the (partial)dA/dt force that occurs when a stationary charged particle is present in a changing magnetic field. A is magnetic vector potential and curl A = B. Hence the curl of -(partial)dA/dt leads us to Faraday's law which was one of Heaviside's 1884 Maxwell's equations.

Not only are there the three magnetic force components of the Lorentz force. Maxwell also identified a fourth magnetic force which he attributed to magnetic repulsion and to paramagnetic attraction and to diamagnetic repulsion. That fourth force was the centrifugal force.

In due course, you will realize that it is quite wrong to attempt to explain all magnetic phenomena in terms of the vXB force. It just doesn't work in every situation.

I will no longer revert your other edit about moving charge because you have now at least acknowledged the phenomenon of electric current and bar magnets. However, I think you will find that every case of a moving charged particle that occurs in nature will necessarily be tied up with a closed electric circuit. The long straight infinite wire does not exist in practice. Even when charge flows from a thundercloud to Earth, there are solenoidal lines of displacement current that close the circuit. The closed circuit is the full picture upon which all our magnetic laws are based. The single charged particle only possesses part of a magnetic field. It is a fragmentary case rather than being the most general or most naturally occuring case. (81.158.161.160 20:56, 30 June 2007 (UTC))

Sorry, no - but I do think I understand you better. The dA/dt is not a magnetic force - it creates an induced electric field, and that electric field is what pushes on the charge. You might argue that it's a game of semantics, but that's what Ampere's law says (undo the curl of Ampere's and you get the dA/dt that you're talking about). So by today's physics terminology the dA/dt gives rise to an electric field force, not a magnetic field force.

Also, a displacement current is a fictitious current (just like the centrifugal force is a fictitious force) - it doesn't correspond to an actual movement of charged particles. It was a way of fitting the dE/dt component (Maxwell's correction) into the nomenclature that existed in Faraday's equation. To quote Griffith pg. 323, displacement current is "a misleading name, since [it] has nothing to do with current, except that it adds to J in Ampere's law." Maxwell explained this term away as a current in the ether, which we know now doesn't exist (at least in the way Maxwell et al understood it). --FyzixFighter 22:33, 30 June 2007 (UTC)

Your argument is very much semantics. I could equally divide F =qvXB by q and then say that F/q = E = vXB and that vXB is hence an electric field.

Anyway, let's look at a very simple case of magnetic attraction. Two circular loops of current placed side by side with their equatorial planes parallel. They share a common axis and the current is flowing in the same direction in each loop.

The magnetic force will pull these two loops together. The magnetic field lines will flow dircectly between the two loops. Hence the current in loop one will be perpendicular to the magnetic field lines of loop two. The magnetic vXB force must be perpendicular to the field lines, and hence the force of attraction cannot come from vXB. I say that it must come from the Gauss force, and I can cite Maxwell to back me up on that.

Now let's reverse the current direction in one of the loops. We now get a repulsive force. The major difference is that the magnetic field lines now spread sideways and outwards. Loop one no longer comes into contact with the magnetic field of loop two, yet a repulsion is still experienced. According to Maxwell, the seat of the repulsive force is in the field lines themselves. According to Maxwell, the repulsion is due to centrifugal force acting at right angles to the magnetic field lines.

I have noticed that you are denying the (partial)dA/dt term as a magnetic force even though it is a force that arises from a changing magnetic field. I notice that you have written off displacement current as fictititious. I notice that you have written off centrifugal force as fictitious. I notice that you have denied the obvious that a vxB force cannot act in the direction of B. You have also denied that anything physically real exists in Faraday's lines of force/Maxwell's aether. You will of course be at a total loss to explain how loop two's magnetic field can push on loop one without touching it.

You have finally brought the censors in to protect the article after my revisions have been deleted and you have dismissed me as a mere anti-relativist.

I would suggest that you are living in a world of total delusion in which you refuse to contemplate the works of Maxwell, despite the fact that he is the man responsible for the laws of magnetism that are presented in any modern physics textbook. (81.158.161.160 10:38, 1 July 2007 (UTC))

The case you cite is not much different than the one I tried my hand at. It's the same thing, and same difference in understanding between you and I. Most university physics textbooks, when they first treat this example explain it with vxB. The key is that you must ignore the magnetic field produced by the loop who is feeling the force. But even in this case, it isn't the magnetic field that does the work, it's whatever force is holding the loop together - magnetic fields can't do work. You could go the stress tensor way to find the force if you want to do it in you're paradigm of "lines of forces" and flows of momentum, but the stress tensor is derived via vxB.

It's not me that's denying dA/dt is a magnetic force, that's what every physics text (and Maxwell) says: that dA/dt induces a measurable electric field so the force is not directly from the magnetic field (it is indirectly from it).

I don't believe the field lines are physical, I do believe the fields are physical, of which the field lines are representations. Again, it's not me saying that the displacement current is a misnomer and a fictitious current, it's modern physics textbooks (modern physics textbooks also say that the centrifugal force is a fictitious force except as a mathematical construct due to real forces being transformed into a rotating, non-inertial frame).

I have no problem admitting that Maxwell articulated the Lorentz force law before Lorentz and Einstein. He did not, however, "derive" it. He quantified an observation and quantified how electric fields and magnetic fields are connected, giving rise to electromagnetics. SR "derives" the magnetic force and field given just an electric field and force to start with, and explains why electric fields and magnetic fields have to be connected.

And the article has been protected, not censored - there is a difference. --FyzixFighter 14:38, 1 July 2007 (UTC)

Finally protected

It was good move to finally protect this article, because influence from anti-relativity anons and similar anons was little bit more than destructive. It shuold stay this way. --83.131.29.160 01:25, 1 July 2007 (UTC)

While I'm glad that it is now protected, I do think there is enormous room for improvement - we have been kind of distracted as of late dealing with the non-relativity anons. The section discussing H is noticeably weak and lacking. Also the intro does need some work - I had originally tried to model after the intro of electric field, but it doesn't really flow as an intro either; another thing lacking from the intro is the discussion of induced magnetic fields by time-varying electric fields (right now it only lists moving charges as the sources of magnetic fields). I think it would also be useful to have a section on Faraday's intuitive "lines of force", and how those are quantized by Maxwell's stress tensor, which in turn can be derived from the Lorentz force equation and Maxwell's equation (Gauss' and the corrected Ampere's). Such a section would help address the issues of those who learned that way of visualizing magnetic field and show them how that paradigm can arise from and is consistent with today's understanding of magnetism. And we definitely need some kind of statement/section addressing how B fields do no work and how the paradoxes to this are resolved (two bar magnets coming together for example). The key IMO, however, will be to stay close to reliable sources - the whole edit war arose from us (myself included in this fault) trying to qualify statements with our own arguments, and not reliable sources. If we all agree to that rule, then it shouldn't be hard to keep the physics accurate. However, if any side in the debate refuses to abide by reliable sources, then we'll just be back to the same old back and forth. I've got my undergrad copy of Griffith at home, but Jackson and most of my other EM related texts are at my office. The library on campus also has the two-volume "History of EM" if we need it. So let's see what we can hash out during the week of protection. --FyzixFighter 06:54, 1 July 2007 (UTC)

Regarding reliable sources, I presume you mean that Maxwell's papers fall into the unreliable category. Mid-nineteenth century foundation papers on electromagnetism are of course original research and are therefore banned by wikipedia policy. So let's stick to mainstream stuff written in 2006.

It ill becomes you to even talk about Maxwell when you clearly haven't got a clue about what he has written and have refused to admit what you saw before your very own eyes. The Lorentz force first appeared as equation (77) in Maxwell's 1861 paper and you are still trying to perpetuate the myth that it has got something to do with Lorentz transformations. You want the vXB issue dealt with properly and yet any high school pupil knows that a vector cross product is perpendicular to its component vectors. And yet you want to tell us all that the vXB force acts along the B lines to cause magnetic attraction! And you are confident that you are absolutely right. (81.158.161.160 10:52, 1 July 2007 (UTC))

I guess mentioning WP:AGF yet again won't help. Maxwell is a reliable source, but I question you're interpretation. I used the Waser paper you directed me to in order to help me decode it so I don't know what you're problem is. Also modern textbook interpretations of Maxwell trump your (or my) OR interpretation of Maxwell any day on wikipedia. Alright, let's see if I can find something to navigate by in your paradigm. Is the "tension" force of Faraday's "lines of force" quantified by Maxwell's stress tensor? --FyzixFighter 14:06, 1 July 2007 (UTC)

Maxwell's original papers used a very different language to discuss electromagnetism than is used today. While this can be quite interesting historically, it's a terrible idea to try and learn and understand E&M from them. Modern textbooks will present the ideas in a way that's much easier to understand, and much harder to misinterpret. Jackson and Griffiths are much better sources to reference here, because one can point to direct quotes which are relevant. Whereas to write an encylopedia entry in modern language, you'd have to not just reference Maxwell but also "translate" his words, and this strays into the area of original research.

If you think there's a contradiction between what Maxwell says and what is cited in Jackson and other textbooks, I'd strongly encourage you to study the matter for yourself, and perhaps engage in discussions elsewhere on the internet. But at the end of the day you'd discover that the modern books are perfectly consistent with Maxwell; besides, the important thing to remember is that what modern books say is the consensus view of scientists. And this article needs to reflect that view.

If you can find a reputable, modern source which backs your claims, you're welcome to provide it. But your own interpretation of what Maxwell wrote just doesn't cut it. --Starwed 14:28, 1 July 2007 (UTC)

Magnetic Force and Electric Field

An electric field means a force per unit charge. A Magnetic force means a force that arises out of magnetism. Hence an electric field can also be a magnetic force. So let's drop the semantics out of this argument.

It strikes me that this edit war is all about whether or not vXB is the only magnetic force. The controversy seems to have focused around the magnetic force of attraction between two magnets.

Maxwell identified four kinds of force that arise in electromagnetism. He identified the vXB force. The vXB force can be seen at equation (77) in his 1861 paper 'On Physical Lines of Force'. He also identified a centrifugal force as being responsible for ferromagnetic and electromagnetic repulsion, as well as for diamagnetic repulsion and paramagnetic attraction. He identified an irrotational Gauss force as being the cause of the tension in magnetic field lines, and he attributed this force to ferromagnetic and electromagnetic attraction. He also identified a force given by the expression (partial)dA/dt which he linked to electromagnetic induction.

If it is inconvenient to discuss Maxwell's work in this article, then one should be able to ascertain by other means whether or not the vXB force is the only magnetic force.

We are all agreed that vXB must be perpendicular to B. That is an algebraic fact of vector cross product algebra. No references are needed for that. We also know that magnetic force of attraction acts in the direction of the magnetic field lines. No references are needed for that. Therefore we sould be able to conclude quite easily without references to any sources ancient or modern, that the vXB force is not responsible for magnetic attraction and that therefore it is not the only magnetic force.

I challenge anybody to show me a reference that categorically states that vXB is the only magnetic force. (86.155.136.126 20:21, 1 July 2007 (UTC))

To answer that question, then I need to ask if you believe that Maxwell's stress tensor is what is used to quantify the "tension" force of the "lines of force"? --FyzixFighter 21:49, 1 July 2007 (UTC)

I shouldn't really have to answer this question because it is a side track. It is not relevant. But in order to show that I am not ducking it, I will answer it. The electric field term E in Maxwell's stress tensor is exclusively given by the (partial)dA/dt force. I think I might even be able to dig up an on-line reference for this. Maxwell's stress tensor deals exclusively with the magnetic force that is involved in EM radiation ie. (partial)dA/dt.

A Lorentz transformation, or a Galilean transformation on this stress tensor can produce the vXB component because the vXB component is the convective counterpart to (partial)dA/dt.

So to answer your question, no, the magnetic force in Maxwell's stress tensor is not the force involved in magnetic attraction and neither is it the vXB force.

That of course was a side track. The onus is on you to explain how a vXB force can act in the direction of B. It is impossible, yet you are claiming that the attractive force along B lines is given by vXB.

I think you need to open your mind to the fact that vXB is not the only magnetic force. (86.155.136.126 14:15, 2 July 2007 (UTC))

Honestly, I wasn't trying to side-track you. It was an honest question as I try to understand where you are coming from. So let me get back to your original question: references that vxB is the only magnetic force. Griffiths, pg 204,

"In fact, the magnetic force on a charge Q, moving with velocity v in a magnetic field B, is F_mag=Q(vxB)."

Griffiths page 233,

"It takes a moving electric charge to produce a magnetic field, and it takes another moving electric charge to "feel" a magnetic field."

Jackons pg 260 (eq. 6.113),

"The total electromagnetic force on a charged particle is F=q(E+vxB)."

And then there's my favorite from Griffiths pg 207,

"Magnetic forces may alter the direction in which a particle moves, but they cannot speed it up or slow it down. The fact that magnetic forces do no work is an elementary and direct consequence of the Lorentz force law, but there are many situations in which it appears so manifestly false that one's confidence is bound to waver. When a magnetic crane lifts the carcass of a junked car, for instance, something is obviously doing work, and it seems perverse to deny that the magnetic force is responsible. Well, perverse or not, deny it we must, and it can be a very subtle matter to figure out what agency does deserve the credit in such circumstances."

There's a few other good statements, but these are more to the point. The attractive and repulsive forces between bar magnets that high school students learn can be explained by vxB when applied correctly, ie including only the external magnetic fields (not the field of the bar magnet feeling the force) and treating the bar magnet as loops of current.

