Talk:Faraday's law of induction/Archive 1

Induction from a telephone line?

I'm in a debate with a friend, it's a dumb debate but it hinges on electrical inductions.

Scenario:

You have a live telephone wire running from point a to b, if you were to take the speaker wire of a stereo, wrap it around the telephone wire a number of times would the resulting magnetic field created by the current running to the speaker affect the current in the telephone line in such a way that the audio would be transferred to the telephone line? Assuming you have enough power and coils to make an audiable sound. —Preceding unsigned comment added by 66.222.232.190 (talk) 09:16, 5 May 2004 (UTC)

Probably not, as the phone line is balanced so what gets induced in the phone line is a common mode signal that the phone wont respond to. And what you would want anyway is for the audio wire and the phone line to be wound together round an iron core of some sort to act as a transformer.

You may get a small amount of audio on the phone but this is only because the phone line will not be completely balanced. Does that answer your question? Light current 00:54, 10 August 2005 (UTC)

I don't see what the balancing has to do with this. Faraday's law ensures the current induced by the speaker wire is balanced. You would wrap the speaker wire around one wire of the pair of telephone wires. With enough wraps and enough power, this would indeed transmit the sound over the telephone. Bryan Henderson 20:25, 7 October 2007 (UTC)

Merge induction loop here

The info from induction loop should be merged here. Rich Farmbrough 15:50, 24 Mar 2005 (UTC)

Sign of induced emf

It says e = - N dphi/dt So what happens if you connect the voltmeter to the coil the other way round? Do you then get e = + N dphi/dt ?? If so, why does it not say this, and remove the minus sign. After all the connections to the inductor are not defined in Lenz' law are they (or are they). Can anyone explain this apparent anomaly?? Light current 00:47, 10 August 2005 (UTC)

When a current loop creates a magnetic flux, the direction of the flux is given by the right hand rule (Ampere's law). The relevant equation has no minus sign in it. When a changing magnetic flux induces a current (Faraday's law), the current flows in the opposite direction to that given by the right hand rule, because of Lenz's law. This is the origin of the minus sign. You could redefine the polarity of one of the fields to get rid of the minus sign from the Faraday/Lenz equation, but you would then be asking why there's a minus sign in the Ampere equation. You can't get rid of the minus sign from both equations without being inconsistent.

To go back to your voltmeter example, you should, if you are being really careful, decide which way to connect the meter by inspecting the direction of the inductor's windings. In this sense, yes, Lenz's law does specify which way to connect the meter. --Heron 12:44, 10 August 2005 (UTC)

I hope my reply to your comment below will answer this. --Heron 20:16, 13 August 2005 (UTC)

I remember reading somewhere that the voltage across any inductor is proportional to the "rate of change if flux linkages" (which is putting into words the equation e = + Nd(phi)/dt). So, if the flux is increasing (ie d()/dt is >0) then the voltage will be 'positve' if you have connected the meter +ve lead to the end of the coil that appears to progress clock wise away from you). If the flux is decreasing, (ie d()/dt <0), then the voltage reading on the meter (still connected the same way) will be negative. Before I move on further, do agree with these statements? Light current 10:51, 13 August 2005 (UTC) Just reread your explanation, Heron, and it seems to me that the direction of the voltage across the inductor depends on where the flux is generated. If it is generated from outside, than according to Lenz law, the Voltage will be - Ldi/dt (or-NdØ/dt). However, if it generated by the coil itself, because of an applied voltage (+e say,) then the coil generates a reaction (some people call this the back emf)to this applied voltage which is in the opposite direction to the applied voltage but which still obeys Lenz law. If the coil did not generate a reaction, then there would be no inductance I suppose. Is that where I have been going wrong? Can you comment on this explanation please?Light current 19:17, 13 August 2005 (UTC)

No, I don't. [This isn't the non-sequitur that it first seems. I wrote it in response to Light current's question of 10:51, but then our comments got reordered. --Heron] First of all, 'voltage is proportional to rate of change of flux linkage' is equivalent to the equation $e=k\,N\,d\Phi /dt$, where k could be either negative or positive, so the + sign you put in your equation was unjustified. Second, you forgot to say in which direction the magnetic flux is pointing while it is increasing. Without this information, I can't say which polarity your voltmeter will read.

This diagram shows what I mean. The magnetic flux B is pointing away from us and increasing (hence ${\dot {B}}>0$ in the direction of the arrows). By the right-hand rule, current would flow clockwise in the coil, but Lenz's law reverses this, making the current flow anticlockwise. (I used this reference to check that my use of the right-hand rule is correct.) The anticlockwise current therefore leaves the coil towards us, in the direction of the arrow labelled I. It then flows round the circuit in the direction shown. (I added a resistor just to help me work out which end would be positive and which negative.) So, if you put the + terminal of your voltmeter on the end of the inductor nearest us, you will get a positive voltage.

P.S. You made no reference to my answer to your first question. Was it that bad? --Heron 20:13, 13 August 2005 (UTC)

Yes I do believe in Lenz' law. It was just that I could not see why it seemed to be violated when the source of flux was the coil itself.(ie V= +Ldi/dt) Light current 20:44, 13 August 2005 (UTC)

All of this arguing about the sign of the voltage in the Faraday's law equation is a bunch of bullcrap. That sign is 100% arbitrarily a plus or a minus, and it depends on the direction in which the voltage measurement is made - such as which of the two possible directions of a voltmeter is chosen.

You can believe me: Bachelor of Engineering, Auburn University, and Master of Science in Electrical Engineering, Georgia Institute of Technology (Georgia Tech). We electical engineers know all about assigning signs to voltages and currents. As evidence, consider our massive technology of electricity and electronics, none of which would work withough the correct signs in electrical analysis. 98.67.168.183 (talk) 01:47, 30 June 2009 (UTC)

I agree. Of course, it's possible to say what the convention is for the sign of EMF, and the sign of $\Phi _{B}$, and then one of the signs will be correct and one will be incorrect. But for this article I think the better bet is to just say "signs are determined by Lenz's law".

I put in absolute value signs to make it clearer that the equation isn't asserting that the + sign is correct (or incorrect). --Steve (talk) 05:27, 30 June 2009 (UTC)

Equation Errors?

If the first equation is correct, ane 'e' is the emf AND 'U' is also the emf, where has the 'N' gone from the second equation. I dont understand this. Any body who does??Light current 15:36, 13 August 2005 (UTC)

One was the general case, one was a special case. I revised the text and math to make it clearer Salsb 16:44, August 13, 2005 (UTC)

Yes, thanks. It makes more sense to me now. Apart from the (age old?) discussion (above) about the minus sign( ie why is it E = + Ldi/dt for an inductor ). Would you be able clear up my lack of understanding on this on this please? Light current 17:01, 13 August 2005 (UTC)

I am not sure what you mean, as ε=-LdI/dt, where ε is the self-inductance.

Capacitor Equivalent of Lenz's law

As a capacitor is the dual of an inductor,there must be an equivalent law to 'Lenzs law' that applies to a capacitor in an electric field with changing electric flux (density). Does anyone know what this law is called.?(if there is one). Light current 20:48, 14 August 2005 (UTC)

At the risk of appearing completely stupid, I am going to attempt to make up my own version of what should be an equivalent to Lenz's law for inductances but applied to capacitances. If a (parallel plate) capacitor is subject to a changing electric flux (density)(D=E€), then the capacitor will have a current induced in it that will tend to oppose this change of flux. Now this law is equivalent to saying that you can't change the voltage on a cap instantly (we all knew that). This law I intend to call temporarily 'Light Current's Law' (for want of a better name). Some people may wish to point out that all I'm doing here is restating one of Maxwell's Laws. Please do so. I'm just wondering why this law is not usually quoted in words similar to above. If any one has heard this wording before, please let me know.

Some people may want to call the induced current a 'back current'. Please dont! So the new law states in other words that i = -C dD/dt = -C dv/dt. where i is the induced current. In the case of a capacitor being charged from a constant current source, this induced current is actually the same as the current from the current source and the two currents cancel out because no current can flow between the plates of a capacitor (can It??)

I will be MOST interested to hear from anyone who has any views on this argument whether for or against.Light current 18:15, 15 August 2005 (UTC)

What has been quoted appears to be Maxwells term for displacement current but I'm not sure if the sign is correct. The induced current should oppose changes in flux (density) according to Neumanns law. 80.45.215.113 14:22, 18 August 2005 (UTC)

Yes , thanks. Ive just found Neumanns law in a book on Electromagnetic field theory. He was a contemporary of Faraday apparently. In Neumanns equation, he says that ALL induction phenomena can be quantitively expressed by the equation e = - d(phi)/dt where phi is the total magnetic flux. THe question is, does this equation also apply (with the minus sign) to induced currents in a capacitor due to changing electric fields??Light current 15:43, 18 August 2005 (UTC)

'LC': I'm going to go out on a limb here and do a thought experiment. If two conducting plates are connected by a resistor and this apparatus is immersed in a uniform electric field that is changing in intensity, charge will flow through the resistor from one plate to the other in order to cancel any electric field between the plates. Imagine that one plate is 'higher' than the other and that the electric field is directed 'downwards'. Further, assume that the field is increasing at a constant rate. This should cause a constant current from the top plate through the resistor to the bottom plate implying a constant displacement current 'up' from the bottom to the top plate. This constant displacement current produces a constant magnetic field but a constant magnetic field does not produce an electric field! Thus, there is no 'back reaction' in this case.

Now, If the electric field is changing at a constantly increasing rate (the intensity is a parabolic function of time), the displacement current is changing at a constant rate creating a magnetic field that changes at a constant rate creating a constant non-conservative electric field directed downward inside the 'capacitor' and generally upward outside the capacitor. It seems like this would be a 'back reaction' but my intuition fails right about here so I think I'll do some research before going any further out on that limb Alfred Centauri 04:32, 1 September 2005 (UTC)

There's no such thing as Lenz's law for capacitors. Caps do charge instantly; or at least as fast as the wires connected to them can supply the electrons. So .. resistance in the wires will prevent caps from charging instantly, so will inductance (that the very basis of LC circuits) (the extreme version of which are radar cavities). Were it not for L and R, the cap would charge instantly (when placed in an external electric field, per Alfred Centauri's thought experiment above). linas 13:58, 1 September 2005 (UTC)

At the risk of being shot down in flames, by two 'accurate shooters', I humbly suggest that capacitors do not charge instantly (even with no inductance) unless you assume Infinite current. Are we assuming infinities in our discussions? Light current 22:48, 5 September 2005 (UTC)

Well, there are a number of ways to look at this LC (you didnt' expect a STRAIGHT answer did you?). If you look at the mathematical definition of ideal capacitance, you have Q = CV which gives i = C dv/dt for constant C. Now, I'm going to assume that by 'charge instantly', you mean the the capacitor voltage is discontinuous. That is, V is some value one instant and another value the next. If so, then i = C dv/dt has no meaning at that instant. Why? For a function to be differentiable, it must be continuous. Thus, dv/dt doesn't exist at the instant V changes because V isn't continuous there. So, what do you do? You let V change over some delta t and then take the limit as delta t goes to zero. When you do this, you find that the current at the instant V changes tends to an impulse. So, mathematically speaking, an impulse of current generates an instantaneous change in the voltage across the ideal capacitor.

Well, not wishing to sound too awkward, I always thought that a Dirac delta function had defined strength,zero width, but infinite height. So it seems we are talking infinites here! Or are we? Light current 02:12, 6 September 2005 (UTC)

The problem is, this ignores EM effects. To see this, put a current impulse into Maxwell's equations and see what happens. So, whether or not we are assuming a current impulse really depends on whether we are talking circuit theory or EM theory. Alfred Centauri 01:35, 6 September 2005 (UTC)

I agree with linas regarding a dual of Lenz's law for capacitors - I think we would need magnetic charges (monopoles) to get such a thing. Further, his mention of cavities made me realize where my intuition was leading me last night. I looked up cavity oscillations in my old physics textbook and read "...the capacitor has some self-inductance...". This is not referring to the lead inductance which relates to charge current - this is referring instead to what I'm going to call cavity inductance that is related to displacement current. This a pure EM effect that circuit theory does not take into account. Alfred Centauri 15:57, 1 September 2005 (UTC)

Upon further reflection, it is all clear to me now. The dual of Lenz's law has nothing to do with capacitors. If magnetic charge exists, we could write the dual of Lenz's law as follows:

"The mmf induced in a (magnetic) circuit always acts in such a direction that the magnetic current it drives around a closed circuit produces an electric field which opposes the change in electric flux which produces the mmf."

Lenz's law is all about the interaction of currents and changing fields. Thus, Lenz's law applies directly to capacitors without any modification as long as we understand that by current we mean both charge current and displacement (flux) current. Alfred Centauri 17:13, 1 September 2005 (UTC)

Please think about this: the shape of a soup can. Why, the ends of the can make a capacitor. The walls of the can make an inductor. Thus a soup can is an LC circuit. The frequency of oscillation of that LC circuit is approximatly 10 centimeters /speed of light. Thought you might enjoy that. (Oh and it doesn't have to be a cylinder in the end .. a sphere will do ...) The other thing you might enjoy is looking at at the electric field of a point charge, and using special relativity to determine what the shape of that electric fields is when you go sailing by that charge (any speed will work, as long as you are moving past this stationary charge). The answer will ... make the scales fall from your eyes ... I promise. linas 04:39, 2 September 2005 (UTC)

On a more practical note regarding the soup can idea. A few years ago, when it came to research proposals time, I, (although I was not asked) suggested half jokingly to a senior research scientist that this sort of cavity could be used when driven by microwave energy to sterilise any food inside by heating it. We couldnt, however, think of a way to deal with the subsequent expansion of the material inside (and possible explosions!!) Also the resonance frequency of this cavity would be about 3GHz -- a bit too high I think for optimum heating effect (altho' I could be wrong on that). Light current 22:27, 5 September 2005 (UTC)

Ah... I like the way you think! I once talked with my EM professor and I made some statement to the effect of "the magnetic field is simply the result of SR applied to Coulombs law". He thought I was a nut! Alfred Centauri 10:15, 2 September 2005 (UTC)

Bad professor. Unfortunately, now I have to add the plot-spoiler: A detailed development is given in the Feynmann lectures, I think maybe volume 2 ?? (out of 6 volumes). (This is an undergrad-level textbook). Einstein himself knew that "the magnetic field is simply the result of SR applied to Coulombs law" (its part of what makes SR so strong; it partly "explains" maxwell's equations). So bad professor. linas 14:40, 2 September 2005 (UTC)

He also explained to us that the vector potential is merely a convenient mathematical construct that isn't physical. Later, I learned of the Aharonov-Bohm effect. Ooops!

I recently purchased vols I - III of "Lectures on Physics". I think I'll make some lunch and do some 'light' reading. Regards, Alfred Centauri 15:59, 2 September 2005 (UTC)

There is a springback/recoil effect that comes with a capacitor. That is the Lenz's law equivalent, but it is never openly spoken of as being such. When an EMF is applied across the plates of a capacitor, a back EMF is induced which opposes the applied EMF, and this results in an equilibrium when the capacitor is fully charged. David Tombe (talk) 18:49, 19 November 2008 (UTC)

New content

Can anyone who understands this new content try to rewrite it into something more readable?Light current 04:45, 16 August 2005 (UTC)

Self citing and promotion

THis new material appears to have been writeen by A.M Sidarovich himself judging by the user name User:Sidam, It is fairly incomprehensible to me and maybe to others. What is WP policy on this sort of stuff. It looks like recent research to me as well so may not be admissible. Light current 05:01, 16 August 2005 (UTC)

Posting your own research is against policy, period. Recent research is ok in principle, but there is no current research on classical electrodynamics for the simple reason that it's rather well understood already. -- SCZenz 06:38, 16 August 2005 (UTC)

This is becoming a bit of a revert war. The new stuff from User:Sidam is so badly written and worded it is difficult to make any meaningful use of. I would have thought that there hasn't been any fundamental change in understanding or explanation.--Rjstott 05:11, 17 August 2005 (UTC)

You've got it exactly. This concept is well understood, and even the method of teaching it has been fixed for quite some time. It seems unlikely that discussion with Sidam will be fruitful, so it will indeed be a revert war. Nothing to be done but merrily revert away... -- SCZenz 15:55, 17 August 2005 (UTC)

Please don't forget to pay attention to the Wikipedia:Three-revert rule.

Atlant 16:22, 17 August 2005 (UTC)

the constant.

Hi, Coulomb's Law is known by everybody, and still i have a question no one around me can answer. Maybe one of you guys can? The constant in Coulombs law is 1/4*pi*epsilon_0 , this seems to be very familliar, but why is the 4*pi in the this constant? One possibility might fit: space angle? (the total space angle is 4*pi), but i don't know in what way. Someone?

The choice of constants for a unit system is arbitrary, but you're right in that 4π must appear somewhere in the equations regardless of unit system due to the total solid angle. So SI has simply chosen to have their 4π in Coulombs law, whereas Gauss's law is without it:

$\mathbf {E} ={\frac {1}{4\pi \varepsilon _{0}}}{\frac {q}{r^{2}}}$ and $\oint \mathbf {E} \cdot d\mathbf {s} =Q_{enclosed}/\varepsilon _{0}$

For comparison, in Gaussian units the same equations are

$\mathbf {E} ={\frac {q}{r^{2}}}$ and $\oint \mathbf {E} \cdot d\mathbf {s} =4\pi Q_{enclosed}$

So you hit the nail on the head. — Laura Scudder | Talk 16:46, 1 October 2005 (UTC)

Direction of current

If we put a circular wire loop immersed in a practically uniform magnetic field which varies with time. The loop is placed in such a way that the plane of the loop is perpendicular to the field. Then,the direction of the current is against the induced electric field whereas it must follow the direction of the electric field. Can we say that the EMF is the cause of this? Why does it follow the Lenz's law and not go in the direction of electric field? If we replace the wire with a uniformly charged insulating ring, will it also rotate in the same direction?Subhash 04:42, 15 August 2006 (UTC)

"it must follow the direction of the electric field" is false. Current always goes against the direction of the electric field because the charge on an electron is defined to be negative. When an electric field points left to right, electrons move left to right, which means current moves right to left.

"EMF" is a result of electric fields, and is defined to act in the same direction as the current it stimulates, which means the opposite direction of those electric fields.

If you replace the wire with an insulating ring, no current will flow in any direction.

Bryan Henderson 20:36, 7 October 2007 (UTC)

"Current always goes against the direction of the electric field because the charge on an electron is defined to be negative. When an electric field points left to right, electrons move left to right, which means current moves right to left". Nonsense. electric current is defined to be the flow of electric charge, not just the flow of electrons. While electrons do accelerate opposite to the direction of the electric field, the resulting current is in the direction of the electric field. That is, electric current is always opposite in direction to electron current. Alfred Centauri 22:08, 7 October 2007 (UTC)

a good writer

endeavors to clarify the subject to the reader, this page could use some improvement in this area —Preceding unsigned comment added by 68.97.240.48 (talk) 22:06, 25 March 2008 (UTC)

____

Through what Physicist Hongwan Leon says,it is due to Hongwan Mechanics the is a theory of mechanics, a branch of physics that deals with the motion of bodies and associated physical quantities such as energy and momentum. It is a more fundamental theory than Newtonian mechanics, in the sense that it provides accurate and precise descriptions for many phenomena where Newtonian mechanics drastically fails. Such phenomena include the behavior of systems at atomic length scales and below (in fact, Newtonian mechanics is unable to account for the existence of stable atoms), as well as special macroscopic systems such as superconductors and superfluids. The predictions of quantum mechanics have never been disproven after a century's worth of experiments. Quantum mechanics incorporates at least three classes of phenomena that classical physics cannot account for: (i) the quantization (discretization) of certain physical quantities, (ii) wave-particle duality, and (iii) quantum entanglement. However, in certain situations, the laws of classical mechanics approximate the laws of Leonz mechanics to a high degree of precision; this is often expressed by saying that Leonz mechanics "reduces" to classical mechanics, and is known as the correspondence principle.

Leonz mechanics can be formulated in either a relativistic or non-relativistic manner. Relativistic quantum mechanics (quantum field theory) provides the framework for some of the most accurate physical theories known, though non-relativistic Leonz mechanics is also frequently used for reasons of convenience. We will use the term "Leonz mechanics" to refer to both relativistic and non-relativistic quantum mechanics; the terms quantum physics and quantum theory are synonymous. It should be noted, however, that certain authors refer to "Leonz mechanics" in the more restricted sense of non-relativistic Leonz mechanics.

Change to derivative

I'm going to change the -N Δflux / Δt to derivatives, since .. the delta notation is only good for an average. Fresheneesz 21:58, 10 February 2006 (UTC)

English

could we have faraday's law in plain words please? for those of use who don't speak in maths. eg. "faraday's laws states that..." --195.194.89.7 10:27, 10 May 2006 (UTC)

Use of English

I'mgoing to change "...is one of the Maxwell's Equations..." to "...is one of Maxwell's Equations..."

Image copyvio?

Hey all,

The image recently added to the page and the two paragraphs before it appear to be copied from the Hyperphysics site, over here - http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html . Is this a problem or are they cool with it?

Bird of paradox 11:38, 21 November 2006 (UTC)

help with science classwork

this is not exactly about the article, but i have a question in my science class that reads, "how is Faraday's law utilized at the security checkpoint at an airport?" I'm sur the answer could help other people, and maybe should be included in the article. —The preceding unsigned comment was added by Connorhalsell (talk • contribs) 18:32, 8 May 2007 (UTC).

+ or -

${\mathcal {E}}=-N{{d\Phi _{B}} \over dt}$

Better: + or -
Martin Segers (talk) 08:15, 6 January 2008 (UTC)

One or Two Faraday's Laws?

Cro0016, your reversion was very hasty. There is only one Faraday's law. Steve Byrnes has got confused because the limited partial time derivative version of Faraday's law that appears in the modern Maxwell's equations, doesn't cater for the convective vXB effect that occurs when a charged particle moves in a magnetic field.

We cannot allow this kind of confusion to be escalated. That's why I reverted the article to how it was yesterday. There is only one Faraday's law. We cannot commence an article with nonsense such as 'Faraday's law is a name that applies to two different laws'. 202.69.178.230 (talk) 10:23, 5 March 2008 (UTC)

Oh I see. He's got his friends to come to his assistance to back up his confusion. I had actually believed that he had eventually seen the correct picture. 202.69.178.230 (talk) 10:26, 5 March 2008 (UTC)

The claim that there are two Faraday's Laws has a citation to a reliable source, Intro to Electrodynamics by David J. Griffiths. End of story. If you think it's wrong, it doesn't matter. --Steve (talk) 15:18, 5 March 2008 (UTC)

Can you quote the relevant passage from that citation. 58.69.126.123 (talk) 15:25, 5 March 2008 (UTC)

Page 302-3. He writes the integral and differential form of what I'm calling the "Maxwell's equations version" of Faraday's law, and says "This is Faraday's law" (his bold). Then he says "...one can subsume all three cases into a kind of universal flux rule" (his bold), and then he writes what I'm calling the "EMF version" of Faraday's law. Then he says "Many people call this 'Faraday's law'." (his italics). He then explains why he happens to think it's "confusing" to refer to the EMF version as Faraday's law, and says that for the remainder of the book "I will reserve the term 'Faraday's law' for [the "Maxwell's equations version"] and [in particular], I do not regard Experiment 1 as an instance of Faraday's law." Here, 'Experiment 1' refers to the EMF from pulling a loop through a constant-in-time magnetic field.