The stress tensor can be applied to static, non-radiative cases. It's derivation can be found on Griffiths pg 351 and Jackson 260-261. The E-field in the stress tensor also arises from the application of Gauss' law into the Lorentz force equation, the other E and B come in by applying Ampere's law into the force equation. So you're wrong on the point that the magnetic force described by the stress tensor doesn't arise from vxB - it does. Actually the onus isn't on me now that I've given references. The onus is on you to provide a reliable source that there is a magnetic force that cannot be traced to vxB. Also what is the equation, ie F=?, for these other magnetic forces? Don't give a qualitative answer like it's an irrotational Gauss force or a Faraday "line of force"; give a quantitative equation of the form F=something please, and then maybe we can start to better understand one another. --FyzixFighter 17:11, 2 July 2007 (UTC)

Maxwell's Stress Tensor

Although this is a total sidetrack to the controversial issue in question, it does nevertheless make an interesting point for analysis. I dug up this google reference on the Lorentz transformation applied to the EM stress tensor. http://hepth.hanyang.ac.kr/~kst/lect/relativity/x850.htm I realize now that it contains the Gauss force in addition to the (partial)dA/dt force. I would personally guess that it is the Gauss force that is involved in magnetic attraction.

At any rate, the vXB force purportedly unfolds following a Lorentz transformation on this tensor. Such would happen anyway simply by applying a Galilean transformation to the Heaviside version of Faraday's law, because all Heaviside did was to remove the convective vXB component that was already present in Maxwell's original equations. You have already seen it for yourself in Maxwell's original papers. The onus is still on you to explain how the vXB force could possibly act along B lines and account for magnetic attraction. I'm merely giving you the Gauss law as a hint. Think about it. Potential energy changes to kinetic energy. That does not happen with vXB. vXB by its very nature is not an attractive force. In fact I would venture to guess that vXB would act such as to precess a closed electric circuit, but not to attract it.(86.155.136.126 14:38, 2 July 2007 (UTC))

Interestingly, equation 6 in the above weblink expands the E term of the Lorentz force and exposes the contents as that which I was saying, and as was backed up by equation (D) in Maxwell's 1865 paper, and as was denied by yourself. (86.155.136.126 14:42, 2 July 2007 (UTC))

You're misreading equation 6. Equation 6 shows how dA/dt gives rise to an induced electric field. Any force the results from dA/dt therefore is due to the induced electric field and is an electric force, not magnetic. This is an example of the continued point of departure between our interpretations of these equations. --FyzixFighter 17:22, 2 July 2007 (UTC)

The Edit War

The only thing that is essentially wrong in the article, as it now stands, is the assertion in the introduction that implies that vXB is the only magnetic force. Modern physics recognizes two more magnetic forces, ie. the Gauss force and the (partial)dA/dt force of EM induction. Ancient physics also recognizes the centrifugal force. Since the vXB issue is delegated to electromagnetic induction and perhaps also ought to be delegated to electric motors, it could be removed from the introduction and hence avoid any controversy.(86.155.136.126 14:57, 2 July 2007 (UTC))

No. As shown from the references I provided above (Griffiths and Jackson, but I'm sure I could find some more), the only magnetic force is vxB. The dA/dt force is an induced electric field force. The vxB is so elementary to modern physics and the understanding magnetic fields that it should be in the intro. It's one of the first things introduced in EM textbooks (page 3 in Jackson). --FyzixFighter 17:27, 2 July 2007 (UTC)

An electric field IS a magnetic force in all the situations that we are discussing here. You are playing on words. (partial)dA/dt is an electric field and a magnetic force. A is the magnetic vector potential. It is directly related to the magnetic field B through curlA =B. (partial)dA/dt is a force that arises from the magnetic field. It is an important force in electromagnetic induction. It is a magnetic force. The full expression for the Lorentz force is F/q = E = -grad (phi)+ (partial)dA/dt + vXB. That is three separate components of magnetic force. The Gauss force, the (partial)dA/dt force and the vXB force.

You actually cited a reference above which more or less admitted that the magnetic attraction force cannot be explained by the vXB force. The other reference which said the opposite failed to explain how.

The EM stress tensor comes about from Heaviside's versions of Maxwell's equations. That means Gauss's law plus the two magnetic curl equations. There is no vXB component present in the Heaviside/Maxwell equations. Heaviside removed it. It was there in the original Maxwell's equations. The vXB force shows up after the Lorentz transformation. If as you say, there already was a vXB component in the stress tensor, then how could the Lorentz transformation claim to be producing the vXB term, as it does claim? The Lorentz transformation restores what had been there before Heaviside tampered.

Do you just want to play a cheap game of quotes from texbooks that are taken out of context? I don't know why your reference said that the stress tensor comes about by including the Gauss force with the Lorentz force. Anybody who knows anything about the subject, knows that it was only referring to the (partial)dA/dt component of the Lorentz force and not the vXB force.

The most honest of your references was the one that admitted that it doesn't make sense to explain a car being pulled up by a magnet at a scrap yard with the vXB force. Whoever wrote that should read Maxwell and then he'd realize that it is the Gauss force. Why do you think that they talk about de-gaussing?

But most importantly of all. You have indeed succeeded in sidetracking me. You have sidetracked this whole discussion away from the fact that a vXB force cannot possibly be in the direction of B. Hence it cannot account for magnetic attraction, or indeed magnetic repulsion.

Again, F=q(E+vxB) when applied correctly does predict magnetic attraction and magnetic repulsion (see problem 5.20 in Jackson pg 230). All modern, university-level physics textbooks describe the force arising from the induced (dA/dt) electric field as an electric force, grouping it in the E of the Lorentz force law. All of these textbooks state that the only magnetic force is vxB. All modern textbooks also derive the stress tensor starting with the Lorentz force equation. Therefore, by WP:RS, that is what should be in the article and is completely correct to say that the magnetic force is perpendicular to both B and v. As another editor said above, if you believe that these texts are inconsistent with Maxwell's original equations, then provide a reliable source that says as much. --FyzixFighter 19:49, 2 July 2007 (UTC)

Let's take a step back: Say I know the E&B fields at a particular point in space and time. I then place a point charge with known velocity at that point. Then, without knowing anything about how the field changes with time, I still know exactly the force acting on that particle due to the electromagnetic field: F = q(E + vXB).

Now the way I've chose to split the electromagnetic field into two parts means that the electromagnetic force law has a suggestive form. It can easily be expressed as the sum of two forces, one involving only E, and the other involving only B. The first I choose to call the electric force, the second the magnetic. (Except that it's not just me: this is the common convention.)

That's it; that's why we call one force "electric" and the other "magnetic." From a certain point of view the separation into two forces is a bit arbitrary, but if you're going to call one of them magnetic, it's pretty clear what it's going to be. If you're going to describe the electromagnetic interaction in terms of a vector and scalar potential, it's not as obvious why you'd make such a distinction. Just remember that to make sense of why a particular force is called the magnetic force, you need to express the environment in terms of magnetic and electric fields. Because that's where the name comes from in the first place!

Hence it cannot account for magnetic attraction, or indeed magnetic repulsion.

The term "magnetic force" has nothing to do with this. The reason you can't explain the interaction of two magnets with just vXB is because that interaction involves both electric and magnetic forces. --Starwed 20:14, 2 July 2007 (UTC)

I'm now pretty sure that my last statement was incorrect; a cursory google (which I really should have done before) indicates that the Lorentz force law itself isn't adequate here: the behavior of magnets is a fundamentally quantum effect. (And no electric fields are necessary when you're looking at the interaction of two magnetized materials.) --Starwed 20:24, 5 July 2007 (UTC)

OK then. I'll use your language. The Lorentz force is F = q (E + vXB). We'll call the qE term the electric force. Starwed tells me that magnetic attraction must involve the electric force. Starwed is correct. Magnetic attraction is indeed caused exclusively by the electric force. The electric force E is itself divided as per equation 6 into a Gauss force and a (partial)dA/dt force. I would venture to guess that we can narrow magnetic attraction down to the Gauss component of the electric force. In other words, magnetic attraction arises from Gauss's law exactly as Maxwell says. It does not arise from the vXB force. It cannot arise from the vXB force because vXB is perpendicular to B. So shall we say then that it is not magnetism that pulls two magnets together, but rather electricity? I'll go along with that.

However, if you are going to mention the Lorentz force in the introduction, why only describe the effects of the magnetic vXB component? Why do we ignore the effects of the electric force component qE? Is qE not an equal partner in the Lorentz force? (86.155.136.126 22:28, 2 July 2007 (UTC))

Electrodynamicist 14:25, 3 July 2007 (UTC)

I agree somewhat. One of the things that I do find lacking in the intro is a mention of induction, both electrically induced fields from time-varying magnetic fields and magnetic fields induced by time-varying electric fields. However, we really shouldn't need to get deeply into qE since that should be treated in the electric field article, and more fully together with the q(vxB) magnetic force in the Lorentz force equation article. Since vxB is the force directly from a magnetic field, it should be mentioned first. We can then later mention that a magnetic field can induce an electric field that will in turn exert a force on a non-moving charged particle.

Another thing lacking from the article is the historical definition of the magnetic field, similar to the electric field's classical definition of F/q; classical (as I understand it) the magnetic field was defined as the force between two wires per unit length per unit current. --FyzixFighter 23:12, 3 July 2007 (UTC)

FyzixFighter, The -(partial)dA/dt term inside qE is no less magnetic in its origins than the vXB force. The two of them work in tandem together in electromagnetic induction. The vXB force is obtained by Galilean transformation of the -(partial)dA/dt force. It first appeared in Maxwell's original papers. A is the magnetic vector potential, so why do you think that -(partial)dA/dt which causes a force per unit charge F/q = E on a charged particle is somehow less magnetic than vXB which causes a force per unit charge F/q = E on a charged particle?

I think that the terminology 'Electric Field' which is inexplicably applied to -(partial)dA/dt yet not to the sister term vXB, seems to have created an artificial barrier in your mind between these two aspects of magnetic force.

You are the very one that wanted to limit the introduction to vXB as being the exclusive magnetic force. I was the one that kept deleting it because I knew that it was not the exclusive magnetic force. Not just because I knew about -(partial)dA/dt, but also because of the Gauss force that causes magnetic attraction. I even know that the Gauss force cannot possibly cause magnetic repulsion. That is a different explanation yet again.

Now you are asking for -(partial)dA/dt to be discussed in the introduction. Your instinct is telling you that it is a magnetic force, but your training and the use of the 'Electric Field' terminology is telling you that it is a topic for the 'Electric Field' article. Well I have started you off. I have amended the 'Electric Field' article to include electric fields that are generated by changing electric currents. (86.149.4.251 23:53, 3 July 2007 (UTC))

The dA/dt term is correctly called an electric force, both in common convention and according to Maxwell (see eq 1.11 in Waser's paper which is Maxwell's quaternion force law translated into modern vector notation). The magnetic force, according to every reliable source, is strictly vxB; I was never against saying that a time-varying magnetic field gives rise to an electric field, but the force on a particle that arises from dA/dt is an electric force, not magnetic. Again, it's not me making this distinction, it's not my interpretation of the physics - it's what every reliable, university physics textbook says. And, unless you have a reliable source that says that Jackson et al's interpretations of Maxwell and Faraday et al are wrong, then that is what goes in the article. The distinction between electric and magnetic forces, as I understand it, is that a magnetic force is only felt by a moving charge (or current in the case of wires or spinning charged particle in the case of magnets and atomic structures - but all moving nonetheless). An electric force is the part of the electromagnetic force that is felt by charges and is independent of the charge's motion. And as Gnixon said below, both magnetic attraction and repulsion can be explained within the formalism of the Lorentz force law, and the 4 conventional Maxwell's equation. We don't have to invent any magnetic charges or any new force law to explain the behavior we see. Unless they get down to the quantum level where QED is required, every single physicist in the world uses just those equations to quantify and predict EM behavior. --FyzixFighter 00:22, 4 July 2007 (UTC)

FyzixFighter, I'm not disputing what the official terminologies are. I know what they are and they are ridiculous. Why should the force caused by a magnetic field on a stationary charged particle not be considered as a magnetic force, when the force caused by a magnetic field on a moving charged particle is? What's the difference? Based on the official terminologies, it ludicrously follows that magnetic attraction is therefore not caused by a magnetic force, because the Gauss force is included within qE.

This ridiculous state of affairs has resulted in you trying to argue that magnetic attraction is caused by the one and only magnetic force vXB. That of course is impossible because vXB cannot be parallel to B. You then produced a reference that admitted that it was impossible but told us that we have to accept it nevertheless because we have no other choice. Are we all to be taken for fools?

Maxwell showed how the Gauss force explains magnetic attraction but you are dismissing this. You are happy to accept Maxwell's equations but you don't want to know how he obtained them. (86.149.4.251 00:57, 4 July 2007 (UTC))

Edit War Summary

So it all came down to terminologies. Despite the fact that -(partial)dA/dt and vXB are both force components in the Lorentz force, and despite the fact that they are both electric fields that arise from magnetic sources, and despite the fact that they work together in tandem in electromagnetic induction, the convention in the textbooks is to refer to -(partial)dA/dt as an electric field E, whereas the vXB component is to be referred to as the one and only magnetic force.

In fact, vXB is the convective counterpart of -dA/dt. If we take the curl of -dA/dt, we get the Heaviside version of Faraday's law -(partial)dB/dt. (remember curl A = B) However, if we take the curl of the entire Lorentz force as it appears in Maxwell's original 1865 equations (equation D), we get a total time derivative version of Faraday's law since the curl of vXB is equal to -(v.grad)B. (We all know that (total)d/dt = (partial)d/dt +v.grad)

So in fact, vXB, which we call the magnetic force is what appears after Galilean transformation of the truncated Heaviside versions of Maxwell's equations.

A Lorentz transformation would do the same thing because at low speeds, a Lorentz transformation tends to a Galilean transformation.

Yet this has been all so widely misunderstood that it has resulted in ridiculous claims that magnetism in its entirety is a result of the Lorentz transformation being applied to the electric field, despite the fact that that electric field -dA/dt is every bit as tied up with electromagnetic induction as the vXB component. The more fundamental electric field that they were all talking about already contained the magnetic vector potential A.

And the situation then got worse. Having thence delegated the magnetic Gauss force under the umbrella of electric field, it then became inappropriate to suggest that magnetic attraction could be caused by an electric field and so attempts were made to explain magnetic attraction exclusively with the vXB force. Now we all know that a vector cross product cannot be parallel to any of its components. We all know that magnetic attraction occurs in the direction of B. Therefore, magnetic attraction cannot possibly be caused by vXB.