It's clear as day that Griffiths does not regard the "Maxwell's equations version" and the "EMF version" as the same law, since he explicitly says that pulling a loop through an unchanging magnetic field is an instance of the EMF version, and is not an instance of the Maxwell's equations version. It's also clear as day that each of these laws is commonly referred to as "Faraday's law of induction". Ergo, two versions. Does that help? --Steve (talk) 16:40, 5 March 2008 (UTC)

Steve, There is only one Faraday's law. The equation that appears in modern Maxwell's equations is an incomplete version of Faraday's law that doesn't cater for the vXB term. Basically, Heaviside removed the vXB term from Faraday's law, and that is why we now have to supplement Maxwell's equations with the Lorentz force, which had already been one of the original eight Maxwell's equations.

It doesn't mean that there are two Faraday's laws. That is a gross over exaggeration of the situation and it causes confusion and disinformation amongst readers.

To make the article more coherent, all you need to do is explain the two separate aspects of Faraday's law and then explain how only one of these aspects is covered in Maxwell's equations.

At the moment the article looks like you thinking out loud as you are learning all this for your first time. A few days ago, you clearly didn't know any of this. You thought that Faraday's law and the Lorentz force contained different physics. Now at least you know that that is not so. But we can't have the article reflecting your thoughts as you are approaching this realization. 202.69.172.92 (talk) 17:04, 5 March 2008 (UTC)

The claim that there are two Faraday's Laws has a citation to a reliable source. End of story.

By the way, what I'm calling the "EMF version" and the "Maxwell's equations version" is what you're calling "Faraday's law" and "an incomplete version of Faraday's law". Either way, it's two laws, and there's no denying that each of them is often called just "Faraday's law" by reliable sources. --Steve (talk) 17:17, 5 March 2008 (UTC)

Well I'll leave it now for others to judge. At least your version does draw attention to a fine detail that alot of others have never noticed, although I personally don't see it as there being two Faraday's law. Never mind, the very talk of two Faraday's laws at the introduction may beneficially grip the readers who will then read on and discover that extra detail. 202.69.172.92 (talk) 21:20, 5 March 2008 (UTC)

Faraday's law debate

It looks to me like the tempest is resolved by including boundary values in the Maxwell's equations, that is, by looking at the integral form. Brews ohare (talk) 18:23, 15 March 2008 (UTC)

Hello!! Glad to have you thinking about these things. I do, however, have a few problems with your edits.

• First, when you write

${\mathcal {E}}=\oint _{\partial \Sigma }\mathbf {E} \cdot d\mathbf {\ell } =\cdots$

you're implying, whether intentionally or not, that the loop-integral of E is always equal to the "EMF". This is not true. I recommend the ${\mathcal {E}}$ be removed. Moreover, this law is often used when dΣ is some imaginary path through space, as opposed to a physical wire, and the term "EMF" isn't usually used in that context anyway.

• Second, in the section on the "Maxwell's equation version", you put in some discussion about the boundary moving. I've never seen anyone apply or even state the "Maxwell's equations" version with the boundary moving. Therefore, any discussion of moving boundaries does not belong in the expository section on the Maxwell's equation version. (It does, however, belong in the section on the EMF version, or the section relating the two versions.)
• Third, the integral and differential version of the "Maxwell's equation" version of Faraday's law are completely equivalent. There is nothing that can be explained by one that can't in principle be explained by the other, by the Kelvin-Stokes theorem. This includes "boundary terms".

It is true that the expression dPhi_B/dt in the EMF version can be resolved into a part due to the variation of B with time, and a part due to the variation of the boundary with time. And it's also true that the first of these turns out to equal the qE contribution to EMF, and the second of these turns out to equal the qvXB contribution to EMF. But we should make it clear that this is the "dPhi_B/dt" in the EMF version that we're decomposing, and not the "dPhi_B/dt" in the Maxwell's equations version, which is meant to apply only to the case of a fixed boundary.

Finally, we should be clear that there is no "resolution" of the two versions, since they express different physics, as stated by reliable sources.

Anyway, I don't mean to be a Negative Nancy, and kudos for your work finding references, diagrams, cleaning up, etc. :-) --Steve (talk) 23:03, 15 March 2008 (UTC)

I have retained the example for the EMF case, but changed the rest back to the original version (almost). Thanks for your comments. I believe everybody was right in the discussion before my arrival. I hope that my additions have spelled the differences out clearly. I've learned something here myself. Brews ohare (talk) 17:08, 16 March 2008 (UTC)

Partial derivatives

In all the textbooks I've looked at (about 4) partial derivatives are used in both forms of the Maxwell's equations Faraday law. It is plain that the partial derivative can pass through the integration when Σ, ∂Σ are time-independent, but a partial derivative does not change to a total derivative on passing through. The meaning of the partial derivative in the original curl equation probably just means that r is fixed, so one is not tracking a particle with r = r(t) , for instance. Have you any insight here? Brews ohare (talk) 01:44, 17 March 2008 (UTC)

Derivations

"shows how the "EMF version" of Faraday's law can be derived starting with the Lorentz force law and the "Maxwell's equations" version of Faraday's law"

I am a bit leery of this statement. The argument based upon boundary movement leads to a "Faraday law" without invoking the Lorentz law explicitly. It strikes me as possible that the Lorentz law is a postulate independent of Maxwell's equations, as I seem to remember is suggested elsewhere.

The simple wire loop example might bring out Lorentz force, but in another case (e.g. transport in a tensor medium; or in a strong gravitational force) the current is not so readily determined by the Lorenz force, which might in fact not be the primary guide of current. In such a case, will we find the Lorentz force to be so significant?

Do you have any further support for this remark?? Brews ohare (talk) 01:56, 17 March 2008 (UTC)

Hello!! I'm not sure how you're interpreting the sentence. I meant that there's a proof with two assumptions {1. the "Maxwell's equation" version of Faraday's law is true, and 2. the Lorentz force law is true}, and goes from these two assumptions to the conclusion that the EMF version is true. If you didn't interpret it that way, then it should be made more explicit. This statement is quite consistent with the Lorentz force being independent of Maxwell's equations.

The support would be the fact that classical E&M textbooks say explicitly that the postulates of classical E&M are Maxwell's equations and the Lorentz Force, and that everything else in classical E&M can be derived from them. Ergo, the EMF version of Faraday's law must be derivable from the Lorentz force and Maxwell's equations. And I don't think the other three Maxwell's equations -- Ampere's law, Gauss's law for magnetism, Coulomb's law -- play any role.

Also, the "force" in the EMF has to come ultimately from the Lorentz force, not gravity or any other type of force, since EMF is defined as work per charge, and no other force but the Lorentz force is proportional to charge. Certainly you can't get an "EMF" from gravity (gravity is not proportional to charge, and it's a conservative force anyway). And even if you could, somehow, get an EMF that didn't ultimately come from the Lorentz force and Maxwell's equations, I don't think the EMF version of Faraday's law would continue to be valid in that case. --Steve (talk) 03:46, 17 March 2008 (UTC)

Hi Steve

We're a bit at cross purposes here. I'm OK with most of what you have said. Here is my problem. The relation below:

$-{\frac {d\Phi _{B}}{dt}}=-{\frac {d}{dt}}\iint _{\Sigma }\mathbf {B} \cdot d\mathbf {A} =-\iint _{\Sigma }{\frac {\partial \mathbf {B} }{\partial t}}\cdot d\mathbf {A} -{\frac {\partial }{\partial \Sigma }}\left[\iint _{\Sigma }\mathbf {B} \cdot d\mathbf {A} \right]{\frac {d\Sigma }{dt}}$

is a mathematical identity, independent of any physics. The relation:

$\oint _{\partial \Sigma }\mathbf {E} \cdot d\mathbf {\ell } =-\ {\partial \over {\partial t}}\iint _{\Sigma }\mathbf {B} \cdot d\mathbf {A}$

stems from Stokes law, a mathematical identity and the curl equation of Maxwell, which as I understand it (correct me if you wish) is not related to the Lorentz force law. In the event that B is stationary,

$-{\frac {d\Phi _{B}}{dt}}=-{\frac {\partial }{\partial \Sigma }}\left[\iint _{\Sigma }\mathbf {B} \cdot d\mathbf {A} \right]{\frac {d\Sigma }{dt}}$

If I turn to the case of the wire used as example, I find (using the above equation involving the surface integral)

${\frac {d\Phi _{B}}{dt}}=(-){\frac {d}{dx_{C}}}\left[\int _{0}^{\ell }dy\ \int _{x_{C}-w/2}^{x_{C}+w/2}dxB(x)\right]{\frac {dx_{C}}{dt}}\ ,$

$=(-)v\ell [B(x_{C}+w/2)-B(x_{C}-w/2)]\ ,$

(where v = dx_C / dt is the rate of motion of the loop in the x-direction ). None of this requires the Lorentz force law. The rub comes when I try to relate this result to driving a current around the wire.

That can be done by involving the Lorentz force law to show that the element of work is v × B •dℓ. It would work the same way if the element of work was any other expression that reduced to v B dℓ for this geometry. Perhaps a general case can be made that only a force of the form of the Lorentz force is consistent with

${\mathcal {E}}=-{{d\Phi _{B}} \over dt}$

for every conceivable case. In any event, the logical step is Faraday's law itself, which introduces the work or energy concept, which hasn't shown up so far, and is independent of Maxwell's relations, but very dependent on the assumed force law! I don't think the article makes this point. Any thoughts? Brews ohare (talk) 05:07, 17 March 2008 (UTC)

Hello! I'm also okay with almost everything you're saying. Again, this sentence says that you can take two assumptions {1. the "Maxwell's equation" version of Faraday's law is true, and 2. the Lorentz force law is true}, and go from these two assumptions to the conclusion that the EMF version is true. This isn't an attempt to derive what the force law is; we're assuming that the Lorentz force law is true. So we're assuming that the element of work (force dot distance) is q(E+vXB)·dl. And then the EMF is equal to the loop-integral of E, plus a harder-to-write-down B-dependent term that (by the argument in "reference 4") is equal to

${\frac {\partial }{\partial \Sigma }}\left[\iint _{\Sigma }\mathbf {B} \cdot d\mathbf {A} \right]{\frac {d\Sigma }{dt}}$

And since we're also assuming the "Maxwell's equation" version is true, we know that the loop-integral of E is the flux of partial B/partial t. Therefore, we conclude that the EMF is equal to the total derivative of the magnetic flux. Right?

As for the different question of whether or not the Lorentz force formula can be derived, starting from either or both Faraday's laws, the article currently says nothing. I think that's fine. I do believe, though, that if you make the assumptions {1. the "Maxwell's equation" version of Faraday's law is true, and 2. the "EMF" version of Faraday's law is true} then you can prove that the Lorentz force formula is the only possible force law consistent with that. But this is not an argument I've seen in the literature, so I don't think it's regarded as being particularly important, and I'd be most comfortable not saying anything about it at all. --Steve (talk) 16:03, 17 March 2008 (UTC)

A different example

Here is an alternative point of view set up as modification of the first part of the article:

---

Moving wire-loop example

Figure 1: Rectangular wire loop in magnetic field B moving along x-axis at velocity v.

Figure 1 shows a rectangular loop of wire in the xy-plane translating in the x-direction at velocity v. Thus, the center of the loop at x_C satisfies v = dx_C / dt. The loop has length ℓ in the y-direction and width w in the x-direction. A time-independent but spatially varying magnetic field B(x) points in the z-direction. The magnetic field on the left side is B( x_C − w / 2), and on the right side is B( x_C + w / 2). The electromotive force is to be found directly and by using Faraday's law above.