Yet references were produced that acknowledged this fact but nevertheless told us that we would still have to believe that vXB caused magnetic attraction because there is no alternative. (The Gauss alternative having been delegated under the heading of electric field).

No wonder the article was in a complete mess. There had been an attempt to deny the wider picture of magnetism. The old Maxwellian/Faraday vision of solenoidal field lines surrounding electric circuits and pulling magnets together with the Gauss force had become politically incorrect.

A new magnetism was written that began in 1905 with Albert Einstein. It became necessary to focus exclusively on the limited part of a magnetic field that surrounded a single moving charged particle. It became necessary to focus exclusively on one aspect of magnetism, ie. vXB. The other aspects, ie. the Gauss force and the -dA/dt forces were to be hidden under the term electric field. Magnetic attraction, Maxwell, and Faraday's lines of force were to be swept under the carpet.

We were to believe that magnetism was a relativistic effect that was created exclusively from the Lorentz transformation. (86.155.136.126 09:14, 3 July 2007 (UTC))

The lesson to be learned here is that the physics of electromagnetism is not the nice tidy package that is taught in the textbooks. They have been drastically changing, and the magnetism of the textbooks prior to WWII is almost incomprehensible to a student trained with todays textbooks. Hence there is a big problem, that goes beyond the editing of this article. Modern books have ignored the fundamentals in the formulation of new teaching rules and they need to be re-evaluated in light of a clear understanding of the fundamentals. But is is clear from the discussion here, that there is no agreement as to what these fundamentals are. It would certainly be benefical if we returned to the old textbook formulations which were more solidly founded in a correct understanding of electromagnetism than the more recent ones which have been written by teachers who clearly don't understand both the history of electromagnetism and its fundamentals. These textbook writers have influenced a number of incorrect opinions which have been the source of controversy here. It is obvious to me that the article as written lacks even the rudiments of acurate knowledge of the subject and this is fairly evident in all the articles related to electromagnetism.Electrodynamicist 14:25, 3 July 2007 (UTC)

This really isn't as complicated as everyone is making it out to be. Classical electromagnetism is summed up by the Lorentz force law, F=qE+vxB, which gives the force on a charged particle caused by electric and magnetic fields, along with Maxwell's equations, which give the relationships between the electric and magnetic fields and the charge/current densities that source them. That's it. The fact that bar magnets attract each other can be explained within that formalism, and the fact that E and B are frame-dependent doesn't make one field more fundamental than the other in the standard treatment. Follow Wikipedia's policy of basing articles on sources and let this article follow the standard presentations given in texts like Griffiths, Purcell, and Jackson, which present E&M as it is understood by the entirety of the physics community. Gnixon 17:20, 3 July 2007 (UTC)

Excuse me for asking but what kind of a charged particle do you propose to make this definition apply to? Does it have a spin? In which case where is the spin accounted for in your equation? How do you propose to perform this operational definition? Can I use any velocity I like, or must I choose a certain velocity and a certain direction? Do I do this only in free space? What happens if my magnetic field is produced by a magnet? Does this definition apply inside it? I assume your definition applies for a free charge so it is not bound to an atom, but wait, why should that be a restriction? Finally, just where are these moving charged particles inside the magnet? I sure would like to know more about them and exactly how they produce a magnetic field given your definition of it. Oh by the way, I dont particularly think that Griffith's, Purcell, and Jackson are the texts that I would choose to use as my model. I prefer Faraday, Maxwell, William Thomson (Lord kelvin), both Thompsons(J.J. and Silvaneous), Poynting, Jeans, Page, and Jefimenko. Once you have read them, and demonstrated that you have acqured the requsite skills and philosophical mastery of the subject matter, then maybe your opinion will carry some weight.In the mean time I think it best not to use the currently proposed definition included with this article.72.84.71.56 19:14, 3 July 2007 (UTC)

Answers: Any charged particle. Frequently. Via the magnetic moment, which seems to be explained below. I don't understand this question. Use the particle's velocity. Any area of space you like. Nothing exceptional. I wouldn't call it a definition, but yes. It's not a restriction. They're protons and electrons in atoms. The atoms have magnetic moments, but the full story is complicated by quantum mechanics. Gnixon 03:55, 11 July 2007 (UTC)

Regarding sources, I don't understand why you prefer such old ones. This article is about the magnetic field, not the history of understanding it (although that might make an interesting subsection). For analogy, I haven't read the Principia, but I'm pretty good at calculus and Newtonian mechanics. In fact, an argument could be made that I understand both better than Newton, since I benefit from the shoulders of three centuries worth of giants standing on his. I'm quite confident that Jackson's text is more valuable than Maxwell's paper for the purpose of understanding E&M, regardless of how interesting it may be for historical purposes. Surely you're not suggesting there's something about E&M that appears in Maxwell's paper but generations of physicists in recent history have failed to understand! I apologize if my original note was a little brusque. Let's try to keep this all civil, and I hope my opinion will carry more weight with you in the future. Gnixon 03:55, 11 July 2007 (UTC)

I didn't actually write the entry that you are replying to but I'd like to answer one part of your reply to him/her. I would personally suggest that there are many aspects of E&M that appear in Maxwell's papers but that generations of physicists in recent history have failed to understand. I think that the present state of knowledge is appallling. Physics has been re-written around the Heaviside versions of Maxwell's equations. (217.44.98.235 09:17, 11 July 2007 (UTC))

The Lorentz force equation applies to any charged particle, whether it's free or bound to an atom, it doesn't matter. If it's spinning then it has a magnetic moment, which can be derived from the charge distribution within the particle or measured empirically. The velocity used is the velocity of the particle within the same frame of reference for which E and B are given. These definitions work as well in material as well as in free space, though the physics gets a bit more involved when working in material. However, these are the equations that every physicist and engineer uses in every single lab across the globe. The moving charges that produce a ferromagnet's magnetic field are the electrons in the atom, caused by the spin alignment of those electrons (a rotating charge).

Sorry, but your comments on which sources to use are entirely contradictory to WP:RS. If we use Maxwell and others before atomic theory, does that mean we have to present the whole mess of magnetic charges and the hodgepodge of magnetostatics that they invented to explain how magnetic charges interact, something we don't have to do now in view of the atomic theory and quantum mechanics? While you may be loathe to admit it, Maxwell and them got somethings wrong, and certainly there are somethings modern physics probably gets wrong, but we should use the most current sources as they are the best. Also, we will certainly have disagreements (see the lengthy debate above) over how these original equations translate into the modern convention. No editor's opinion carries any weight, that is WP:OR. Reliable sources carry weight, and Purcell and Jackson and Griffiths are reliable sources per wikipedia's criteria - Jackson especially, which has been in use for the past several decades and is the quintessential compendium of EM theory at the graduate level. If you think they're wrong, then provide a reference that they are wrong - but your low opinion of them (OR) is not enough to throw them out as reliable sources. --FyzixFighter 23:35, 3 July 2007 (UTC)

I want to speak to Gnixon now. Gnixon, you tell us that the Lorentz force and Maxwell's equations are all that we need. In actual fact, the Lorentz force was one of Maxwell's original equations. Yet I notice right above, that FyzixFighter is telling us that Maxwell got some things wrong and as such we shouldn't refer to him. It's OK to use his equations as the sole basis for electromagnetic theory, but not OK to refer to his scientific papers that would tell us how he arrived at those equations.

Also, if as you say, all we need is Maxwell, then why was this article telling us that the magnetic field is the relativistic component of the more fundamental electric field? Why cloud the whole issue with relativity if all we need is Maxwell?

One more point. You quoted the Lorentz force and told us all that magnetic attraction is explained by that force. You didn't tell us whether it is explained by the qE component or the vXB component. That is a crucial issue because if as I suggest, and as Starwed has suggested, that it comes from the qE component, then clearly magnetic attraction is not a consequence of relativity contrary to what this article has been preaching.

And by the way, magnetic repulsion cannot be explained by any of the terms in the Lorentz force. A repelled magnet doesn't even come into contact with the magnetic field lines of the repelling source.

It is most certainly not all as simple as your whitewashing statement is trying to make out. (86.149.4.251 00:06, 4 July 2007 (UTC))

I would prefer that the article treat E and B on an equal footing and avoid issues of relativity, at least until after the lead sentences. I agree we shouldn't cloud the issue. No reason comes to mind why E-fields are somehow fundamentally involved in the attraction of bar magnets, but I'm used to thinking about such problems in other terms, and I think others have probably explained the situation well enough. There is a magnetic field line at every point in space around a magnet, including any point where there is a repelled magnet. Gnixon 03:55, 11 July 2007 (UTC)

Again, don't twist my words. Maxwell is a great source if we interpret it correctly. Modern university physics textbooks do that, and it's with those that you are being challenged. Maxwell did get some things wrong, but we know now why he erred - he simply lacked a more complete model of atomic structure.

Per your recent addendum about magnetic repulsion - thank you for making a classic freshman physics mistake. When calculating the force from magnetic dipole 1 on the magnetic dipole 2, you have to ignore the magnetic field of dipole 2. This is the same thing you do when calculating the force of an electric field on a charged particle, you have to ignore the particle's own E-field. Alternatively you could use a Maxwell stress tensor approach when looking at the net electromagnetic fields to determine the repulsive force, but that also can be derived from the Lorentz force equation as seen in Griffiths and Jackson. Also, once again, the field is the actual physical entity, not the field lines; the field lines are intuitive representations of the fields. Still waiting for a reliable source that says Griffiths and Jackson have interpreted Maxwell incorrectly. And out of curiosity, how many university physics courses have you taken on this subject, or are you entirely self taught in this subject (with the exception of what you were taught in high school)? --FyzixFighter 09:28, 4 July 2007 (UTC)

FyzixFighter, If modern physics textbooks were interpreting Maxwell correctly, we would have been taught all about a sea of molecular vortices.

Maxwell viewed magnetic repulsion as centrifugal force acting in the equatorial plane of his molecular vortices. The action occured right in the field where the two sets of field lines spread away from each other. Maxwell, just like the freshmen that you describe above, did not ignore the field of the magnet that is being repelled. He kept to the exact physical picture.

Whether you agree with Maxwell or not is up to you. But you needn't try to tell me that modern textbooks are interpretating Maxwell correctly. They are clearly not interpreting him at all. They use his equations but then build a totally different physical picture around those equations.

This argument broke out because some editors tried to deny that magnetic field lines are lines of force. We are all now agreed that they are lines of force, even if official terminology means that the force in question is defined as an E force. The E force is still there and it runs parallel to the B lines.

Regarding your last question, I'm sorry that the issue of university courses seems to have become of any relevance. But since you have asked, yes, I have taken advanced university courses in electromagnetism from both the physics and the applied mathematics departments. I have also carried out years of extensive research into the subject.

I am particularly sorry that you have failed to grasp the fact that the vXB force cannot possibly act parallel to B. That's high school vector algebra.

The E force that acts along the B lines and pulls magnets together is the Gauss force. It is contained within the Lorentz force. During the second world war the iron ships in the Atlantic had to be de-gaussed. Nobody talked about de=vXB'ing them.

All you need to do is go back to your original edit and point out that a magnetic field gives rise to forces that are described by the Lorentz force equation. You can then point out, if you so wish, that one of the components of the Lorentz force deals with the force on a moving charged particle and that that force is at right angles to the magnetic field. (86.149.4.251 10:09, 4 July 2007 (UTC))

In what sense are the magnetic field lines "lines of force"? Gnixon 03:55, 11 July 2007 (UTC)

Gnixon, Magnetic field lines are lines of force in the sense that they pull magnets together with a force of attraction. This is a standard terminology. It was good enough for Faraday and Maxwell and it was used in school textbooks at least into the early 1980's. I haven't checked more recent textbooks but I can't think what would have changed in magnetism in the last 30 years. (217.44.98.235 09:10, 11 July 2007 (UTC))

Interaction between magnets explained solely by vxB field

Let me try to explain, using only q(vxB) force, how can two cylindrical magnets placed along axis of magnetization in same direction repel each other if they have unlike orientations (visually: (NS)(SN)) and attract each other if they have like orientations (visually: (NS)(NS)). Or in other (and more common) words how can they repel each other if they are facing each other with like poles and attract each other if they are facing each other with unlike poles. Important thing to notice is that magnets attract and repel each others (depending on their relative orientation) not their poles, because there are actually no magnetic poles, we use "poles" only to label sides of magnets, they are not physical, and it is questionable if magnetic monopoles are mathematically consistent, but this is offtopic here.

When considering magnet-magnet interaction in case which I described in first sentence, it is true that B that goes through middle of the magnet is in direction of experimentally observed force between this two magnets. But don't just quickly jump to conclusion that this B is causing the mentioned interaction.

In magnet, there are small loops of electric current likely orientated which give magnetization to the magnet. When such loops of equal current are next to each other, so that one part of the loop is common, their effects will cancel in that part, and effectively it will be the same as if there is only one bigger loop, produced by initial two loops, through which the same current flows. If many such loops of equal current are placed together in 2D pile in such way, it will effectively be the same as if current of initial loops flows around the pile. See Stokes' theorem. This means that homogeneously magnetized cylindric magnet will effectively be same as there is loop of current (with width) of the same shape.

Let's see how does magnetic field of other magnet act upon this loop of current. In the middle of the loop B field have only axial (in direction of magnetization) component, but field isn't homogeneous, and in part of loop where current actually flows it also has a radial (perpendicular to axial) component. Current in the loop have only azimuthal (around the axial) direction, so axial components of B will produce radial forces on the loop which will cancel in case of cylindric symmetry, and radial components will produce axial components of same direction and net force will be in direction of the magnet. It is important to note that besides vxB, forces which keep magnet rigid are also required to neutralize effects of radial components of vxB.

Thank you. --antiXt 14:00, 5 July 2007 (UTC)

Hmm. It seems to me that when you are looking at a classical loop of current, the magnetic field acts on each electron individually. For the wire itself to move must be a result of interaction between the electrons and the wire: this is the rigid force you mention, and it's this force which is microscopically responsible for the work.