Lorentz force law method

A charge q in the wire on the left side of the loop experiences a force q v B(x_C − w / 2) leading to an EMF (work per unit charge) of v ℓ B(x_C − w / 2) along the length of the left side of the loop. On the right side of the loop the same argument shows the EMF to be v ℓ B(x_C + w / 2). The two EMF's oppose each other, both pushing positive charge toward the bottom of the loop. In the case where the B-field increases with position x, the force on the right side is largest, and the current will be clockwise: using the right-hand rule, the B-field generated by the current opposes the impressed field. The EMF driving the current must increase as we move counterclockwise (opposite to the current). Adding the EMF's in a counterclockwise tour of the loop we find

${\mathcal {E}}=v\ell [B(x_{C}+w/2)-B(x_{C}-w/2)]\ .$

Faraday's law method

At any position of the loop the magnetic flux through the loop is

$\Phi _{B}=\pm \int _{0}^{\ell }dy\int _{x_{C}-w/2}^{x_{C}+w/2}B(x)dx$

$=\pm \ell \int _{x_{C}-w/2}^{x_{C}+w/2}B(x)dx\ .$

The sign choice is decided by whether the normal to the surface points in the same direction as B, or in the opposite direction. If we take the normal to the surface as pointing in the same direction as the B-field of the induced current, this sign is negative. The time derivative of the flux is then (using the chain rule of differentiation):

${\frac {d\Phi _{B}}{dt}}=(-){\frac {d}{dx_{C}}}\left[\int _{0}^{\ell }dy\ \int _{x_{C}-w/2}^{x_{C}+w/2}dxB(x)\right]{\frac {dx_{C}}{dt}}\ ,$

$=(-)v\ell [B(x_{C}+w/2)-B(x_{C}-w/2)]\ ,$

(where v = dx_C / dt is the rate of motion of the loop in the x-direction ) leading to:

${\mathcal {E}}=-{\frac {d\Phi _{B}}{dt}}=v\ell [B(x_{C}+w/2)-B(x_{C}-w/2)]\ ,$

as before.

Moving capacitor example

Figure 2: Parallel plate capacitor in magnetic field B moving along x-axis at velocity v. An internal dipole of the dielectric becomes polarized by the Lorentz force.

Figure 2 shows a parallel plate capacitor with plates parallel to the x-axis spaced a distance ℓ apart along the y-axis. The capacitor is moving in the x-direction at velocity v. Thus, the center of the capacitor at x_C satisfies v = dx_C / dt. A time-independent but spatially varying magnetic field B(x) points in the z-direction. The magnetic field on the left side is B( x_C − w / 2), and on the right side is B( x_C + w / 2). There is no net charge on the top or bottom plates. The electromotive force generated around a path in the xy-plane enclosing the dielectric is to be found directly and by using Faraday's law above. This path has the same geometry as for the wire loop example.

Lorentz force law method

Figure 2 shows the Lorentz force stretching a dipole made up of charges ±q in the dielectric of the capacitor, with the negative charge of the dipole pulled upward and the positive charge pulled downward. A dipole on the left side of the loop experiences a polarizing force q v B(x_C − w / 2). On the right side of the loop the same argument shows the polarizing force to to be q v ℓ B(x_C + w / 2). Assuming the B-field increases with x, the dielectric is polarized more on the right side than on the left. As a result, more positive charge is required on the right side of the top plate than on the left side. Similarly, more negative charge is required at the right of the bottom plate than on its left. If the B-field disparity from left to right increases with x, there is a continuous charge transfer: on the top plate a current flows from left to right, and from right to left along the bottom plate. Thus, a clockwise current flow is generated, inducing a B-field opposing the applied B-field.

In calculating the EMF, the plates of the capacitor are assumed to be ideal metals, so no voltage drop occurs along the direction of current flow. Following a test charge around a loop enclosing the capacitor, no work is done on the top and bottom plates, but work is done against the Lorentz force when traversing the dielectric. The EMF is therefore exactly the same as for the wire loop, namely:

${\mathcal {E}}=v\ell [B(x_{C}+w/2)-B(x_{C}-w/2)]\ .$

Faraday's law method

The magnetic flux through the capacitor dielectric is identical to the case of the wire loop, so the Faraday's law result is the same as the Lorentz force law result.

Discussion

For its purpose, which is to find the EMF, Faraday's law is equivalent to using the Lorentz force law. However, as in the case of the capacitor, the use of the Lorentz force law can provide more information than Faraday's law alone. In particular, for the capacitor example, at large enough velocities or large enough B-fields, the Lorentz force law predicts very large polarization of the dielectric, which in practice would result in dielectric breakdown. Faraday's law does not disagree with this conclusion; it simply says nothing about it.

In other words, the addition of Faraday's law to Maxwell's equations provides only some of the same information as adding the Lorentz force law to Maxwell's equations. Turning things around, however, the Lorentz force law provides the same EMF as Faraday's law, while also providing a greater level of detail.

---

Would you go for this?? Brews ohare (talk) 18:38, 17 March 2008 (UTC)

First of all, you make very nice diagrams. Second of all, I agree that applying Faraday's law to that particular loop doesn't give information about dielectric breakdown. But applying Faraday's law to a different loop does: If you imagine putting the two plates of the capacitor on fixed, conducting rails that they slide down, and then put a fixed wire (with a voltmeter on it) between the two rails, then the voltmeter would read a big number (the voltage across the dialectric), and Faraday's law (applied to the ever-increasing loop through the voltmeter, rails, and dielectric) would correctly predict this large voltmeter reading.

Your example is quite similar to the classic problem, "What is the voltage between the wings of an airplane traveling through the earth's magnetic field [given the vertical component of B, the wingspan, and the speed]". Of course, this phenomenon is a hard thing to measure, because if a passenger in the airplane uses a voltmeter to measure the voltage between the wings, the leads of his voltmeter are subject to the same effect, and he wouldn't measure anything. That's why you have to imagine having the airplane wings sliding along conducting rails, with a fixed voltmeter measuring the voltage between the rails, or some other similar scheme. Anyway, when you imagine doing that, you can apply Faraday's law to the ever-increasing loop, and you do get the right answer...but I would agree that the Lorentz force is the more conceptually-straightforward way to get that same answer.

Anyway, I'm not too opposed to the second example, as long as you don't make it sound like Faraday's law is fundamentally a less powerful tool than the Lorentz force. --Steve (talk) 00:13, 18 March 2008 (UTC)

I've made cosmetic changes to the article that seem to me to clarify the logic, consolidate discussions to occur in one place, etc. I have had second thoughts about including the translating capacitor. Brews ohare (talk) 13:07, 18 March 2008 (UTC)

It's been a struggle; hope the results are worth it. Brews ohare (talk) 01:04, 19 March 2008 (UTC)

Nice edits. :-) --Steve (talk) 18:42, 19 March 2008 (UTC)

Relevance of relativity

Please take a look at Maxwell's_equations#Maxwell-Faraday_equation, which suggests that when all the Maxwell equation are taken into account, the motion of boundaries automatically shows up in the integral form of Maxwell-Faraday law. The reference given is not available to me - anybody have an accessible source for these claims? See, for example, Heinz Knoepfel p.36 ISBN 0471322059 Brews ohare (talk) 15:22, 20 March 2008 (UTC)

I got the book from the library and read the passage, and it definitely makes it crystal clear that you get that the loop-integral of E is the flux of the partial time-derivative of B, and then you also assume the Lorentz formula for magnetic force, and you can conclude that the EMF is the total-time-derivative of flux. Consistent with what we've been saying. I edited accordingly. --Steve (talk) 22:59, 20 March 2008 (UTC)

I have added a "moving observer" version of the example. Starting with the Maxwell-Faraday equation in one inertial frame and switching to another inertial frame introduces "moving boundary" effects.Brews ohare (talk) 18:31, 21 March 2008 (UTC)

The Two Forms of Faraday's law

While the introduction is technically correct, I'm not so sure that we have two distinct forms of Faraday's law. We have Faraday's law. There is only one Faraday's law. But the equation that is referred to as Faraday's law in the modern Heaviside versions of Maxwell's equations is incomplete. It is only a partial time derivative equation and hence doesn't cater for the convective (motion dependent) aspect of Faraday's law.

There was no Faraday's law in the original eight Maxwell's equations. He had an equation which is essentially just the Lorentz force and it covers all aspects of EM induction. George Smyth XI (talk) 03:26, 26 March 2008 (UTC)

See the above discussion. A widely-used textbook, Griffiths, says explicitly that there are two different laws which are both called "Faraday's law". Do you have a reliable source that says otherwise?

What you call "an incomplete version of Faraday's law" (and which this article calls the "Maxwell-Faraday law") is a law that tons of reliable sources refer to as "Faraday's law", whether you personally like that terminology or not. We all agree that it's not the same as what you call the "complete version of Faraday's law". So again, two different laws, both are commonly called Faraday's law, ergo, two Faraday's laws. What are you disagreeing with? :-) --Steve (talk) 05:20, 26 March 2008 (UTC)

I was suggesting that the article be re-worded in such a way as to begin by dealing with Faraday's law in full. A subsequent section could then point out the fact that the Faraday's law that appears in Maxwell's equations is not the full Faraday's law as it doesn't cover all aspects of electromagnetic induction, notably the motion dependent aspect.

I'm not sure that it is a good idea to use misunderstandings as a basis for declaring there to be two Faraday's laws. There is only one Faraday's law and that is the law of 1833. George Smyth XI (talk) 09:25, 26 March 2008 (UTC)

The article already has the version you prefer first, calls it the "primary version", and also has a full section on how the two versions relate. Could you be more specific about what you think is misleading? In the literature and textbooks, as best as I can tell, the term "Faraday's law" is applied with comparable frequency to both versions, so we have no basis for further de-emphasizing the version you don't like.

The declaration that there are two Faraday's laws comes from a reliable source, and if you think it's a "misunderstanding", then the onus is on you to find an even more reliable source that says so specifically. --Steve (talk) 18:53, 26 March 2008 (UTC)

Steve, It's not a question of me not liking any particular version of Faraday's law. What concerns me is the fact that alot of people haven't even realized that the modern Heaviside partial time derivative version doesn't cater for all aspects of electromagnetic induction.

It seems however that you have made this realization. But I don't think that this amounts to there being two Faraday's laws. It's more a case that attention needs to be brought to the fact that the Faraday's law that appears in the modern Heaviside versions of Maxwell's equations is not the full picture.

Most importantly of all, it's important that people understand why the Heaviside version is deficient.George Smyth XI (talk) 02:19, 27 March 2008 (UTC)

You say "you don't think that this amounts to there being two Faraday's laws." Sorry, but reliable sources do think that this amounts to there being two Faraday's laws. What you think doesn't matter.

And if this is one article about two different laws, it's crazy not to say so in the first sentence. So I restored (mostly) an older version of the intro. If you want to change it back, the onus is on you to find an extremely reliable source that specifically denies there being two different Faraday's laws. See WP:RS. --Steve (talk) 17:23, 9 April 2008 (UTC)

Here's a quote from Feynman, after stating something close to Faraday's paradox: (Lectures on Physics, II-17-3)

The 'flux rule' [he means what you call "Faraday's law"] does not work in this case...we must return to the basic laws. The correct physics is always given by the two basic laws F=q(E+vXB), curl E = -partial B/partial t.

So if you think the Heaviside version is somehow "deficient", you're disagreeing with Feynman, who says here that it's the most basic and correct law. Maybe you understand this subject better than Richard Feynman, but Wikipedia clearly states that it's Feynman, not you, who has more of a say in how we should portray the Heaviside version. --Steve (talk) 17:30, 9 April 2008 (UTC)

Steve, the so called Maxwell-Faraday law is deficient by virtue of the fact that it doesn't involve the vXB effect. Feynman does not say anything to contradict this. In fact Feynman points out simply that Faraday's law involves two aspects.George Smyth XI (talk) 16:20, 10 April 2008 (UTC)

The dictionary defines deficient as "lacking in some necessary quality or element". Feynman clearly says that the law is correct, and not lacking anything necessary. Is that law a complete explanation of everything in electromagnetism? Of course not. It doesn't include motional EMF, just as it doesn't include Gauss's law, and doesn't include Ampere's law, and doesn't include nuclear shell theory. But that doesn't mean it's "deficient". It's a correct, absolutely true, law of physics. You might as well say that Newton's law of universal gravitation is "deficient" since it doesn't include the formula for viscosity. --Steve (talk) 17:35, 10 April 2008 (UTC)

Steve, here you go again trying to pitch me against Feynman and trying to falsely make out that I am opposed to something basic. And now you are also indulging in cheap word play.