The attraction/repulsion caused by a magnet is somewhat different: it comes down to the fact that even stationary electrons interact with the magnetic field, and this is an entirely quantum effect which goes beyond the Lorentz force. This might be a bit pedantic, but there is a fundamental difference between an electron's dipole moment and the effective dipole moment of a loop of current: one is explainable entirely through Maxwell's laws, the other isn't. --Starwed 20:39, 5 July 2007 (UTC)

Sorry, but could you explain what it is that you just said, in a way that someone can understand? I thought the purpose was to write so that the concepts could be understood, but that is apparently pretty difficult. I certainly hope you are not writing this article, since what you said makes no sense to me.71.251.185.60 18:17, 5 July 2007 (UTC)

Starwed, does this mean that we need to use quantum mechanics to explain the magnetic attraction between two loops of electric current? (86.149.4.251 00:21, 6 July 2007 (UTC))

No: I clearly claimed above that you can explain that entirely with Maxwell's equations. But try explaining why a stationary electron interacts with a magnetic field using only classical mechanics! It's a quantum effect. --Starwed 03:28, 6 July 2007 (UTC)

Hmm, to be clear: once you assign to electrons a magnetic dipole moment, I don't think you need to invoke quantum mechanics to explain magnets. I'm just saying that the existence of the magnetic moment is itself a quantum effect: unlike for a real loop of wire, there's no way to derive it from just the Lorentz force law that I'm aware of. --Starwed 06:22, 6 July 2007 (UTC)

Starwed, you seem to be straying away from the issue in question. Does magnetic attraction come under the jurisdiction of the Lorentz force? I say that it does, and that the Lorentz force is one of Maxwell's original equations. We both know that magnetic attraction can't be attributed to the vxB component of the Lorentz force. Hence your original assertion that it comes under the qE term is correct. Maxwell would back you up on that matter. The Gauss force that acts along magnetic field lines is what causes magnetic attraction. Why this culture of accepting Maxwell's equations but denying how Maxwell derived them? (86.149.4.251 09:30, 6 July 2007 (UTC))

There was evidence that both Starwed and FizixFighter could instinctively see that the force of magnetic attraction arises out of the qE component of the Lorentz Force. However, it would seem that the use of the term 'Electric Field' has masked the magnetic origins of this term and that neither Starwed nor FizixFighter can envisage how a Coulomb force might be caused to act along the direction of Faraday's lines of force.

I would put the blame on the fact that modern textbooks have neglected Maxwell, and that wikipedians seem to be too focused on the misinformed viewpoint of Edmund Purcell, derived in 1963, that a magnetic field is the relativistic component of the more fundamental electric field.

In actual fact, the electric field within the context of Faraday's lines of force has got fundamental magnetic origins. (86.155.139.178 10:58, 8 July 2007 (UTC))

Magnetic field (B) is not an component of electric field (E). It is impossible because E and B have different dimensions. But magnetic field is relativistic consequence of electric field, and vxB is component of electric field in reference frame of particle moving with velocity v.

Curled electric field is produced by changing magnetic field, but any magnetic field is produced by changing electric field, so magnetic origins of curled electric field are not so fundamental, while electric ones are.

And lines of magnetic field are not lines of force. They are directions perpendicular to planes of possible directions of magnetic force, so they aren't even lines in higher dimensional spaces. (un)luckly, we live in 3-dimensional space, so we can represent magnetic field simply by pseudovector, and we don't have to use more general skew-symmetric tensor (which in n-dimensional space has n(n-1)/2 components) instead of any pseudovector. This makes some things easier to work with, but also blurs distinction between vectors and pseudovectors. --antiXt 13:34, 8 July 2007 (UTC)

Here the assertion is being made that there is no such thing as magnetic field and no magnetic force. You are saying that magnetism and electricity are the same thing and there is no difference. That is the implication of your position. So why bother with magnetic field at all? I suggest deleting all of the articles relating to magnetism if what you say is correct.71.251.190.224 14:00, 8 July 2007 (UTC)

Nobody said that there is no magnetic field or magnetic forces. Only that magnetic field is not fundamental and that there no magnetic forces in direction of magnetic field pseudovector, only perpendicular to it. --antiXt 16:24, 8 July 2007 (UTC)

Ok, If that is what you think, then please explain the difference between electricity and magnetism if the magnetic field is not fundamental and there are no magnetic forces that are different from the electric ones. 71.251.190.224 18:39, 8 July 2007 (UTC)

Antixt claims that magnetic field B is not a component of electric field E. Nobody ever said that it was. But -(partial)dA/dt is a component of E, and that clearly has got magnetic origins, because A is the magnetic vector potential which is related to B by the equation curl A = B. Antixt seems to think that the changing magnetic field implied by -(partial)dA/dt ultimately comes from a changing electric field. If that were true, it would mean that the electric field ultimately comes from a changing electric field.

Let's have an example of a changing electric field causing a magnetic field. (86.155.139.178 19:10, 8 July 2007 (UTC))

It would also seem that Antixt doesn't want to pay any attention to the very obvious fact that vXB, which first appeared in Maxwell's original papers, is an axial vector that is perpendicular to B. Since magnetic attraction is in the direction of B, then this attraction can't possibly be caused by vXB. (86.155.139.178 19:15, 8 July 2007 (UTC))

First, vxB is not an pseudovector, because v is an vector and B is an pseudovector and cross product of vector and pseudovector yields an vector.

Second, magnetic attraction/repulsion is generally not in direction of B, it only coincides with B in case of coaxially placed magnets.

Third, electric field does not ultimately come from a changing electric field (though it can be indirectly caused by it), it ultimately comes from electric charges. --antiXt 21:47, 8 July 2007 (UTC)

Antixt, magnetic attraction is always in the direction of magnetic field lines. And how can you possibly say that electric field ultimately comes from electric charge in the case where electric field is given by -(partial)dA/dt? In the latter case, div E equals zero whereas in the former case div E equals charge density ρ. We clearly have at least two distinct primary sources of electric field. vXB is a third source of electric field because F/q = E = vXB. vXB comes about from a Galilean transformation of -(partial)dA/dt. You can juggle about with the terminologies 'Electric Field' and 'Magnetic Force' all you like but you can't change the underlying physics. -(partial)dA/dt and vXB are both electric fields and they are both magnetic forces. One is the convective aspect of the other under Galilean transformation. (86.155.139.178 22:11, 8 July 2007 (UTC))

The electric field ultimately does come from electric charge. To claim that there are two primary sources of the electric field is to ignore or be ignorant of the notion of boundary conditions. Alfred Centauri 00:21, 10 July 2007 (UTC)

Remind me again of what relevance this discussion has to the article?--Starwed 04:04, 9 July 2007 (UTC)

Starwed, the argument began because certain editors were objecting to the use of the term 'Lines of Force' for magnetic field lines. They were pointing out the fact that vXB is perpendicular to the magnetic field lines. While that is a true fact in its own right, it neglects the fact that there is another force of attraction running along magnetic field lines that pulls two magnets together.

If the term "Lines of Force" is used in the modern literature, provide a source. Otherwise, it is only of historical interest.--Starwed 04:03, 10 July 2007 (UTC)

The argument then developed into whether or not vXB was the only magnet force. On realizing that the vXB force could not possibly acount for magnetic force, being perependicular to B, it was then realized by most in the argument that magnetic attraction must therefore be explained by the qE term in the Lorentz force. This idea is backed up in Maxwell's original papers.

As stated both below and above, the Lorentz force does not encompass every aspect of electromagnetic behavior. --Starwed 04:03, 10 July 2007 (UTC)

The argument then got bogged down in semantics with editors claiming that since E is electric field, it cannot therefore also be a magnetic force. I was trying to point out that when E is equal to -(partial)dA/dt that it is steeped in magnetic origins just like vXB. In fact vXB is the convective aspect of -(partial)dA/dt under Galilean (or Lorentz) transformation.

The origin has no bearing on the terminology: provide a source stating that -(partial)dA/dt can be called a "magnetic force" or drop the issue on wikipedia. --Starwed 04:03, 10 July 2007 (UTC)

The issue to be resolved now in the main article is whether or not to mention the Lorentz force in full in the introduction. At the moment, emphasis is only being put on the vXB component of the Lorentz force. I personally think that the Lorentz force could wait for a separate section or be delegated.

Also there is too much empahsis in the article's introduction of an obscure theory of the 1950's/1960's by either Rosser or Purcell claiming that a magnetic field is the relativistic component of the more fundamental electric field. This is not textbook magnetism and it is easily demonstrated to be wrong. In fact, I do believe that the idea has fallen from favour within the scientific community.

While the current phrasing is terrible, the form of the magnetic field can indeed be deduced from the electric field and SR. There are (modern) sources cited earlier in the talk page which show this, so whether any editor remains convinced of this or not has no bearing. Again, provide a citation saying otherwise, or drop the issue.--Starwed 04:03, 10 July 2007 (UTC)

The wikipedians have been pushing this narrow Rosser/Purcell vision at the expense of the more traditional Maxwell/Faraday vision of solenoidal lines of force around electric circuits and bar magnets. They have been attempting to narrow the vision down to vXB only, and to the limited part of the magnetic field that is associated with single charged particles. (86.155.139.178 10:54, 9 July 2007 (UTC))

Pardon me for 'butting in' to this rather lengthy discussion but it occurs to me that F = q(E + v X B) is the Lorentz Force on a point charge. If I'm not mistaken, a point charge cannot (classically) possess a magnetic moment. However, the electron does have a magnetic moment despite appearing to be point-like otherwise. As we know, the magnetic 'lines of force' are, to a magnetic charge, what the electric 'lines of force' are to an electric charge. However, all we appear to have are magnetic dipoles (e.g., the 'spinning' electron), not magnetic charges. Dipoles are not point charges but are extended bodies. An equation valid for a point charge can hardly be expected to explain the complete magnetic interaction of an object with a magnetic dipole moment, right? Alfred Centauri 23:00, 9 July 2007 (UTC)

I assume that you are therefore agreeing with me that vXB cannot possibly cause the force of magnetic attraction and that there is therefore more to magnetic force than just vXB. (86.155.139.178 05:55, 10 July 2007 (UTC))

Consider two isolated (classical) electrons momentarily stationary with respect to each other. In the frame of reference where both electrons are at rest, there is only an electric repulsion between them. In any other frame of reference, there is also a magnetic attraction between them that is due entirely to qvXB thus refuting your statement above to the contrary. Alfred Centauri 14:13, 10 July 2007 (UTC)

For that magnetic force to be a force of attraction, it would have to act along the direction of the B lines between the two electrons. Hence it can't be caused by qvXB because qvXB can never be in the direction of B.(81.158.161.160 16:06, 10 July 2007 (UTC))

86.155.139.178, IMHO to explain interaction between magnets, besides qvXB, forces that are needed to be taken in account are the ones that keep magnet solid and magnetized. And no other. Intro post on this section gives such explanation, but it is little bit hard to comprehend. --83.131.77.66 14:25, 10 July 2007 (UTC)

86.155.139.178, you are claiming that there exist forces which are in direction of B (in general case), and more precisely, that magnetic attraction is in direction of B (it's strange why would only attracion be in direction of B, since atteraction and repulsion are sort of symmetric).

Can you give any reliable sources that magnetic interaction (or only attraction, as you claim) is in direction of B?

The force felt by a dipole with magnetic moment m is $\mathbf {F} =\nabla (\mathbf {m} \cdot \mathbf {B} )$. (Griffiths Introduction to Electrodynamics.) This can be in the direction of B. For an illustration of the field between two barmagnets, try this page, for instance.) --Starwed 18:24, 10 July 2007 (UTC)

Thank you Starwed for answering this trivial question on my behalf. It's a pity that somebody should demand references for such an obvious and fundamental phenomenon. Magnets pull together in the direction of the B lines. End of story. This person obviously hasn't been reading the debate carefully. The argument was not about whether or not a magnetic force exists along the B lines. The argument was about whether it is caused by the Gauss/Coulomb force or by the vXB force. This person also seems to have failed to realize that attraction and repulsion are not symmetric. In magnetic repulsion, the magnetic field lines spread away from each other.

Anyway, you were asking me for a modern reference regarding the use of the term 'Lines of Force'. Nelkon&Parker, Advanced Level Physics (fourth Edition) (1977(1979 reprint)). Chapter 36 entitled 'Magnetic Field and Force on Conductor', pages 772 to 773, section entitled 'Magnetic Fields'. Quote A bar of soft iron placed north-south becomes magnetised by induction by the earth's field, and the lines of force become concentrated in the soft iron (Fig.36.1 (iii)). The tangent to a line of force at a point gives the direction of the magnetic field at that point. (81.158.161.160 18:47, 10 July 2007 (UTC))

Ah, but a (magnetic) dipole is not actually composed of two magnetic monopoles that would, if they existed, feel a force in the direction of B. Instead, a magnetic dipole is formed by current loops where electric charge circulates in a plane normal to the axis of the dipole. Saying that a dipole 'feels' a force parallel to B implies that the current loop forming the dipole feels a force perpendicular to B. So, it's not, as you say, end of story. You are playing games with terms here.

Your usage of the phrase magnetic attraction seems peculiar to me. A force directed along the line connecting two particles is either attractive or repulsive. Further, if this force is magnetic in character, i.e., couples to electric charge in motion, then we have either magnetic attraction or magnetic repulsion. In the case I described above, the magnetic force is directed along the line connecting the two electrons and it is attractive in the sense that this force acts to decrease the distance between the electrons.

Now, consider two identical current loops arranged along a common central axis (say a vertical axis) but at different heights. For each current element in the 'top' loop we can match an identical current element in the 'bottom' loop. Using an argument similar to the one I made above, it's easy to see that there is a magnetic force between the matched current elements that acts to bring the current elements together (magnetic attraction). When the contributions of other non-matched current elements are added in and then the force on all current elements are added up, it can be shown that the resultant magnetic force has a component that acts to bring the loops together.

Please note that each current element in one loop feels a force perpendicular to the B field of the other loop but the resultant force through the axis of the loops is parallel to the B field there. But this is what we would expect. The current loops form magnetic dipoles which, in this case, are aligned on a common axis and arranged to attract. Alfred Centauri 19:41, 10 July 2007 (UTC)

Alfred Centauri, we don't need to go into those details. Two magnets either repel or attract each other, and it doesn't matter whether they are electromagnets or ferromagnets.

In the case of magnetic attraction, the force of attraction is directed along the B lines and hence it cannot arise from the qvXB component of the Lorentz Force. It must arise from the Gauss force component of the Lorentz force. It doesn't matter whether or not we fully understand the link between magnetic charge and magnetic dipoles. Failure to understand this link does not make vXB capable of filling this gap in our knowledge. Maxwell showed us that the force of magnetic attraction must come from the Gauss force and this is echoed in the magnetostatics sections of modern textbooks.

It seems to me that you are demanding the impossible from vXB simply because you do not understand magnetic charge. vXB can never be parallel to B. (81.158.161.160 22:58, 10 July 2007 (UTC))

Anonymous, you sound like a broken record - repeating over and over the phrase "vXB can never be parallel to B". Yet, anyone that has been introduced to vector calculus knows that the cross-product of two vectors is perpendicular to the two vectors and no one here has claimed otherwise. Yet, you keep repeating this so, the question is, why on Earth do you think this is relevant at all? That fact that this is apparently the crux of your 'argument' reveals your own lack of understanding. Don't you see that the qvXB force is a point force on a point charge? Don't you see that magnets and magnetic dipoles are not points? Don't you see that your so-called magnetic attraction along the direction of B is simply the resultant force from the addition of many point forces that are perpendicular to B? Why is it so hard to understand this simple concept?

If you choose to reply to this, I ask that you please not repeat "vXB can never be parallel to B" for the simple reason that this is common knowledge and that I have never claimed otherwise. More importantly, please show how the attraction between the two current loops I described is due to something other than the vector sum of the qvXB forces on the current elements of the loops as I've shown in this image:

Alfred Centauri 23:31, 10 July 2007 (UTC)

What is this "Gauss force" and where is it supposedly discussed in magnetostatics sections of modern textbooks? Google reports 81 hits, none of which are helpful. Pfalstad 00:50, 11 July 2007 (UTC)

I don't totally understand antiXt's posting at the top of this section but I think he has the right idea. v x B alone can explain magnetic attraction, for either a current loop or a magnet (which can be thought of as a bundle of current loops). I've modeled it in a simulation I wrote. It works fine. It's not very intuitive though. Pfalstad 00:53, 11 July 2007 (UTC)

Anon said:In magnetic repulsion, the magnetic field lines spread away from each other.

Ah, I see one of your mistakes now. You are looking at the net magnetic field caused by both dipoles. But a dipole's magnetic field doesn't interact with itself... so when you say the repulsion is perpendicular to the field lines, you're not thinking of what magnetic field the dipole sees, but what you see. --Starwed 04:34, 11 July 2007 (UTC)

Pfalstad, Alfred Centauri, and Starwed, magnetic attraction was first formulated by Gauss and Coulomb. It doesn't matter what we know or don't know about magnetic charge. The Coulomb force, which is one of the components of the Lorentz force, is responsible for magnetic attraction. This was confirmed by Maxwell.

It seems to me that you have all decided that magnetic attraction can be explained by the vXB force, but it can't.

You mean, even despite us saying several times that it can't? Given your unwillingness to actually read responses to you, it's clearly time to abandon this discussion. --Starwed 13:26, 11 July 2007 (UTC)

It is not within the nature of the vXB force to explain magnetic attraction. There is no potential energy associated with the vXB force and it acts in the wrong direction whether we examine single current elements or summations of current elements.

You are all playing out a game of academic whist in which you call trumps. You are all deluding yourselves. (217.44.98.235 09:03, 11 July 2007 (UTC))

Spoken like a true usenet crank. I did expect that you would at least try to support your claims with some attempt at a logical, coherent argument sprinkled with just enough math to look legit. But, you have disappointed me. It appears that the very best you can do, when presented with a concrete example contradicting your claims, is to sidestep the challenge altogether and prattle on with your same vague rhetoric. Well, thanks for playing, anonymous, but your time is up! Alfred Centauri 13:43, 11 July 2007 (UTC)

Starwed, please reconsider posting comments in the middle of another comment. Thanks. Alfred Centauri 14:00, 11 July 2007 (UTC)

Archive

It might be good idea to start archiving this talk page beacuse it has become too long. --antiXt 22:15, 8 July 2007 (UTC)

Archiving one discussion (under several headings) might be sufficient. Gnixon 03:15, 11 July 2007 (UTC)

Magnetic Potential Energy

Starwed and FizixFighter both mentioned a point which probably lies at the centre of the dispute. Both Starwed and FizixFighter mentioned that one should ignore the magnetic field of the object that is being acted upon. If we do that, then the F = qvXB effect can indeed be invoked, because the angles will be correct.

This method quite possibly gives a close approximation to the actual force in question but it overlooks the very important issue of potential energy. The forces of magnetic attraction and repulsion both involve an interplay of kinetic and potential energy which is not commensurate with the vXB force. Magnetic forces of attraction and repulsion are irrotational and they have traditionally been formulated by Gauss and Coulomb in the likeness of the electrostatic force.

It is clear to me now that modern textbooks have totally failed to interpret Maxwell and Faraday correctly. Maxwell and Faraday considered the exact picture of the magnetic field lines in any given scenario. Modern physics calculations are denying the correct picture of magnetic field lines crossing directly between two attracting magnets or spreading outwards between two repelling magnets.

If the correct picture were to be employed, as opposed to the hypothetical idea that we should ignore the presence of the very object that is being effected by the force, then we would realize that we need a Coulomb force acting along the magnetic field lines to explain magnetic attraction. According to Maxwell, there will be a centrifugal pressure between the field lines that causes magnetic repulsion and that also pushes from behind a wire in magnetic attraction where the B line hooks around behind the wire. The vXB force quite simply doesn't work perfectly within the context of the actual picture of the magnetic field lines that exist between electric circuits and bar magnets.It is probably a good approximation for moving charged particles in a magnetic field.

In summary, modern physics has ignored the potential energy issue, and it is using a distorted picture of how the magnetic field lines actually exist in a given scenario.

The vXB term is actually the convective aspect of -(partial)dA/dt under Galilean transformation. It first appeared in Maxwell's 1861 paper. We do not need relativity to explain magnetism. (217.44.98.235 18:52, 11 July 2007 (UTC))

"It is clear to me now that modern textbooks have totally failed to interpret Maxwell and Faraday correctly." Perhaps, but they are still considered reliable sources by Wikipedia. This is not the place for original research. Pfalstad 19:50, 11 July 2007 (UTC)

Pfalstad, if Maxwell's original papers of the 1860's are classified as original research, what does that make articles that were only written in 2006, and which have been cited and accepted as evidence by wikipedian editors for the ludicrous case of the vXB force being directly derivable from the Coulomb force? I very much detect a game of textbook whist in all of this, with the editors calling trumps. (217.44.98.235 23:34, 11 July 2007 (UTC))

Are you referring to something in the article, or something on the talk page? Only the article has to be sourced. For physics articles, I think we need recent sources, not hundred-year-old ones, because Maxwell had some ideas which are discredited today. Pfalstad 00:26, 12 July 2007 (UTC) Also, please note that "synthesis of published material" counts as original research if it would advance a novel interpretation of physics, something that is not mainstream. Pfalstad 00:37, 12 July 2007 (UTC)

Is that 2006 research paper, that is referenced in the introduction of the main article, counted as mainstream or original research?

I never interpreted Maxwell. The points which I mentioned, such as the presence of vXB in his articles, are manifestly plain to see by anybody who cares to look at these original papers. I even provided a link and gave the precise page and equation numbers. vXB was already there in 1861. It is not justified as per this 2006 reference in the introduction which you have sanctioned, and which is clearly false, and which is clearly original research. (217.44.98.235 08:14, 12 July 2007 (UTC))

The 2006 research paper is not original research; it's in a reputable journal (Physica Scripta). I'm not sure about the points you mentioned above, since I don't have time to wade through this entire talk page and figure out which points you are referring to, which IP addresses are yours and which are someone elses, etc. Pfalstad 18:02, 12 July 2007 (UTC)

Application to Relativity

To 83.131.82.23, I reverted your edits for the following reasons. The very reference that you supplied was none other than Einstein's famous 1905 paper in which the special theory of relativity first appeared.

If you actually read Einstein's 1905 paper you will be in no doubt whatsoever that we need to have the full Maxwell-Hertz equations before we can apply the Lorentz transformation. Therefore you had no reason to delete that paragraph. The magnetic field is indeed pre-supposed before we apply the Lorentz transformation. And you can check out Maxwell's 1861 paper to see that vXB already exists independently of the Lorentz transformation.

The point which you are trying to press first came about in the late 1950's from a man called Rosser, but more famously in 1963 from Edmund Purcell.

If you think that your point is backed up by Einstein's 1905 paper, then let's please have the page number and line number. (217.44.98.235 09:24, 13 July 2007 (UTC))

Can't you selectively revert instead of blindly reverting entire change(s)? No offense. --83.131.8.131 09:59, 13 July 2007 (UTC)

83.131.8.131, you say that the bit that you deleted was unsourced. The source was in fact the very reference which you have given ie. Einstein's 1905 paper. Why don't you read it yourself since you are so keen on quoting it. If you were to read it, you would see that the Maxwell-Hertz equations which the Lorentz transformation acts on already contains magnetic field terms.

You are getting confused between Einstein's 1905 paper and Edmund Purcell's 1963 theory in which he claimed to have produced a charge density in a neutral wire by selective application of the Lorentz contraction.

I'm going to revert again because you are claiming things to be unsourced that you have actually sourced yourself and yet seem to be oblivious to the contents. (217.44.98.235 16:54, 13 July 2007 (UTC))

Einstein's 1905 Paper

83.131.8.131, Einstein's 1905 paper deals with Maxwell's equations being subjected to the Lorentz transformation. Maxwell's equations involve magnetic fields.

You have failed to give a reference showing that Einstein was able to produce magnetic fields purely from electric fields. He produced vXB from -(partial)dA/dt by doing a Lorentz transformation on Heaviside's version of Maxwell's equations. That is not the same thing as producing magnetic fields from electric fields.

You are misinforming the public. You are clearly determined to push this Purcell vision to the fore. You want it in the introduction. You want the world to think that magnetism comes from Einstein's theories of relativity, and you are so wrong.

And the wikipedia editors are letting you do it. I suppose I'll return in a few months and see that all references to solenoidal field lines have been removed, as will all references to lines of force, all diagrams showing the pattern of magnetic lines of force, all references to closed electric current sources and bar magnets, and all references to Maxwell, Faraday, and Ampère etc.

We will be looking at a cult article in which the full picture of the magnetic field has been eclipsed so that all we can see is moving single charges and the vXB force, and we will all be told that Einstein created the vXB force from a Lorentz transformation on Electric fields.

You are promoting total rubbish. Who are you trying to impress? The public won't understand the Purcell vision at all, and you are deluding yourself that you are so clever because you think that you understand something that you haven't got the first clue about. (217.44.98.235 22:24, 13 July 2007 (UTC))

Relativistic origin of magnetic field should be in the intro to demystify the magnetic field. There is no mention in this or any other provided reference (which btw isn't mine - it's in the article for very long time) that the Lorentz transformation cannot be applied to electric fields unless it already presupposes the existence of magnetic fields and their inter relationship with electric fields under the terms of Maxwell's equations. It's your POV. And you changed "Einstein explained in 1905" to "Purcell tried to explain in 1963", while given reference is paper written by einstein in 1905, not by Purcell in 1963 And wikilink "Purcell" with which you replaced "Einstein" redirects to Henry Purcell who died in 1695. With such edits, you seem to be an anti-relativity troll.

So please revert the mess you made to this article. Thank you. --83.131.24.185 09:59, 14 July 2007 (UTC)

Intro

The biggest problem I see with:

In physics, a magnetic field is a solenoidal vector field in the space surrounding moving electric charges, such as those in electric currents and bar magnets.

Is that I read it four times thinking that there are moving charges in electric currents and bar magnets, and I kept trying to remember where the charges move in the bar magnets. In other words, you have a misplaced metaphor. 199.125.109.127 05:05, 14 July 2007 (UTC)

You are addressing that comment to FizixFighter. FizixFighter wrote that introduction. My wording was different. I only mentioned electric current and bar magnets in the introduction that I wrote. It was FizixFighter that insisted upon putting the emphasis on electric charge. I tried to keep it as electric current. FizixFigher kept reverting to moving single electrically charged particles. Eventually he compromised by allowing it to be mentioned that moving charges occur in electric current and bar magnets. (217.44.98.235 19:17, 14 July 2007 (UTC))

Enough! Wikipedia articles are not the place for editorial and adversarial edits!

Edits such: "Purcell tried to explain" and "(However, the Lorentz transformation cannot be applied to electric fields unless it already presupposes the existence of magnetic fields and their inter relationship with electric fields under the terms of Maxwell's equations. As such, the magnetic field can hardly be considered as a by-product of the Lorentz transformation.)" are not acceptable. Write what you want on the talk page anonymous, but the article is not the forum for POV, editorial, and adversarial style edits. Please stop.

Wikipedia is not about the 'truth' as you see it. It doesn't matter if, in your opinion all the textbooks have it wrong. Wikipedia is not here to 'correct' them.

For what it's worth, I don't agree with the present wording of the sections in question. The magnetic field doesn't spring forth from the Lorentz transform, however, magnetism can be deduced when Coulomb's law is made consistent with relativity. Yes, one has to presuppose the existence of a 'vector potential' simply because a scalar electric potential is not Lorentz covariant since energy is not a Lorentz scalar but is instead, a component of a four-vector. But, this type of info is not appropriate for the magnetic field article, IMHO. Alfred Centauri

Hutchinson's Encyclopaedia

I'll copy verbatim what is written under 'Magnetic Field' in the 1996 Hutchinson's Encyclopaedia.