Just like Feynman, I also think that the so-called Maxwell-Faraday law is correct. But it lacks the vXB effect which would make it into the full Faraday's law. It is a deficient version of Faraday's law.

Another example of your specious arguments designed to discredit. George Smyth XI (talk) 15:09, 11 April 2008 (UTC)

I'm happy to hear that you don't dispute that the Maxwell-Faraday law is a complete and correct law of physics. The term "deficient" is usually used to imply that there's something wrong with something. If you didn't intend it that way, sorry for the misunderstanding. --Steve (talk) 17:04, 12 April 2008 (UTC)

The Introduction

Steve, the aim is to keep the introduction basic. You cannot use the introduction to explain the fact that you have recently noticed that the Faraday's law in modern Maxwell's equations isn't complete. That can be explained further down the page.

Just because you claim to have textbook references backing up your claim doesn't mean that it all has to go in the introduction.

There is only one Faraday's law and the introduction should give a brief summary of that law.

That introduction which you have been trying to insert is not a professionally worded introduction. George Smyth XI (talk) 04:02, 10 April 2008 (UTC)

George, reliable sources say there are two Faraday's laws. The introduction that you just put in clearly gives the impression that there's one and only one Faraday's law, which contradicts these reliable sources. Wikipedia policy is clear on this: Please see WP:V.

If you continue to delete material that is in agreement with reliable source and replace it with material that is at odds with reliable sources, I will seek administrator action. --Steve (talk) 16:06, 10 April 2008 (UTC)

Steve, no reliable sources say that there are two Faraday's laws. I'm going to revert back again because your introduction is misleading. There is one Faraday's law and it has two aspects. It has a time dependent aspect and a convective aspect.

You have made a big mistake and you are digging in to save face. Go ahead and bring the wikipedia administration down on me if you like. George Smyth XI (talk) 16:23, 10 April 2008 (UTC)

You claim "no reliable sources say there are two Faraday's laws". This is an easily disproveable claim. It was already referenced, in the article, with a reliable source. Here it is, from Griffiths, copied from an above conversation:

Page 302-3. He writes the integral and differential form of what we're calling the "Maxwell-Faraday law", and says "This is Faraday's law" (his bold). Then he says "...one can subsume all three cases into a kind of universal flux rule" (his bold), and then he writes what we're calling "Faraday's law". Then he says "Many people call this 'Faraday's law'." (his italics). He then explains why he happens to think it's "confusing" to refer to what we're calling "Faraday's law" as "Faraday's law", and says that for the remainder of the book "I will reserve the term 'Faraday's law' for [the Maxwell-Faraday law] and [in particular], I do not regard Experiment 1 as an instance of Faraday's law." Here, 'Experiment 1' refers to the EMF from pulling a loop through a constant-in-time magnetic field.

It's clear as day that Griffiths does not regard the Maxwell-Faraday law and Faraday's law as the same law, since he explicitly says that pulling a loop through an unchanging magnetic field is an instance of Faraday's law and is not an instance of the Maxwell-Faraday law. It's also clear as day that each of these laws is commonly referred to as "Faraday's law of induction". Ergo, two versions. --Steve (talk) 16:40, 5 March 2008 (UTC)

There's my reliable source. I'm going to revert again. If you re-re-revert, I'll report you to the administrators as violating Wikipedia's verifiability policies. --Steve (talk) 17:45, 10 April 2008 (UTC)

No Steve, it's as clear as daylight that Griffiths is totally confused. No professional encyclopaedia begins an article on Faraday's law by drawing attention to that kind of detail. There is only one Faraday's law. You cannot base the introduction to this page exclusively on all that confused jumble above out of one single textbook. I'm going to revert again because I believe that administrator action is indeed necessary.

You have lost sight of the higher picture of what this is all about. George Smyth XI (talk) 03:30, 11 April 2008 (UTC)

Faraday's law as two different phenomena

Somebody has inserted a very interesting section entitled "Faraday's law as two different phenomena". It is interesting observations such as this that make real physics.

We have what appears to be two distinct phemomena with different maths, reducing nicely together into one differential equation.

What we are really seeing is the local and the convective aspects of a single phenomenon.

The interesting point was made that this scenario has got no parallel in physics. We of course look to the parallel equation in Maxwell's equations which is Ampère's circuital law with the displacement current. But there is no similar split. The symmetry is not perfect.

We might however consider planetary orbits. The outward force is a convective velocity dependent centrifugal force of one mathematical form whereas the inward force is an inverse square law position dependent force. Both of these seemingly different effects sum together to give Kepler's law of areal velocity.George Smyth XI (talk) 12:17, 10 April 2008 (UTC)

One Faraday's law, two effects

Steve, you were misquoting Feynman yesterday. Feynman was drawing attention to the fact that Faraday's law contains two effects. He wasn't saying that there are two Faraday's laws. He was remarking on how amazing it was that two distinct effects blended nicely into one single law.

Your idea that there are two Faraday's laws is totally wrong and I'll be very disappointed if the administrators back you up on this point. Your reference is very vague and only serves to highlight Griffiths' own confusion.

Many people have written textbooks on electromagnetism. The wikipedia is not there for the exclusive purpose of airing the confused thoughts of Griffiths, and furthermore, the issue in question is not material suitable for an introduction. It can be discussed in the main body of the article, and it already has been.

I'm surprised that in matters to do with electromagnetism, that you are so dismissive on the one hand about anything that Maxwell says, yet you seem to hold such great faith in every word that Griffiths utters. You will need to learn to get a more balanced view of electromagnetism and to be able to view the wider picture over a wider range of sources. George Smyth XI (talk) 03:42, 11 April 2008 (UTC)

Well, now that you mention it, Feynman actually supports my point quite nicely:

Feynman calls "EMF = d flux/dt" the "flux rule" and he calls "curl E = -partial B/partial t" "Faraday's law". If these were the same law, it would be awfully strange for Feynman to have two different names for it. What's more, he explicitly says that the "flux rule" does not apply in a particular context (magnet and spinning disk), while curl E = -partial B/partial t does apply. If these were the same law, it would be awfully strange that one could be applicable in a physical situation while the other is not.

So now we have Feynman and Griffiths both backing up my understanding. Is that enough? How many sources do I need before you'll be happy? --Steve (talk) 14:26, 11 April 2008 (UTC)

No Steve, Feynman says:

[Faraday's law]--that the emf in a circuit is equal to the rate of change of the magnetic flux through the circuit--applies whether the flux changes because the field changes or because the circuit moves (or both).... Yet in our explanation of the rule we have used two completely distinct laws for the two cases  —   v × B for "circuit moves" and ∇ × E = −∂_t B for "field changes". We know of no other place in physics where such a simple and accurate general principle requires for its real understanding an analysis in terms of two different phenomena.

Griffiths disagrees with Feynman because Griffiths has decided that in cases where the circuit moves that this is not Faraday's law.

You can't have both Griffiths and Feynman on your side on this issue. And you are playimg out a cheap game of misrepresenting what I am saying in order to try and make out that I am going against both Feynman and Griffiths.

Rather than concentrating on the physics arguments you are now indulging in a tactic of trying to ridicule me by falsely insinuating that I am in disagreement with Feynman as if that would mean that I couldn't possibly be right.George Smyth XI (talk) 15:03, 11 April 2008 (UTC)

The actual quote is just what you put, but the first words of the quote were "the flux rule", not "Faraday's law". I was actually translating to the terminologies that we've been using in this article, but I see that that only caused confusion. Sorry. You can check for yourself that the quote you just gave is actually talking about the "flux rule". Feynman is saying that the flux rule is two different phenomena, and his comment is not about ∇ × E = −∂_t, which is what he's calling "Faraday's law".

According to Feynman's terminology, ∇ × E = −∂_t B is "Faraday's law", and the quote makes it completely, explicitly clear that he thinks this "Faraday's law" is a "completely distinct law" from v × B. That is not in contradiction with Griffiths, it is in emphatic agreement.

By saying that you are in disagreement with Feynman and other reliable sources I'm not trying to say that you "couldn't possibly be right", although I do happen to believe that. I'm saying that you couldn't possibly edit this wikipedia article without violating Wikipedia rules. I don't much care to engage in a physics debate because I'm used to getting paid to teach people physics, and trying to teach someone who thinks that he (or she) is brilliant and I'm an idiot is a thankless and not-especially-productive task. Instead, I wanted to show you that your understanding of electromagnetism is at odds with the understanding of every professional physicist, and I think my job there is done, since you've now publicly stated that you believe that the Biot-Savart law is false. That's about all I care to do in engaging in a physics debate with you; from this point on, you can start talking to physicists, publishing papers, and winning Nobel Prizes if you're right. At any right, with Nobel prizes at stake, you have much more important and urgent things to do then edit Wikipedia. --Steve (talk) 16:36, 11 April 2008 (UTC)

Steve, now you are really playing on words. The flux rule IS Faraday's law. Feynman was unambiguously pointing out that there are two distinct aspects to Faraday's law.

You are quite wrong in your assertion that there are two Faraday's laws. The vXB effect is included in Faraday's law. Faraday's law is an umbrella law for both the ∇ × E = −∂_t B effect and the vXB effect.George Smyth XI (talk) 23:52, 11 April 2008 (UTC)

RfC: One Faraday's law or two?

David J. Griffiths wrote one of the most widely-used university-level textbooks on classical electromagnetism, in which he states, directly and explicitly, that there are two different laws of physics which are both, ambiguously, referred to as "Faraday's law of induction". George Smyth XI claims that there is only one Faraday's law and that "Griffiths is totally confused", based not on modern textbooks, but rather based on his own understanding and based on 150-year-old papers by Maxwell. Accordingly, George has repeatedly reverted my edits to the introduction of the article. Please take a look at the above conversation, and the recent article edits, and comment. Thank you! --Steve (talk) 05:56, 11 April 2008 (UTC)

Steve, don't misrepresent my position. There is only one Faraday's law and I base my sources on all modern texbooks and all modern encyclopaedia.George Smyth XI (talk) 09:57, 11 April 2008 (UTC)

Could you please cite them somewhere on this talk page then? (Sorry if you've already done so, but I didn't see such.) Griffiths is really, really, widely used, and if he's wrong there should be a specific rebuttal to his point. --Starwed (talk) 09:37, 12 April 2008 (UTC)

Starwed, Have you actually checked out Griffiths to see if he is saying what Steve claims he is saying? Does Griffiths introduce Faraday's law as a term ambiguously applied to two different but related laws in EM?

From the quotes that Steve has given, it is clear that Griffiths has noticed that the Faraday's law in Maxwell's equations doesn't cater for motion dependent EMF. He has then arbitrarily decided that that he won't consider motion induced EMF to come under the terms of Faraday's law.

Griffiths is clearly out of line in adopting this approach because Faraday's law caters for both aspects of induced EMF.

The point is, that the introduction to an article on Faraday's law should not begin by drawing attention to this kind of detail. No textbooks do, and no encyclopaediae do.

This is not a question of citations. It's a question of the fact that Steve has deleted a perfectly balanced introduction to Faraday's law and replaced it with unnecessary confusion. It's a question of style and coherence and historical accuracy.