Magnetic Field. Physical field or region around a permanent magnet, or around a conductor carrying an electric current, in which a force acts on a moving charge or on a magnet placed in the field. The field can be represented by lines of force, which by convention link north and south poles and are parallel to the directions of a small compass needle placed on them.

Hutchinson's obviously don't feel the need to cloud the issue with obscure POV interpretations of relativity. The Einstein reference that has been given unequivocally demonstrates the application of Lorentz transformation on Maxwell's equation and so magnetic field is already assumed. Therefore I will delete the false reference in the introduction that claims that magnetism comes from relativity.(217.44.98.235 18:17, 14 July 2007 (UTC))

The material you deleted in the introduction does not claim that magnetism comes from relativity. The first sentence says "According to special relativity, the magnetic field is not a fundamental field but is simply the relativistic part of an electric field when the latter is seen by a moving observer." (emphasis is mine).

Note that this statement is not POV, it is a fact - within the context of STR, the magnetic field does not need to be postulated as a separate entity but is instead, a natural part of a Lorentz covariant force field. This result of STR is cited in numerous text books and papers. You are removing factual and cited material. Please stop. It is the general consensus of the editors of this article that this material is appropriate. Removing this material is not a good faith edit because you are aware of this consensus and have admitted to it. To continue to remove this material is not acceptable. Please stop. Alfred Centauri 19:12, 14 July 2007 (UTC)

You have totally ignored the Hutchinson's reference above just as Starwed ignored the Nelkon&Parker reference. You guys are not promoting general textbook magnetism. You are promoting your own cult POV interpretations of relativity and polluting the magnetic field article with them. I don't know whether you actually believe this nonsense or not, or whether you simply think it is cool. But whatever, you are so wrong. Just take a leaf out of Hutchinson's encyclopaedia and see how an introduction should really be. (217.44.98.235 19:24, 14 July 2007 (UTC))

I'm not totally happy with the article as it stands but I will revert the "Purcell tried to explain..." nonsense if I see it again. And the other stuff you added is unsourced. The Hutchinson's quote above doesn't address the issue at all. Pfalstad 19:33, 14 July 2007 (UTC)

Anonymous, you still don't 'get it'. It's irrelevant what I, you, or any other editor 'believe' or whether we are right or wrong in our beliefs. All that matters, is that the Wikipedia articles accurately reflect the generally accepted understanding of the subject and, if notable, alternative understandings. Please take a look at the user page for EMS57cva to get an idea of how to 'disagree' with the mainstream while being a valuable, welcome, and active Wikipedia contributor. Alfred Centauri 22:29, 14 July 2007 (UTC)

The purpose of the Hutchinson's Encyclopaedia reference was to give an example of how an introduction should look. It is actually very like what I had once written in wikipedia before FizixFighter altered it. It mentions 'Lines of Force' and 'Electric Currents'. The term 'Lines of Force' was fiercely objected to by many wikipedians and I was asked to provide modern citations. Hence I provided a Nelkon&Parker citation which was ignored, and now I have provided the Hutchinson's citation. I could also have provided a 1978 Collins encyclopaedia citation but I didn't copy it down verbatim in the library. It did however refer to 'Lines of Force'. It was 'Lines of Force' that started the whole argument off. I don't see any comment which I ever made that has been unsourced. (217.44.98.235 09:06, 15 July 2007 (UTC)).

The way I would see it now is that the introduction needs to be amended to acknowledge the phenomenon of magnetic attraction, just as the Hutchinson's article does. Magnetic attraction as a phenomemnon was fierceley opposed by certain wikipedians at first. Later they tried to bury it under the vXB force. At the moment, the introduction only mentions the vXB force. I think that this is somewhat misleading. (217.44.98.235 12:19, 15 July 2007 (UTC))

I'm not sure I like "magnetic attraction" since magnetic dipoles aren't attracted to anything in a uniform magnetic field. They just line up with the field. But I agree that the introduction should be accessible. We should mention magnets, not just currents.. I don't think you can accurately describe a magnet or a particle w/ spin using currents. Pfalstad 17:04, 15 July 2007 (UTC)

Pfalstad, I fail to comprehend this fierce resistance to the fact that two magnets pull each other together. It seems to be so politically incorrect. But I agree with you that magnets, and not just electric currents should be mentioned in the introduction. In my introduction, magnets were indeed mentioned. Even FizixFighter allowed them to remain. They have only now just been deleted by an anonymous which wasn't me. (217.44.98.235 21:16, 15 July 2007 (UTC))

Relativity in Electromagnetism

The Lorentz transformation acts on the entire electromagnetic field tensor which already contains the magnetic vector potenial A. It does not act exclusively on the Coulomb force. If you remove the A terms and do the transformation, you will lose the vXB and the vXE results. See this web link, http://hepth.hanyang.ac.kr/~kst/lect/relativity/x850.htm (217.44.98.235 15:46, 15 July 2007 (UTC))

The electromagnetic field tensor does not contain the magnetic vector potential. The Lorentz transformation acts on the four-potential which does contain the magnetic vector potential as the spatial part and the scalar electric potential as the time part (assume natural units here). The Lorentz transformation also acts on the electromagnetic field tensor which is a rank 2 anti-symmetric tensor that is derived from a (loosely speaking) 4D curl operation on the four-potential.

The Coulomb force is not Lorentz covariant so the Lorentz transformation cannot act on it - that's trivial and adds nothing to the debate. The bottom line is this: Without STR, there appears to be no apparent reason for the magnetic field - it simply exists, Within STR however, the magnetic field is required for the Coulomb force (potential) field to be Lorentz covariant. That is, you can't remove the A terms in STR without destroying Lorentz covariance.

Lastly, and for your enjoyment, here are excerpts from the first two physics textbooks I pulled from my home library:

First, an excerpt from the Physics textbook (PHYSICS, 2nd edition, O'Hanian) I used in college physics:

"Hence, we can regard the magnetic force that acts on the particle in any other reference frame as resulting from a transformation of the electric force in the rest frame. In this sense, magnetic forces can be regarded as a consequence of electric forces and of relativity." (pg 1018)

Second, an excerpt from the textbook "Basic Concepts in Relativity and Early Quantum Theory", 2nd edition, Resnick and Halliday"

"One striking result we obtain from relativity is this. If all we knew in electromagnetism was Coulomb's law, then, and by using special relativity and the invariance of charge, we could prove that magnetic field must exist. There is no need to postulate magnetic fields separately from electric fields. The magnetic field enters relativity in a most natural way..." (pg 116)

The emphasis in the above excerpts are mine. As I have said before, it is irrelevant whether you believe these texts to be incorrect, this type of information belongs in the magnetic field article. Alfred Centauri 20:15, 15 July 2007 (UTC)

I certainly don't believe it. Neither do I believe that it is mainstream texbook magnetism even if you can produce some textbooks which promote it. There have been alot of crank papers and texbooks written since the second world war.

Anyway, if you believe it, by all means put it in. But you are aware that this is highly controversial and POV material. Hence it should be restricted to a special section on relativity. I can easily show you that relativity is not needed to account for magnetic fields. I think you and AntiXt and others have got it so wrong. You only have to read nineteenth century papers on electromagnetism. The Lorentz transformation only adds gamma and beta factors to the Galilean transformation. The Galilean transformation and hydrodynamics can adequately account for -(partial)dA/dt and its relationship to both the Coulomb force and the vXB force. I think that you have been fooled big time but that you want to believe it because it all sounds so cool. (217.44.98.235 21:26, 15 July 2007 (UTC))

"But you are aware that this is highly controversial and POV material." LOL. Prove it with citations.

"I can easily show you that relativity is not needed to account for magnetic fields." So can I. But, you've missed the point entirely. It's not that STR is needed to account for magnetic fields, it's that STR requires magnetic fields.

"The Lorentz transformation only adds gamma and beta factors to the Galilean transformation." This is well known - the Lorentz transformation and the Galilean transformation are members of a continuous set of transformations with an invariant speed (a speed that is measured the same by all observers in inertial motion) that can be deduced from just the POR and the homogeneity and isotropy of space and time. The Galilean transform is recovered from this general transform by letting the invariant speed tend to infinity. So, what have you gained by pointing out the obvious?

"The Galilean transformation and hydrodynamics can adequately account for -(partial)dA/dt and its relationship to both the Coulomb force and the vXB force." I'll take your word for it. But again, so what? In the STR, A arises out of necessity for Lorentz covariance. What principle do you invoke to account for the existence of A?

"alot (sic) of crank papers and texbooks (sic) written since the second world war." I'll bet you are referring to much of modern mainstream physics.

"I think that you have been fooled big time but that you want to believe it because it all sounds so cool". Nice try but I'm not taking the bait.

And, once again, what I believe, what you believe I believe and what you believe I choose to believe is utterly irrelevant to Wikipedia. Please remember, Wikipedia is not a soapbox. All that matters is the material in an article is relevant to the subject and is backed by citations from authoritative sources. I've provided two citations that directly contradict some of your claims yet, you have not provided a single citation that directly contradicts the material I've cited. All we have from you is your blustering claims that the other editors of this article are deluded and foolish. Well, you're right - I'm quite foolish to (once again) have spent this much time feeding a troll and also quite deluded to have the faintest hope that you might actually have any valid points to make. Alfred Centauri 23:15, 15 July 2007 (UTC)

Alfred Centauri, right at the top of this section, I provided a citation. That citation shows that the vXB term comes out of a Lorentz transformation purely as a result of the presence of the magnetic vector potential term A in equation (11). (The crucial part of the proof is between equations (17) and (18)). Take the vector A away and you will have a hard job of obtaining vXB from just the electrostatic potential. Here is the citation again, http://hepth.hanyang.ac.kr/~kst/lect/relativity/x850.htm This citation is standard textbook stuff and it very much contradicts those citations that you have given claiming that the Coulomb force alone can produce a magnetic field in conjunction with relativity. All that stuff which you wish to believe is too controversial to take prominence in an article about magnetism for general readership. Take a leaf out of Hutchinson's encyclopaedia. You are obviously obsessed with this false idea that a magnetic field comes from relativity. It is not true, it is not mainstream, and it is not a suitable idea for a general encyclopaedia. It is you, and not me, that is trying to destroy this article with your own pet notions. I am trying to give a balanced picture of magnetism for the lay reader. (217.44.98.235 23:30, 15 July 2007 (UTC))

Mr. 235, you haven't proven anything with your citation. You've just given us a derivation which you've interpreted in such a way that it contradicts what AC has stated (and proven with cites of reliable sources). What you need to do is find a reliable source that says, in so many words, the conclusion you are drawing from that derivation. If there's a controversy, cite a source which discusses the controversy. Shouldn't be hard to find; if a controversy exists, I assume that a lot of people are writing about it. Pfalstad 00:08, 16 July 2007 (UTC)

Feynman Lectures, section II 1-5: "What we are saying, then, is that magnetism is really a relativistic effect.... It is the near-perfect cancellation of electrical effects which allowed relativity effects (that is, magnetism) to be studied...." Pfalstad 00:24, 16 July 2007 (UTC)

Anonymous, I have said several times in different ways that the STR requires an A field for Lorentz covariance and, having asked you find a citation to refute this, the very best you can come up with is the statement "Take the vector A away and you will have a hard job of obtaining vXB from just the electrostatic potential"?. Is that really the best you can do? Is that really what you want to go on record with? As trolls go, you're not very good. We're done here. Alfred Centauri 00:59, 16 July 2007 (UTC)

Alfred Centauri, At least we are now in agreement. STR requires an A field for Lorentz covariance. STR can not therefore be the cause of the magnetic field. The magnetic field is the curl of A. (217.44.98.235 09:39, 16 July 2007 (UTC))

Correct, the magnetic field is the curl of A and the STR isn't the cause of the magnetic field (vector potential) -within the STR, Lorentz covariance is the cause of A'.

On the other hand, in the model you promote, there is no cause for an A field - the A field is inserted into that model in an ad-hoc manner. Perhaps one day, when you grow up, you'll understand the signficance of this. Alfred Centauri 13:34, 16 July 2007 (UTC)

Alfred Centauri, The magnetic vector potential A is the most fundamental of all physical quantities. Its existence is a consequence of the fact that magnetic field lines are solenoidal. It appears in Maxwell's second equation and also in his 1861 paper. Dirac is on record as pointing out that it refers to a velocity. If we take the total time derivative of A we get the radial Coulomb force, the (partial)dA/dt tangential force, the vXB Coriolis force and also the one term that is missing from the Lorentz force ie. the centrifugal force. Maxwell of course used centrifugal force to account for magnetic repulsion. See equation (58) in Maxwell's 1861 paper.

I appreciate that wikipedia is not the place to discuss original research, however, I was not promoting any original research. I was trying to keep the article plain and basic for average readership. It was other elements that were trying to stamp their own pet theories over the top of this article and simultaneously pretend that these notions were mainstream textbook magnetism.