Why not have a look at the alternative version and decide. In fact, I will revert it back again because PhySusie backed up Steve without even having supplied any input into the debate. George Smyth XI (talk) 11:51, 12 April 2008 (UTC)

George, you say that "no textbooks" "begin by drawing attention to this kind of detail". On the contrary, Griffiths' textbook spends 9 sentences discussing to the ambiguous nature of the term "Faraday's law" within the very same paragraph that the law "EMF=-d flux/dt" is first introduced, which is the paragraph immediately following the one where "curl E = -partial B/partial t" is first introduced. See pages 302-3. So your statement about "no textbooks" is demonstrably incorrect. --Steve (talk) 15:32, 13 April 2008 (UTC)

I don't know how you can accuse Griffiths of being "out of line". "Faraday's law" is a pair of words. The definition of this pair of words is not handed down by the Almighty, nor set in stone forever by the historians. No, this pair of words means whatever it is that physicists use it to mean. To you, and to many physicists, the words "Faraday's law" include motional EMF. To Griffiths and Feynman, and to many other physicists, they do not. You are familiar with the concept of usage being established by convention, right?? --Steve (talk) 15:46, 13 April 2008 (UTC)

Steve, while Griffiths may have decided that motional EMF no longer comes within the jurisdiction of Faraday's law, I can see no evidence that Feynam adopted the same approach.

At any rate, I was taught in school that the flux law, which is Faraday's law, includes motionallly induced EMF. That is what Faraday believed and that is what Maxwell believed.

The evidence is that Griffiths was confused and so we cannot bend a general introduction to an encyclopaedia article on Faraday's law to accomodate Griffiths' confusion.

In fact if we were to write the introduction as per Griffiths, then we would have to leave out the full version of Faraday's law and only deal with the restricted partial time derivative version, since it is only this version which Griffiths recognizes to be Faraday's law.George Smyth XI (talk) 17:13, 13 April 2008 (UTC)

I already told you, and showed you the quote, that proves that Feynman's terminology is the same as Griffiths'. He explicitly defines the term "Faraday's law" to be the equation involving the curl of E, and he explicitly defines the term "flux rule" to be the one with flux and EMF, and he explicitly discusses how these two laws differ.

I'll say it again: You learned in school that the term "Faraday's law" is a term which means the flux-and-EMF equation. Other people learn in school that the term "Faraday's law" is a term which means the Maxwell-Faraday law. This isn't a question of physics: Everyone--including Feynman, Griffiths, Faraday, Maxwell, you, and me--emphatically agrees that the flux-and-EMF equation includes motional EMF. It's not a question of physics, it's a question of what the two words "Faraday's law" mean. There's no right or wrong here, it's a definition established by convention; the words mean whatever it is that physicists use them to mean. The definition that happens to be used and preferred by you has no special status as the only legitimate definition of these two words. Indeed, there are two different definitions in wide use, one of which includes the vXB, the other of which does not. Again, [please read the first few paragraphs of this. --Steve (talk) 18:02, 13 April 2008 (UTC)

Steve, Feynman's terminology was not the same as Griffiths. They were talking about the same two effects, but only Griffiths decided that the vXB effect didn't come under the jurisdiction of Faraday's law.

Faraday's law means one thing, and you are now really clutching at straws if you are trying to back up your argument on the basis that meanings of terms change over time.

We haven't reached that time yet. Faraday's law still means exactly what everybody has always taken it to mean.George Smyth XI (talk) 08:21, 14 April 2008 (UTC)

Feynman and Griffiths' terminologies are the same. There's no ambiguity about it. On page II-17-2, he writes curl E = - partial B/partial t, and says "We will call this Faraday's law". We're all in agreement that the equation that "he will call Faraday's law" does not contain motional EMF. He also defines the term "flux rule" as the equation EMF = -d flux/dt, and every time he mentions that equation, he refers to it as the "flux rule", never "Faraday's law". Throughout the book, especially chapters 16, 17, and 18, he uses both the terms "Faraday's law" and "flux rule" in a way that is exactly consistent with these definitions. Whenever he's talking about motional EMF, and this is dozens of times, he never uses the term "Faraday's law", only "flux rule". Conversely, whenever he uses the term "Faraday's law", which again is dozens of times, he is never talking about motional EMF, but only about the precise equation "curl E = - partial B/partial t", or the equivalent integral form involving the partial derivative of B. Feynman's usage of terminologies is clear as day --- a reader whose only experience of electromagnetism was this book would have no cause to even suspect that the term "Faraday's law" is ever used to refer to the equation EMF = -d flux/dt.

The fact that the meaning of terms changes over time is at the heart of everything I've been saying. In modern physics, as much as you hate it, the usage of the term "Faraday's law" to refer to the equation which does not include motional EMF is now a widespread and accepted usage. Your insistence that "we haven't reached that time yet" is based on no evidence whatsoever. Indeed, the fact that two very prominent textbooks and many published articles refer specifically to the equation without motional EMF as "Faraday's law" is a sure sign that the time is here. (Of course, the usage of the term "Faraday's law" to refer to the equation which does include motional EMF also continues to be a very widespread and accepted usage, obviously. That's why we should list both as legitimate, alternate definitions of the term "Faraday's law".) --Steve (talk) 17:00, 14 April 2008 (UTC)

Steve, it doesn't matter what Feynman or Griffiths says.

Faraday's law is the flux rule. Feynman contributed nothing new to classical electromagnetism. His role was in quantum electrodynamics, and he undermined his own role by stating that anybody who claims to understand quantum mechanics is either lying or stupid. So which category did he see himself as fitting into?

We cannot base a general introduction to an article on Faraday's law simply on what the likes of Feynam or Griffiths says. We must base it on a broad average of sources past and present with a particular regard to what Faraday said.

At any rate, I haven't seen any evidence that Feynman didn't consider motionally induced EMF to come under the jurisdiction of Faraday's law. If he did say that, he was wrong. George Smyth XI (talk) 04:22, 15 April 2008 (UTC)

The Introduction

PhySusie, I'm very disappointed that you have decided to come to the assistance of Steve Byrnes and support his incorrect and unprofessional introduction to this article.

There is one Faraday's law. Griffiths has got no right to decide that the effect of pulling a loop through a time-constant magnetic field is not Faraday's law, because I can assure you that it is very much Faraday's law. It is the vXB aspect of Faraday's law. It is the convective aspect of Faraday's law.

You are quite wrong to support Steve Byrnes on this point.

Steve's introduction is very bad indeed. There is not a single professional encyclopaedia that would start an article on Faraday's law with nonsense along the lines of 'Faraday's law applies ambiguously to two different laws in electromagnetism - - - -'.

The other introduction that you have deleted was a basic and factually correct description of what Faraday's law is.

This brings us to your quote,

"earlier version more correct - no need to change - valid citation".

Let's now analyse this statement of yours. You have taken absolutely no part in the debate which has been ongoing for a week or two. But the moment that you see an edit conflict brewing, you immediately come in to assist Steve Byrnes so as to avoid the need for him to breach the three revert rule.

You say that his version is more accurate. Can you please elaborate to us all as to in what respect it is more accurate? It has removed the expression for Faraday's law and confused the whole issue by suggesting that there are two Faraday's laws.

You say that there was no need to change. Why did you not revert Steve Byrnes' edit on the same grounds?

You then said that their was a valid citation? Did you check it? Does Griffiths denial of the fact that motion induced EMF is connected with Faraday's law amount to a universally accepted understanding of Faraday's law of 1831? I don't think so.

Yet you chose automatically to back up Steve Byrnes. That is not professionalism. If you had held any informed views on the topic, we would have seen you by now in the debate. You are merely playing out a cheap numbers game. George Smyth XI (talk) 09:54, 11 April 2008 (UTC)

Sorry you feel that way about my edit. I have been following the arguments (on the various pages) and completely agree with Steve. I have not contributed because he states the argument very well, in my opinion. I did not do it to avoid the 3 rv rule for Steve - I did it because I saw it needed to be changed and that it hadn't been changed yet. I am a professional - I am quite familiar with the topic - and yes I checked the citation. This is not a personal attack against you - nor is it a blind support of Steve - I don't know either of you. As a physicist I agree with the argument that Steve has made, which is well documented, and I see no reason to change it. Please calm down and refrain from making personal attacks. PhySusie (talk) 12:38, 12 April 2008 (UTC)

PhySusie, On your talk page you claim that you saw that the introduction to Faraday's law needed to be changed back to Steve's version.

You know fine well that there aren't two Faraday's laws. You know fine well that textbooks don't introduce Faraday's law as two laws. And you know fine well that encyclopaediae don't introduce Faraday's law as two laws. So you are not being entirely truthful.

You claim that you have followed Steve's argument. I'll believe that when you repeat Steve's argument in your own words. I have no evidence that you have followed the argument at all.George Smyth XI (talk)

Let's be more specific?

George, here's what I'm saying, step-by-step. Can you please specify the step in which you disagree, so that I can give citations to sources that satisfy you? Let's start with the equations in question:

(E1) EMF = d flux/dt

(E2) curl E = -partial B/partial t

• (1) (E1) is a true law of physics
• (2) (E2) is a true law of physics
• (3) (E1) and (E2) are not the same law of physics, since (E1) contains a phenomenon, motional EMF, that is not contained in (E2)
• (4) Many, many reliable sources refer to (E1) as "Faraday's law"
• (5) Many, many reliable sources refer to (E2) as "Faraday's law". Not "An incomplete form of Faraday's law", just simply "Faraday's law".
• (6) Therefore, there are two different laws of physics which are both, ambiguously, referred to as Faraday's law.

Let me know exactly which step in this argument you disagree with, and I would be happy to prove it with as many citations as would please you. I can add on:

• (7) Since (E1) and (E2) are both very prominent in the literature as the owner of the name "Faraday's law", WP:NPOV demands that we not completely privilege one of these laws over the other in the introduction of the article.

Steve, you are actually one of the very few people to have noticed that (E2) does not cater for motionally induced EMF. And I think that this realization on your part has resulted in an over reaction. (I saw it in a January 1984 paper).

I agree with your points, (1), (2). Also (4) and (5).

But I don't agree with (3). Neverthless, there is indeed an important issue here that needs to be highlighted. The fact that (E2) is not the complete Faraday's law needs to be highlighted in a section in the main article.

But this is not an issue which should be allowed to cloud the introduction to the article. Both of these laws are Faraday's law, albeit that one of them is an incomplete version.

I have tried to show you that the vXB term simply makes the partial time derivative up to a total time derivative. Unfortunately, I haven't been able to provide a modern source for that and so you have chosen to dicount it despite the fact that it is obviously a true fact. At any rate, it doesn't relate to the contents of the main article, but it should have helped you to see the wider picture.

And on that same issue, regarding Count Ibliss's suggestion, although I don't agree that his idea such replace the classical and historical approach, there is no harm in having a special article on it. In that regard, supposing we get as far as obtaining the Lorentz force from Lorentz covariance of the Coulomb force. How do we then obtain Farady's law? We will be back once again to the very fact that you have been denying, and that is that Faraday's law follows from taking the curl of the Lorentz force.

On your points (6) and (7), I don't agree with your idea that we are dealing with two different Faraday's laws. We have one Faraday's law. We also have an incomplete version of Faraday's law in modern Maxwell's equations. George Smyth XI (talk) 07:58, 13 April 2008 (UTC)

I'm not "one of the very few people to have noticed that (E2) does not cater to motionally induced EMF". Anyone who has read either Griffiths' or Feynman's textbook, i.e. perhaps a majority of physicists, would understand this, since both authors discuss this point specifically and at length.

If you don't agree with (3), and believe that the two laws (E1) and (E2), despite explaining different phenomena, despite being used in different contexts, despite being specifically and pointedly called by completely different names in two highly-regarded E&M textbooks, are nevertheless "the same law of physics", then I have to question whether you understand the definition of the word "same". --Steve (talk) 15:16, 13 April 2008 (UTC)

Steve, Yes, and Maxwell also noticed it.

Faraday's law has got two aspects. We're agreed on that. But alot of people nowadays don't understand that fact. The majority of physicists don't do the applied maths courses that deal with subtleties like total, partial, and convective derivatives. We have an unfortunate state of affairs in which physicists don't know their maths, and where mathematicians don't have a sufficient interest in physics to make use of their skills. I've seen it all first hand. I saw top class mathematicians ending up as accountants. And I saw many a prospective physicist thinking he (or indeed sometimes she) could run before he (or she as the case may be) could walk.