Any attempts to show that these ideas were wrong were immediately countered by demands for citations that would of course only be judged acceptable by the little clique that were promoting this Purcellism. I think that it is you that has got alot to learn about magnetism. You were using wikipedia rules to turn science into a game of academic whist. (217.44.98.235 14:14, 16 July 2007 (UTC))

Wow, that response belongs here: [7]. You don't have the slightest idea how silly that response makes you look, do you? Don't you see? You boldly state that "A is the most fundamental of all physical quantities" and then turn right around and state "Its existence is a consequence of the fact that magnetic field lines are solenoidal". So tell my anonymous, if A is the most fundamental physical quantity and yet owes its existence to the character of the magnetic field, then to what honor does the magnetic field rise? Double secret most fundamental physical quantity? Honest-to-gosh-no-kidding-this-time most fundamental physical quantity?? You know, it seems that the more you reply to me, the sillier you appear. Do you really want to continue this? Alfred Centauri 15:13, 16 July 2007 (UTC)

Alfred Centauri, div B = 0 means that B is solenoidal and that there exists a vector A such that curl A = B. I challenge anybody to derive A from any other physical quantity.(217.44.98.235 18:55, 16 July 2007 (UTC))

I think you two are talking past each other. Mr. 235, you seem to have the impression that we are claiming that Maxwell's equations can't be derived without using the Lorentz transformation and/or STR. Obviously not. When Feynman makes the statement that magnetism is a relativistic force, he points to the fact that Maxwell's equations were relativistically correct when formulated. So, a nonrelativistic electromagnetic theory doesn't exist. Pfalstad 19:53, 16 July 2007 (UTC)

Pfalstad, I have studied Maxwell in detail and I can assure you that there is not the remotest trace of relativity in his works. Can you please point out where I should find the gamma and beta factors of the Lorentz transformation anywhere in Maxwell's original papers. Maxwell's works are not even close to Einstein's works despite Einstein's claims that he was influenced by Maxwell's equations. Maxwell had a sea of molecular vortices. Where do we find that in relativity?(217.44.98.235 10:10, 17 July 2007 (UTC))

Anonymous, repeating what is well known does not resolve your contradictory statements. Let's review:

You said: "A is the most fundamental of all physical quantities"

You said: "Its existence is a consequence of the fact that magnetic field lines are solenoidal"

The first says that A is fundamental, the second says that B is fundamental. Your statements contradict each other. How do you explain this? Alfred Centauri 20:16, 16 July 2007 (UTC)

Sirs: Mr Centauri, you are wrong because there does appear in the scientific journals a discussion which has gone on for a rather long time. It has never been resolved. Textbook writiers who have made the claims which you cite as valid mainstream have been refuted in the literature. The Purcell model has been challenged and there are textbook writers who eshew statements of the kind which you are using to support your opinion. It appears that the textbooks which you cite are merely expressing a scientific opinion and other books do not agree on this point.

To the anonymous poster that failed to sign the comment above, your first statement is that I'm wrong. Wrong about what? That mainstream physics textbooks assert that the STR, Coulombs law, and the invariance of electric charge imply magnetic fields must exist? The citations I gave refute that quite handily. You make the bold statement that such assertions have been refuted in the literature, yet you provide not one example. Refuted is a strong term. Are you prepared to support this? Do you understand the difference between refuted and challenged or questioned? If, as you say, it has never been resolved, how can you say an assertion has been refuted.

So, here is a challenge for you. Please refute the statement "the STR, Coulombs law, and the invariance of electric charge imply magnetic fields must exist". Alfred Centauri 20:58, 16 July 2007 (UTC)

Alfred Centauri, I don't want to get dragged into a scientific debate, because I'm likely to be bombarded with requests for citations which will almost certainly be summarily dismissed on the grounds that I am only giving my own interpretations of these citations.

However, I will leave you with something to think about. In hydrodynamics, curl v = Ω, where Ω equals vorticity and where v equals velocity field. Which is more fundamental? Vorticity or velocity? Likewise with A and B. (217.44.98.235 10:04, 17 July 2007 (UTC))

This is not a debate. Your statements contradict each other. Don't you see? If, as you say, A is the most fundamental physical quantity, then it exists... period. It doesn't exist as a consequence of anything else because if some other phenomenon must exist for A to exist, then A is not fundamental. This is not a deep scientific or philosophical point here.

You contradicted yourself, I called you on it, and the best response you can come up with is "I don't want to be dragged into a scientific debate..." Hogwash!

But then it gets worse. Your final paragraph seems to imply that you don't believe that A can be any more fundamental than B or that B can be any more fundamental than A. More hogwash.

I will answer your question to me as follows: is it not true that in a region where Ω is zero, v may be non-zero? Is it not also true that in a region where v is zero, Ω must be zero? Then, would it be proper to say that vs existence is a consequence of the fact that vorticity field lines are solenoidal? I will leave you with that to think about. Alfred Centauri 13:14, 17 July 2007 (UTC)

Mr Centauri, I dont need to refute a statement which was never proved to begin with. You produce the proof. You are making the claim that magnetism should be considered a relativistic effect. It is your duty to prove it is true. While you are about that, please explain why advanced magnetism textbooks don't make this claim, but instead claim that magnetism is a quantum mechanical effect. So which is it? Is magnetism a relativistic or quantum mechanical effect? I would really like to know the answer. The claim which you support only appears in elementary physics textbooks, not advanced ones, and certainly not in any books on the physics of magnetism. So why are you introducing such a confusing subject here?

Furthermore, the statements cited from the textbooks given above don't make any sense. Your conclusion that magnetism is a relativistic effect doesn't follow form the quotations given. They are rather vague unsupported assertions that only imply that magnetism might be cosidered a relativistic effect under certain conditions. You need to explain this in detail, so that any statement made in the article will be clear to the reader and not confusing to him.71.251.188.73 13:56, 17 July 2007 (UTC)

Mr anonymous2, you said "You are making the claim that magnetism should be considered a relativistic effect." No, that is incorrect. You and anonymous just keep making the same mistake over and over and over. The claim I've made here (and please, try to pay attention this time) is that mainstream textbooks make a claim and thus this information belongs in this artice.

Why is it so hard for you to understand this? Do you have trouble understanding the difference between my claim and what you claim I claim? Ok then, let me state my claim again:

I claim that mainstream physics texts assert that the STR, Coulomb's Law, and the invariance of electric charge imply magnetic fields must exist.

Now, in your 'rant' above, you said that I "claim that magnetism should be considered a relativistic effect" - you are wrong. You also said "It is your duty to prove it is true" - you are wrong again since I did not make that claim. So, please explain to me how you could be so wrong here.

Didn't you read my commments where I said "it is completely irrelevant what I believe... - all that matters to Wikipedia is that the material is relevant to the subject matter and is verifiable from authoritative sources". Do you understand this? Would you like for me to explain to you a little slower?

Now, let's look at something you claimed: "Textbook writiers who have made the claims which you cite as valid mainstream have been refuted in the literature." Now, this is your claim. I didn't make, you did. I asked you to support it. You have yet to provide a single citation or outline of such a refutation. This isn't my job to do this. It is your claim and you must support it or withdraw it. Your choice. Alfred Centauri 14:35, 17 July 2007 (UTC)

You didn't answer the questions I posed. In any event, the claim which you are using to justify inclusion in this article is contradicted by the fact that advanced magnetism books do not support it. It appears only in elementary level physics texts. So it it not exactly mainstream as you claim.71.251.188.73 14:48, 17 July 2007 (UTC)

OK, I will answer the questions that you posed and then you'll provide support for your claims, right? (I'll believe it when I see it).

Question 1: "please explain why advanced magnetism textbooks don't make this claim, but instead claim that magnetism is a quantum mechanical effect"

Answer 1: 'Magnetism' is a quantum mechanical effect - magnetic materials are have net magnetic fields because of quantum mechanical effects such as spin spin coupling. Nice try but you are comparing two related but different things. Why some materials are magnetic and others are not requires a quantum mechanical analysis. This is a different problem from why there is a magnetic field associated with moving charge. You do understand the difference don't you?

Question 2: "So which is it?"

Answer 2: 'Magnetism' is a quantum mechanical effect.

Question 3: "Is magnetism a relativistic or quantum mechanical effect?"

Answer 3: 'Magnetism' is a quantum mechanical effect.

Question 4: "So why are you introducing such a confusing subject here?"

Answer 4: What confusing subject have I introduced? (Make sure you can support your answer)

There, I've answered you questions. Now, please support your claim that "Textbook writiers who have made the claims which you cite as valid mainstream have been refuted in the literature." with authoritative references or withdraw it. Alfred Centauri 15:12, 17 July 2007 (UTC)

Magnetism Magnetic fields as an STR effect as Alfred Centauri has described above can be found in Jackson's "Classical Electrodynamics", which is hardly an elementary level physics text - it's a graduate level university text. What advanced texts on magnetism do not support this? --FyzixFighter 15:05, 17 July 2007 (UTC)

Anonymous2 is playing with words. He has apparently tried to dispute the claims of textbooks that the magnetic field is implied by the STR with the claim that magnetism, the alignment of the magnetic dipoles in magnetic materials, is a quantum mechanical effect. Just plain silly. Alfred Centauri 15:20, 17 July 2007 (UTC)

Ah, I see the game of semantics now - editing my own comment to be more specific. Thanks AC. --FyzixFighter 15:24, 17 July 2007 (UTC)

Your answer is that magnetism is a quantum mechanical effect. So that should be included and the reference to relativity should be deleted. Thank you for clarifing this tricky point. By the way. My copy of The Encyclopaedia Of Physics doesn't say anything about magnetism as a relativistic effect. So it is not mainstream.71.251.188.73 15:41, 17 July 2007 (UTC)

Magnetism is indeed a quantum mechanical effect. But article we are discussing here is about magnetic field, while there is separate article about magnetism. Please notice the difference. Magnetic field is relativistic effect and this fact should be accessible to the reades. --antiXt 16:27, 17 July 2007 (UTC)

I am sorry, but I thought you were serious. You are saying that magnetic field is a relativistic effect and magnetism is a quantum mechanical effect. That doesnt make it any clearer for me to understand and I doubt the reader will understand it. My copies of Electrodynamics and Classical Theory Of Fields and Particles by Barut, and Electrodynamics by Sommerfeld don't cite magnetic field as a relativistic effect either. Tried to find it in Electromagnetism and Relativity by Cullwick. But not there. Also not in Electrodynamics of Continuous Media by Landau et. al. Still not mainstream. Not in Classical Electricity and Magnetism by Panofsky and Phillips. I am still looking for that claim in an advanced physics textbook.

71.251.188.73 16:45, 17 July 2007 (UTC)

It's considered appropriate to read a discussion before joining it. Right at the beginning of this section are two instances where physics textbooks support the claim. --Starwed 16:53, 17 July 2007 (UTC)

Anonymous2, anyone older than 13 or so can see that you are acting childish. Your responses don't even have the pretense of being serious. Let's review them:

"Your answer is that magnetism is a quantum mechanical effect. So that should be included and the reference to relativity should be deleted." Do you really think so? Is this the kind of response a serious person gives? When do you plan to grow up?

"My copy of The Encyclopaedia Of Physics doesn't say anything about magnetism as a relativistic effect. So it is not mainstream." Geeeezzzz... This one is even worse. Do you have any idea just how silly your remark is? Do you have any idea just how foolish you appear? How could you think that this is makes your case? Just how old are you?

One last thing: I answered your questions but you still have not provided a single authoritative reference to support your bold claim that "Textbook writiers who have made the claims which you cite as valid mainstream have been refuted in the literature." Do you ever plan to offer any substantiation of this claim? If not, do you plan to withdraw it? Oh, who am I kidding. You're just a juvenille. Of course, you won't, you're not mature enough to do that.

Unless and until you provide authoritative support for you claim, I shall not discuss anything further with you. Alfred Centauri 17:10, 17 July 2007 (UTC)

Starwed, anonymous2 also missed this:

And finally, here is an excerpt from the preface to the original edition of the textbook "Electromagnetics" by R. S. Elliot [8]:

This alternative retains the scope of the senior-graduate sequence but begins with a study of special relativity. With this as a basis, it is possible to develop all of electromagnetic theory from a single experimental postulate founded on Coulomb's law. An enriched understanding of magnetism results, and the Biot-Savart law is a consequence rather than a postulate. The Lorentz force law is seen to be a transformation of Coulomb's law occasioned by the relativistic interpretation of force. Upon accepting the Lorentz force law as fundamental, one is able to derive Faraday's emf law and Maxwell's equations as additional consequences. This procedure provides the further satisfaction of demonstrating that the fields contained in the Lorentz force law and in Maxwell's equations are one and the same, a conclusion not possible in the conventional development of the subject.

Alfred Centauri 13:15, 3 May 2007 (UTC)

This textbook is at the senior graduate level so, I presume, is advanced enough for anonymous2. Alfred Centauri 17:27, 17 July 2007 (UTC)

This doesn't say anything about magnetism being a relativistic effect. At the very least you could cite a specific proof from this book to support your claim and show it here.71.251.188.73 18:32, 17 July 2007 (UTC)

For a nice, straight-forward proof I'd recommend pp. 522-525 of Griffiths' "Introduction to Electrodynamics" (a upper division undergrad university text). He prefaces the proof with the following quote:

"To begin with I'd like to show you why there had to be such a thing as magnetism, given electrostatics and relativity, and how, in particular, you can calculate the magnetic force between a current-carrying wire and a moving charge without ever invoking the laws of magnetism."

Which, while not as broad or formal, agrees with the quote that Mr. Centauri put above that states that all you need are Coulomb's law and special relativity to derive the whole of classical electromagnetic theory. However, it is not for us to provide proofs here - take that to a discussion board. It is enough for us to provide reliable sources, which has been done so many times with non-elementary, mainstream university textbooks that I've lost count (Griffiths, Jackson, Elliot, Resnick and Halliday, Page...). Therefore the STR aspect of the magnetic field stays in the article and will not be relegated to a fringe theory. --FyzixFighter 23:08, 17 July 2007 (UTC)

And just had a brief jaunt over to the library. Both Cullwick and Sommerfeld show how the magnetic force (and therefore field) can be derived using just special relativity, charge invariance, and Coulomb's Law. E.M. Purcell's "Electricity and Magnetism" (1985) explicitly makes the claim that the magnetic force and magnetic field no longer need to be a observation-based postulate of E&M, but become derived concepts based on the STR, Coulomb's Law, and charge invariance. Some of the other books anon2 mentioned do the same, stating rather that the electric field and magnetic field are the same entity (the electromagnetic field), which split differently depending on the frame of reference. Also, it depends on which "Encyclopedia of Physics" you check. Lerner and Trigg's "Encyclopedia of Physics" states (on page 1057 of the 1991 2nd edition) that a magnetic field is a "derived" effect of special relativity. And my favorite (after being led to it from the Elliot pdf above) is L. Page's 1912 paper "A Derivation of the Fundamental Relations of Electrodynamics from Those of Electrostatics". --FyzixFighter 01:09, 18 July 2007 (UTC)

After anonymous2 rattled off that list of textbooks, my first thought was "anonymous2 doesn't have all those textbooks". Now, you've shown that anonymous2 is, shall we say, less than truthful. Well done. Alfred Centauri 02:18, 18 July 2007 (UTC)

More on the Hutchinson's Encyclopaedia Article

I appreciate that wikipedia can not very well use the Hutchinson's introduction verbatim. But it is nevertheless a matter of interest to examine how mainstream encyclopaediae are balancing the complex issue of the magnetic field for a layman readership. Yesterday, I copied out the first part of the Hutchinson's article. See above.