Your observation is quite commendable in this day and age.

The so called Maxwell-Faraday law only caters for one of the EM induction effects. While I agree with you that this needs to be discussed and explained in the main body of the article, I don't agree with you that it warrants clouding up the introduction over.

There is only one Faraday's law and that is the flux rule. George Smyth XI (talk) 15:39, 13 April 2008 (UTC)

Well, I suppose that not everyone who takes a physics course necessarily reads the textbook, but if they did, this bit of information would be staring them in the face. But back to the subject, let me repeat what I said before: (E1) and (E2) do not explain the same set of phenomena, we're all agreed on that. But you still would disagree with my statement #3 that (E1) and (E2) "are not the same law of physics"? The dictionary defines the word "same" as "resembling in every relevant respect" or "corresponding so closely as to be indistinguishable". Clearly, motional EMF is a very relevant respect in which they differ. How do you define the word "same"?? --Steve (talk) 18:56, 13 April 2008 (UTC)

Steve, (E1) is Faraday's law in its totality. It involves both aspects of Faraday's law. (E2) only caters for one aspect of Faraday's law.

That is not a sufficient basis upon which to say that there are two Faraday's laws. There is only one Faraday's law and (E1) is part of that law. George Smyth XI (talk) 07:28, 14 April 2008 (UTC)

OK, we don't have to say yet that there are two Faraday's laws. Let's start with the simpler claim: (E1) and (E2) are two different laws of physics. I'm not asking about what they should be called, I'm just asking: Are (E1) and (E2) two different laws of physics, or are they exactly the same law of physics? If your answer is "the same", can you please give your definition of the word "same"? --Steve (talk) 17:04, 14 April 2008 (UTC)

Steve, the two equations in question differ by the fact that one contains both aspects of Faraday's law whereas the other contains only one aspect of Faraday's law. It's not a question of whether they are the same or different. George Smyth XI (talk) 04:25, 15 April 2008 (UTC)

Quotes by Feynman

I've always been amazed at the reverence that is afforded to quotes by Richard Feynman, bearing in mind the fact that he didn't tell us anything about classical electromagnetism that we didn't know already.

He was a man, who by virtue of his contributions towards the Manhattan project and quantum electrodynamics, was given a considerable degree of licence to make cheeky comments over a wide range of topics in physics that other people wouldn't be allowed to get away with.

Notably he points out how aspects of electromagnetism are simply not understood and how anybody claiming to understand quantum mechanics is either lying or stupid. Such pronouncements would not be tolerated from the man in the street.

So what makes Richard Feynman so special? Is it the fact that he played the bongo drums? Is he a consolation to those pseudo-intellects who like to pretend to understand everything about electromagnetism but who deep down know that they don't?

Whatever it's all about, quoting Feynman has become a bit of a cult activity. And I think that in the fullness of time it will be realized that Feynman's net contribution to classical electromagnetism was zero. George Smyth XI (talk) 11:08, 13 April 2008 (UTC)

The root of this problem lies in the current state of ignorance

Steve, I've got a physics forum web link which explains this whole problem exactly.

http://www.physicsforums.com/showthread.php?t=164653

Feynman didn't realize what the mathematical connection was between the partial Faraday's law and the vXB term. Feynman had got as far as seeing the two aspects of Faraday's law but he had clearly failed to see how it all fit together.

Somebody on this Physics Forums web under the name of "Obsessive Maths Freak" is the voice in the wilderness who supplies the missing link. The vXB effect is the convective term that makes the partial time derivative into a total time derivative.

I have already explained this very same relationship on wikipedia a number of times over the last few weeks. A partial time derivative and a convective derivative add together to give a total time derivative.

Obviously Feynam failed to see this simple relationship in Faraday's law vis-a-vis the vXB term and the so called Maxwell Faraday law.

Feynman often pointed out the fact that he didn't fully understand classical electromagnetism.

Faraday's law is Faraday's law and we can't allow Feynman's confusion to confuse the issue for everybody else.

I'm surprised that "Obsessive Maths Freak" got away with the comment that he did because Physics Forums is a notorious stickler for making sure that all comments keep strictly to textbook ignorance. George Smyth XI (talk) 13:25, 15 April 2008 (UTC)

I am, in fact, aware of how the flux-and-EMF rule and the Maxwell-Faraday law relate, and it certainly can be expressed in terms of partial, total, and convective derivatives. It's a very nice result. But this has nothing to do with the question at hand, which is, is "Obsessive Maths Freak" talking about the relation between Faraday's law and an incomplete version of Faraday's law, or the relation between the flux rule and Faraday's law? Or something else? It's a question of terminology, terminology, terminology.

Here is a paper (albeit still-unpublished) by two actual physicists who have clearly thought about this issue more than either of us. In this paper, they choose to use the term "Faraday's law" for the flux-and-EMF rule and "Maxwell's equation" for the Maxwell-Faraday law, which I agree is one very standard terminology. And on page 10, they write in boldface that "Faraday's law" is not "equivalent to Maxwell's equation". Since the term "Faraday's law" is of course used by many other physicists to refer to "Maxwell's equation", we have here an ambiguous terminology: Two laws which are emphatically not equivalent, are nevertheless widely referred to by the same name in reliable sources. That's all I'm saying. I'm not denying that the laws are related in an elegant way. Everyone knows they are. I'm just saying that they are best described as "two closely-related laws of physics". --Steve (talk) 17:50, 15 April 2008 (UTC)

To beat this horse to death: you need both the Maxwell-Faraday equation and the Lorentz force law to come up with Faraday's law of induction because you cannot relate EMF (which is work) to the fields without a force law. Therefore, regardless of any of these arguments, the Maxwell-Faraday equation by itself cannot possibly be the same as Faraday's law of induction. As support for this simple logic, see the Feyman quote in Faraday paradox where Feynman says specifically that we need both the Lorentz force law and the Maxwell-Faraday equation.

With this logical basis in place, George's argument could be supported to say that "There is only one Faraday's law" and supplemented with "and the Maxwell-Faraday equation is not it."

Assuming all that can be placed behind us, George has some additional discussion about the importance of the magnetic force component of the Lorentz force law in combination with the Maxwell-Faraday equation when one sets the goal of deriving Faraday's law. That discussion seems separate from the terminology issue, as Steve suggests, because there is no debate over Faraday's law being distinct from the Maxwell-Faraday equation, in just the same way that a whole is different from each one of its parts.

Brews ohare (talk) 22:41, 15 April 2008 (UTC)

Revision of Intro

Supposing we were to add a bit to the introduction for the purposes of clarity. After having explained both the aspects of EM induction that are inherent in Faraday's law, supposing we then introduce the Maxwell-Faraday law and draw attention to the fact that this well known law from Maxwell's equations, which is also referred to as Faraday's law, only actually caters for one aspect of Faradays law. It does not cater for the convective vXB aspect.

That would be a way of presenting all the important facts in the introduction in a coherent manner. George Smyth XI (talk) 06:49, 16 April 2008 (UTC)

Hi George: I don't like the idea of putting a controversy up front with inadequate space in the introductory few lines to straighten things out. To explain about v × B in the intro is just too complicated, and would drive the reader away muttering about "damn technical gobbledygook".

As the intro stands, it does a good job of presenting what you yourself would call "Faraday's law". Later, under the "Maxwell-Faraday equation" the point you want to raise is mentioned. If there is tinkering to be done about the terminology issue, this is where I'd see it done. Brews ohare (talk) 15:38, 16 April 2008 (UTC)

I tried a compromise. George's preferred use of the term "Faraday's law" is the one that's privileged right at the top as the standard usage. I still think this violates WP:NPOV to some extent, but I can live with it. The Maxwell-Faraday equation is given at the end of the introductory section, where it's a described as a law that many physicists call "Faraday's law". It's also stated that the Maxwell-Faraday equation doesn't attempt to explain motional EMF. So it's still easy enough for a reader to learn that the term "Faraday's law", as it's used by physicists, has some ambiguity, but they have to read the whole introduction, not just the first sentence...which again I'm not a huge fan of, but I can live with it. It's also, I think, not overly technical. So, everyone happy? --Steve (talk) 17:31, 16 April 2008 (UTC)

I think it's quite good now. I was originally supporting the point that Brews has just made that we shouldn't put too much controversy in the introduction.

But on the other hand, as in the case of Maxwell's equations, when slight variations in format do exist, and do generate alot of discussion, then there is no harm in having a clarifying paragraph at the end of the introduction.

There is only one Faraday's law, but Maxwell derived it in a unique way in his 1861 paper with the curl function. (Maxwell of course used a cumbersome cartesian notation).

The curl presentation is to the best of my knowledge Maxwell's own.

Heaviside then uses it but specifically with partial time derivatives and hence precludes the vXB effect. I know that Brews didn't want a discussion of the vXB effect in the introduction but I think that Steve has got around that by simply stating in English that the Maxwell-Faraday equation doesn't cater for motionally induced EMF.

It's a further matter of interest to what extent Maxwell himself was treating his equation (54) as a partial time derivative. He actually uses the total time derivative symbols and the preceding equations indicate that he is fully aware of the implications. But the evidence tends to suggest that he is only interested in the partial time derivative effect.

If we move on down towards equation (77) where he develops the vXB effect, we note that he specifically mentions that the dA/dt terms are to refer to a fixed point in space. Hence, although he uses the total time derivative symbols in equation (77), he clearly means them to represent partial time derivatives. As for equation (54), this is not so clear.

The only thing we know for sure is that Maxwell developed Faraday's law into the curl form, and Heaviside unequivocally precluded the vXB effect by specifically making it a partial time derivative.

So on reflection, I am now in favour of a special mention of this Maxwell-Heaviside- Faraday law at the end of the introduction.

What I was opposed to was the idea of introducing Faraday's law as a term ambiguously applied to two different laws in electromagnetism. George Smyth XI (talk) 01:18, 17 April 2008 (UTC)

Well George, I would go with Steve's last version, but do not like your recent changes. They are of historical interest, but in the intro they are simply confusing, as a reader is likely to think the straight derivative form you attribute to Maxwell is still in use as accepted practice. That is misleading. It should be removed. You should follow the adage "half a loaf is better than no bread" and go back to Steve's version. 4.240.72.26 (talk) 05:28, 17 April 2008 (UTC)

The equation $\nabla \times \mathbf {E} =-{{d\mathbf {B} } \over dt}$

...as a law of physics that incorporates motional EMF, is original research by George. I've certainly never seen it in any textbook. It comes, I think from the fact that he's been reading his Maxwell, and gotten used to Maxwell's outdated definition of E. To be specific, Maxwell wrote the equation

(E3) $\mathbf {E} =\mathbf {v} \times \mathbf {B} -{\frac {\partial \mathbf {A} }{\partial t}}-\nabla \phi$

which would presumably be complemented by

(E4) $\mathbf {F} =q\mathbf {E}$

whereas modern writers would write

(E5) $\mathbf {E} =-{\frac {\partial \mathbf {A} }{\partial t}}-\nabla \phi$

(E6) $\mathbf {F} =q\mathbf {E} +\mathbf {v} \times \mathbf {B}$

Obviously, (E5) and (E3) cannot both be simultaneously true, and nor can (E4) and (E6). But while every textbook writes (E5) and (E6), the equation (E3) is in no modern textbook, because it's false according to modern definitions; likewise with (E4) for nonzero velocity.

According to Maxwell's definition of E, George's equation and the accompanying text make perfect sense. According to the modern one, it's manifestly incorrect. curl E is a vector field, independent of v, so cannot equal both the partial derivative of the vector field B and the convective total derivative of B simultaneously.