As a matter of curiosity, I will now copy out the article in full as an illustration of how to word an article for the benefit of lay readership.

Magnetic Field. Physical field or region around a permanent magnet, or around a conductor carrying an electric current, in which a force acts on a moving charge or on a magnet placed in the field. The field can be represented by lines of force, which by convention link north and south poles and are parallel to the directions of a small compass needle placed on them.

It's magnitude and direction are given by the magnetic flux density, expressed in teslas.

Experiments have confirmed that homing pigeons and some other animals rely on their perception of the Earth's magnetic field for their sense of direction, and by 1979 it was suggested that humans to some extent share this sense. (217.44.98.235 16:27, 15 July 2007 (UTC))

Regarding "lines of force"

Sometimes term "lines of force" is used instead of "field lines". However, this can generate confusion that there is force that is direction of that vector field. I suggest changing "lines of force" with more correct term "field lines" anywhere where there are no forces in direction of the field. And by "force in direction of the field" I mean the force that is some scalar (which don't have to be constant) multiplied by the vector of that field. This is not the case with magnetic field, so applying the term "lines of force" is not appropriate, it would be much better to use "field lines". Or, if more precise term is requied: "lines of alignment of magnetic dipoles".

And there are really no forces in direction of B. There are only $q\mathbf {v} \times \mathbf {B}$ for moving charges (and electric currents as well) and $\nabla (\mathbf {m} \cdot \mathbf {B} )$ for magnetic dipoles. And none of them is in direction of B. And I don't understand why did some pro-"lines of force" anons capitalize term as "Lines of Force". Looks a bit cranky to me. --antiXt 18:36, 15 July 2007 (UTC)

AntiXt, we've been over all this before. Two magnets pull together in the direction of the field lines that join them. It's as simple as that.

The term was good enough for Faraday and it exists in modern sources. I don't see what your problem is. There seems to be a cult that wants to shy away from the fact that two magnets can attract or repel each other. (217.44.98.235 21:11, 15 July 2007 (UTC))

We should use the terms that physicists use, not invent new ones for wikipedia (like "lines of alignment of magnetic dipoles"). If "field lines" is preferred in the literature, use that. If "lines of force" is used sometimes, it might be useful to mention that too, with appropriate caveats. Pfalstad 00:32, 16 July 2007 (UTC) Mr 235, Re "Two magnets pull together in the direction of the field lines that join them," Enormousdude gave you at least one counterexample above and your response was pretty content-free. Also, a magnet in a uniform field does not feel any attraction towards whatever is generating the field. It's not "as simple as that". Pfalstad 00:49, 16 July 2007 (UTC)

Pfalstad, it wasn't me that suggested the term "lines of alignment of magnetic dipole". I actually intervened because of such terms. I was trying to get things looking more like a normal encyclopaedia. On that other other point, I think you were pushing it to suggest that I was merely giving my own interpretation of the reference that I provided. That suggestion could easily be used in reverse any time that somebody provides a citation. It only takes a little clique of fanatics to call trumps on interpretations. I was pointing out the rather obvious fact that the vXB term in the final result was totally dependent on the presence of A terms between equations (17) and (18). You are pushing it to doubt that fact on the grounds that it is only my interpretation.

Also, you can't be serious when you are challenging me to prove with citations that this issue about the magnetic field being the relativistic component of the electric field is controversial. The entire subject of relativity in general is highly controversial and has been since its foundation. A google search will bring up no end of literature written by anti-relativists. Whether you agree with them or not is irrelevant. But it is quite pathetic for you to sit there and claim that there is no controversy. Didn't Professor Herbert Dingle write a book away back in 1972 'Science at the Crossroads'? That was only the tip of the iceberg. Tesla never agreed with Einstein's theories. There is no end of controversy on this issue.

I wasn't even criticizing relativity anyway. I was merely criticizing the claim that magnetism is a relativistic effect. I actually showed you further up the page that the link between vXB and -(partial)dA/dt is a Galilean transformation. I showed you reliable Maxwellian sources proving that Maxwell already had vXB when Lorentz was still very young.

You have got to ask yourself whther you want this article to be about the Magnetic Field, or do you want it to be a vehicle to promote a cult theory that stems from relativity and is being supported by obsessed fanatics. (217.44.98.235 09:59, 16 July 2007 (UTC))

Random crank websites aren't reliable sources. Anti-relativists are not in the mainstream. Please find a reputable source (emphasis on reputable) that make the specific claims you are making. We have found many reliable sources that say magnetism is a relativistic effect. I'm not interested in reading your proof that it is not. Even if it's correct (which it's not) it's original research. (Your claim that magnetism can't be relativistic because it was discovered before relativity is mistaken. Read the Feynman Lectures reference I gave you above to see why.) Pfalstad 17:21, 16 July 2007 (UTC)

Pfalstad, I think you have missed the point here. I am not criticizing relativity itself. I'm critizing the notion that magnetism is a relativistic effect. I showed you yesterday, from a mainstream source, that vXB arises from a Lorentz transformation provided that A is already assumed. You then turned around and claimed that this was only my own interpretation. Did you not see all those A's between equations (17) and (18)?

I also cited three modern mainstream sources that mentioned lines of force. Today, I noted in the library that the Oxford Pictorial Dictionary and the Encyclopaedia Britannica (Micropaedia) both use the term lines of force for magnetic fields.

If you look up Maxwell's 1861 paper and follow through from equation (58) to equation (77), you will see how he derives the Lorentz force from A as a fundamental quantity.

We'll have to agree to differ on the issue of whether or not magnetism is a relativistic effect. I altered the introduction recently to bring it more into line with what I had learned about magnetism at university but my alterations were immediately reverted by persons anonymous (with usernames) who seemed to take offense at the term 'lines of force' and at the mention of electric currents and bar magnets. It became obvious to me that attempts were being made to eclipse the full picture of the magnetic field and to delete magnetic history prior to 1905 and to claim the erroneous theories of Rosser/Purcell for Einstein. Faraday's lines of force, Maxwell, and Tesla were to be written out completely.

Relativity is indeed as you say, mainstream science. But at least try to interpret it correctly. I did advanced courses in relativity at university but the idea that magnetism was a relativistic effect was never suggested to me until I read wikipedia recently. I have known for years that vXB can be derived from a Lorentz transformation.

Re magnetism being a relativistic effect, it's not my interpretation, it's the interpretation of several reputable sources. I don't care how many A's there are between (17) and (18). Re lines of force, I was partially agreeing with you above, when I said that we should use whatever terms are in common use rather than making a judgment on which is more correct. Pfalstad 19:32, 16 July 2007 (UTC)

The claim that magnetism is a relativistic effect is questionable physics. It is an opinion that has appeared in textbooks since 1960. The claim has generated controversy, and has never been clearly established by any proof that can withstand criticism. In the textbooks cited above it was based upon a questionable model that was the subject of criticism in the scientific journals. It appears in elementary textbooks where the required rigor to prove it is absent. 72.84.72.48 20:35, 16 July 2007 (UTC)

Sources? Pfalstad 20:41, 16 July 2007 (UTC)

Magnetic Vector Potential A is the most Fundamental of all Quantities

Alfred Centauri, the fact that magnetic field lines are solenoidal means that div B = 0. It therefore follows that there must exist a vector A such that curl A = B. Maxwell used this vector A to derive the entire Lorentz Force. A is therefore the most fundamental of all physical quantities. It is the parent quantity for both vXB and the Coulomb force. If you would study the hydrodynamics of Maxwell's sea of molecular vortices it might help you to visualize the set up. (217.44.98.235 22:05,17 July 2007 (UTC))

Anonymous, let's review your contradictory claims that you just repeated for all to see:

(1) You said "Magnetic Vector Potential A is the most Fundamental of all Quantities"

(2) You said "... magnetic field lines are solenoidal means that div B = 0. It therefore follows that there must exist a vector A..."

(1) claims A exists period. No need to rely on the existence and character of anything else. That's what " most Fundamental of all Quantities" means. If you believe "most Fundamental of all Quantities" means something else, then please explain to me what you think it means.

(2) claims that A exists because B exists and is solenoidal. But, if this is true, A cannot be the "most Fundamental of all Quantities"

Anonymous, didn't you read my response to you regarding the example you gave to 'enlighten' me? If not, I'll repeat it here:

You said: "However, I will leave you with something to think about. In hydrodynamics, curl v = Ω, where Ω equals vorticity and where v equals velocity field. Which is more fundamental? Vorticity or velocity? Likewise with A and B."

I said: "I will answer your question to me as follows: is it not true that in a region where Ω is zero, v may be non-zero? Is it not also true that in a region where v is zero, Ω must be zero? Then, would it be proper to say that vs existence is a consequence of the fact that vorticity field lines are solenoidal? I will leave you with that to think about."

So, once again, how do you explain your contradictory statements?

No Alfred Centauri, A doesn't require the existence of B in order to exist. Velocity doesn't require the existence of vorticity in order for itself to exist.

However, when we know that vorticity does exist, we also know that velocity must exist.

From div B = 0, we can deduce that A must already exist.217.44.98.235 09:49, 18 July 2007 (UTC))

Mainstream Encyclopaediae

Most mainstream encyclopaediae use the term 'Lines of Force' for magnetic field lines. Most of them talk about magnetic fields as lines of force in the region surrounding bar magnets and electric currents. Some of them also mention moving charged particles as well as electric currents.

None of the mainstream encyclopaediae mention relativity in connection with the magnetic field. None of my university EM textbooks claimed that magnetism is a relativistic effect. I have however read textbooks that claim that ferromagnetism is a quantum mechanical effect.

So when a group of editors are fanatically trying to suppress the mention of lines of force, and the fact that magnets attract each other, and the fact that electric currents cause magnetic fields, we need to ask why. What are they trying to hide? And they were indeed trying to suppress these basic ideas. Even right now on the main article, they are incapable of heading a section by the simple title 'Magnetic Field Surrounding an Electric Current'. Instead, they have to quibble about whether to say 'Current flow of charges' or 'Current of charges'. This is political correctness gone mad in science. Just as political correctness forced the Police Force to be renamed the Police Service, we'll soon be seeing them referring to 'lines of force' as 'lines of service'.(217.44.98.235 22:23, 17 July 2007 (UTC))

Anonymous, you are making a mountain out of a molehill. And don't forget, it is you that have been deleting sections from the article that are supported with citations from authoritative sources. Why are you trying to suppress this idea? Let's look at some of your claims:

You said "None of the mainstream encyclopaediae mention relativity in connection with the magnetic field." That's a bold statement. Prove it.

You said "None of my university EM textbooks claimed that magnetism is a relativistic effect." So? My university textbooks do mention it.

But, it gets much worse:

You said "So when a group of editors are fanatically trying to suppress the mention..., [of] the fact that magnets attract each other" ?????? You've got to be kidding! Please provide evidence of this preposterous claim.

You said "So when a group of editors are fanatically trying to suppress the mention..., [of] the fact that electric currents cause magnetic fields"  ?????? You've got to be kidding! Please provide evidence of this preposterous claim.

Anonymous, you've made some preposterous claims in your rant. Until you withdraw this nonsense and apologize to the editors you have impugned, I will have no further discussions with you. Alfred Centauri 22:58, 17 July 2007 (UTC)

Some editors have been writing in overnight claiming to have found sources which say that magnetism can be derived directly from Coulomb's law, charge invariance, and relativity. I would fully believe their claims because I have a similar source right in front of me now. Contrary to what I said yesterday, one of my university textbooks does indeed mention this idea. 'Electromagnetism' by I.S. Grant and W.R. Phillips deals with this issue in a special section entitled 'Electromagnetism and Special Relativity' at the very end of the book.

It says on page 460 "Accepting charge invariance and conservation, what else do we need to know? If we start with Coulomb's law for the force between stationary charges, is it possible, by using arguments based on relativity, to deduce the laws of magnetism?"

It then goes on to say,

"The answer to this question is that although a rigorous deduction is not possible, it can be made very plausible that the laws embodied in Maxwell's equations represent the simplest conceivable generalization of Coulomb's law which is consistent with relativity."

This is hardly a basis for deciding that this is a mainstream idea which ought to take prime place in an article about magnetic fields for lay readers. Why not take a leaf out of the mainstream encyclopaediae and drop the controversy altogether, or at least relegate it to the relativity section.

I know that none of you are ever shy to make it quite clear that you hold any of my opinions in total contempt, and that you don't consider my opinions to be in the least bit of any importance.

Nevertheless, I will point out that the attempted proof which follows in this textbook and states "the search is made considerably easier by the fact that we know the answer beforehand" is in total contradiction of Purcell's 1963 version of the same proof. Purcell depends on the fact that charge density is altered due to selective application of the Lorentz-Fitzgerald contraction. This textbook operates on the basis that charge density must be conserved.

The common factor in the two proofs is that they both convert Coulomb's law into the Biot-Savart law. In Grant&Philipps, the method used is to arbitrarily extend the charge density term in Coulomb's law to include a current density term with the correct coefficient needed to make it commensurate with the Biot-Savart law. The basis of this extension is the fraud in the derivation. It is based on the idea of playing about like a child with the three components of current density within a symmetry matrix, all disguised under big words such as 'Four Vector'. (217.44.98.235 10:12, 18 July 2007 (UTC))

Article hard to read

This is hard to read because every time B or H is referred to in the text, the math tag is used, making the letter huge. —Preceding unsigned comment added by 71.112.193.232 (talk) 08:28, 29 February 2008 (UTC)