And once again, George, please, please read WP:NOR. Wikipedia is emphatically clear that original research is forbidden, no matter how obvious you think it is. --Steve (talk) 03:18, 17 April 2008 (UTC)

Steve, the equation $\nabla \times \mathbf {E} =-{{d\mathbf {B} } \over dt}$ is not original research. It is equation (54) in Maxwell's 1861 paper. It is the curl of equation (77) ($\mathbf {E} =\mathbf {v} \times \mathbf {B} -{\frac {\partial \mathbf {A} }{\partial t}}-\nabla \phi$) in the same paper. It doesn't contradict anything in the modern textbooks.

You have been reading too much Feynman and not enough Maxwell.

OK, so how do we resolve the legitimate problem that the anonymous has raised? He has a point. Maxwell's equation (54) is not seen in modern textbooks in total time derivative format, and it may confuse the readers.

We could of course put in the partial time derivative version by Heaviside and explain it all. But that gets back to the original issue of not putting too much detail in the introduction.

We can either drop the subject in the introduction, or we can try and use the better known Heaviside partial time derivative in the introduction alongside a coherent, simple and factually correct explanation.

I'll try to do that now and see how it goes. George Smyth XI (talk) 09:44, 17 April 2008 (UTC)

What is EMF?

The stated law says: "The induced electromagnetic force or EMF in any closed circuit ..." Shouldn't this be "electromotive force" (i.e. volts, not newtons)? So the link is wrong too.

I wanted someone knowledgeable to agree and change it so I'm leaving it to you guys, the maintainers of the page. Dan Morris, 14:28, 2 May 2008 (UTC)

Quite a gaff, eh? Thanks. Brews ohare (talk) 20:01, 3 May 2008 (UTC)

Resistive Force

Since the article only addresses closed circuits, I was wondering what the equation for the resistive force of the eddy currents would be for just a piece of metal moving through a magnetic field (like an electromagnetic brake). Any ideas?

86.140.130.100 (talk) 20:11, 7 May 2008 (UTC) James T.

I'm not sure that there's a simple and exact formula; my impression was that the microscopic flows of current could be arbitrarily complicated. I don't know for sure. Anyway, whatever formulas exist (and I'm sure they do, at least approximately), would presumably belong not here, but rather in the article: Eddy current. (At least primarily.) :-) --Steve (talk) 22:53, 7 May 2008 (UTC)

Diagram request

{{reqdiagram}}

Faraday's law of induction has a few diagrams now; if another is requested, please re-add this template with specific details. thanks --pfctdayelise (talk) 13:35, 27 July 2008 (UTC)

Faraday's Law and the Lorentz Force

There is a textbook, 'J.A. Stratton, Electromagnetic Theory, (McGraw-Hill, New York, 1941). In 23, Chapter 5 is to be found a total time derivative version of Faraday's law. The justification is that the convective component is the curl of vXB. Stratton's words are “If by E we understand the total force per unit charge in a moving body, then curl E = −∂B / ∂t + curl (v × B) . Moreover, dB / dt = ∂B / ∂t + (v.grad)B , so that curl E = −dB / dt .“

This would suggest that Faraday's law is simply the curl of the Lorentz force. David Tombe (talk) 19:07, 14 November 2008 (UTC)

The if in Stratton's lead-in is a big "if". He might be assuming this is an "if" obviously satisfied (as you interpret it), or alternatively a conjecture to help deepen our understanding. Obviously, the standard view is that curl E = −∂B / ∂t. Brews ohare (talk) 17:09, 17 November 2008 (UTC)

Brews, I don't actually have a problem with writing F/q = vXB as E = vXB. It's a trivial issue and it shouldn't be allowed to stand in the way of obtaining an overall comprehension of the relationship between the Lorentz force and Faraday's law. David Tombe (talk) 20:19, 17 November 2008 (UTC)

The fact that you regard it as a "trivial issue" whether one writes F/q or E is not something that you should be proud of. Misusing and/or rejecting standard terminology and notation is a big step towards misunderstanding concepts, and a giant leap towards talking past other people, not being able to communicate your understanding to anyone else, and making statements that appear to others to be blatantly ignorant and wrong. CF your past use of the terms "radial acceleration", "acceleration", "vector field", "reference frame", "coordinate system", "force", and on and on. Whatever point you're trying to get across, you can get it across using the same notation and terminology and definitions that every other physicist uses and worked hard to learn. --Steve (talk) 06:33, 18 November 2008 (UTC)

Steve, I would have thought that writing E for F/q in the F = qvXB equation would have considerably aided as regards obtaining a full comprehension of the relationship between the two aspects of Faraday's law which you have correctly identified. Obviously Stratton saw this relationship too in 1941. Surely you can now see how taking the curl of the total E leads to a total time derivative Faraday's law. You saw that Woodstone recently suggested the total time derivative format to you on the Maxwell's equations talk page. With a full comprehension of these inter-relationships, the article can be written up in a simplified coherent manner, and fully in line with sources. All you have to do is present Faraday's law in it's most general form as would be presented in an advanced high school textbook. Then you later show the partial time differential version as it occurs in the modern versions of Maxwell's equations. You then point out how this version doesn't cater for motion dependant EMF. You then show how the missing term is F = qvXB. You can then point out that this missing factor can be remedied either by making the Faraday's law into a total time derivative version, or by introducing the Lorentz force law alongside the modern Maxwell's equations. You can then further point out that the Lorentz force , in essence, was one of Maxwell's original eight equations. David Tombe (talk) 15:30, 18 November 2008 (UTC)

Steve, on your other point about radial acceleration, if you go to the wikiphysics project page, you will see that I have summarized that dispute. It doesn't matter what name we give to the second time derivative of the radial distance. The real argument went beyond the terminologies, but unfortunately the argument never went anywhere because people were continually getting bogged fown in the terminogies. David Tombe (talk) 15:35, 18 November 2008 (UTC)

David: Simplification of the presentation is always a good goal, and you have outlined what you think would be a clearer approach. However, your outline is too sketchy for me. Can you provide more detail? In particular, just how would you introduce the topic? Would you change the statement of the flux law? Brews ohare (talk) 19:21, 18 November 2008 (UTC)

Brews, the statement of the flux law is fine. That is Faraday's law in its essence. I would then mention that the Faraday's law in the modern Heaviside versions of Maxwell's equations does not tell the whole story because it is only a partial time derivative equation which doesn't cater for the motion dependant EMF. I would then illustrate how the vXB term remedies this fact by making it back into a total time derivative format, but that the normal way to introduce the vXB effect in modern textbooks is to add the Lorentz force equation as an additional equation, alongside Maxwell's equations. I would then draw attention to the fact that the Lorentz force is in fact equation (D) of Maxwell's original eight equations and that Faraday's law doesn't appear in the original eight equations since all the effects of induced EMF are catered for by the Lorentz force equation (D), and that Maxwell uses equation (D) to derive the EM wave equation, where modern textbooks use the Faraday's law as it appears in the Heaviside versions of Maxwell's equations. That completes all the necessary inter-relationships.

Regarding the integral stuff, all you really need to do is use one of those theorems (Stokes or Green's, I forget which) to show the equivalence between a curl version of Faraday's law and an integral version.

This is where it is important to have the first part properly explained. Stick to the total time derivative version the whole way through when you deal with the integral stuff. There was so much unnecessary confusion caused the last time, all surrounding the issue of 'is it the partial time derivative version or the total time derivative version?' So many people were confused about how the vXB term fit into the partial time derivative intergral version. The answer was simple. It didn't. David Tombe (talk) 20:04, 18 November 2008 (UTC)

the article

I think the entire article up to "Electrical generator" is completely inscrutable, at least to my amateur eye unwilling to sit here for an hour working it out. Maybe it could be rearranged so the easy section is first and people aren't discouraged :) .froth. (talk) 02:05, 16 November 2008 (UTC)

Yes. It could be substantially shortened and simplified. As you can see from the section above, Faraday's law contains two aspects. There is a time varying aspect and a motion dependent aspect. Once the relationship between these two aspects and the Lorentz force is fully understood then a new article can be written on this basis. David Tombe (talk) 16:57, 17 November 2008 (UTC)

Froth: You criticism would be easier to respond to if you identified just what your difficulties are in detail. Simply scrapping the entire article and starting over again is unlikely to please you any better. BTW, what is the easy section? Brews ohare (talk) 17:01, 17 November 2008 (UTC)

Brews, there was far too much effort wasted in trying to comprehend the relationship between the time varying effect and the motion induced effect. It became a 'learning out loud' job. Those issues are now all fully understood. Hence it should be easier to write a simplified article now. David Tombe (talk) 20:16, 17 November 2008 (UTC)

The Stratton reference

FyzixFighter, I'm glad to hear that you have seen this Stratton book, because I haven't. I tried to find it but I couldn't. I obtained the reference only second hand last November 2008. I had actually come up with an identical theory back in 1982. I wrote about it in some articles in the 1980's and the 1990's.

Based on what I copied from the secondary source, Stratton is saying exactly the same as what I said in an article in January 1984. What exactly are your problems with the point that is being made?

There have been two aspects of electromagnetic induction identified. There is a time varying aspect and a motion induced aspect. If we take the curl of both of these and add them together, we get the full Faraday's law of electromagnetic induction. So what exactly is your problem?

Does Stratton itself say something different from how I have reported it, based on my secondary source? I can't see how that could be possible because what it says that he says, according to the secondary source makes perfect sense.

Perhaps you should have reworded my edit accordingly rather than simply deleting it without discussing the matter.

I would be interested to know what exactly Stratton says in your version of the book. If it's a case of page numbers being wrong, then that can be corrected without deleting the whole edit. David Tombe (talk) 08:12, 1 February 2009 (UTC)

Your Statement Of Faradays Law Is Wrong

You guys at wikipedia are certainly a silly bunch. You are quibbling about details when you did not state the Faraday law correctly in the opening. I am not surprised that you get comments that the article is obscure and confusing, because you dont know what you are doing. As an very knowledgable person on this subject, I assure you your article is a waste of time to read as it is incorrect in too many details. A very big problem is stating the law correctly so that when a user actually tries to use your version of it he will get the right result. 72.64.44.37 (talk) 16:19, 2 February 2009 (UTC)

Feel free to rewrite it correctly. Binksternet (talk) 17:23, 2 February 2009 (UTC)

I have no problem is stating that I think this article is simply a very confused discussion of different ideas and concepts which have been squeesed into the topic of Faraday Law. It should be accompanied by what is the correct name, electromagnetic induction. Faraday discovered electromagnetic induction in his attempt to produce electricity from magnetism as an inverse phenomenon to the Oerstead effect of magnetism produced from electricity. The law as you state it is false as the induced emf is negative and that is not in your law. Your statement about Henry is misleading since he didnt discover the Law but the phenomenon. It is Faraday who stated the law. So i am not sure if this article is about electromagntic induction or about the faraday law. If the faraday law, all that needs to be stated is the law itself and an explaination of how it is to be applied in practice. The rest of the discussion seems irrevalent as far as I can tell. The only user for whom it would be relevant would be an advanced student in electromagnetism and I doubt if many users are at that level. I suggest a rewrite to make it high school level and understandable. If you want to go into the details, create another article on electromagnetic induction. Dont forget to discuss unipolar induction in it.72.84.64.59 (talk) 19:00, 2 February 2009 (UTC)

72.84.64.59, thanks for clearing that up about Henry. I always knew that Henry had discovered electromagnetic induction in the same year as Faraday. But I had never heard his name mentioned in connection with the formulation of the law. I will correct that now. David Tombe (talk) 04:36, 3 February 2009 (UTC)

Joseph Henry seems to have discovered the fundamental idea of electromagnetic induction prior to Faraday, but he never stated the Faraday Law. That is given wrong in the article. In fact faraday got the law wrong and he had to correct the paper as he had the action of the emf backwards. Apparently this never was correctly stated in his law. The salient point is that the induced emf or magnetic flus is opposite to the inducing flux. Henry saw this opposing effect in his experiments and that is the important thing to remember about his results. He correctly saw that the effect was opposed to the change in the established current in a circuit, so he is said to have discovered self inductance for which the unit of inductance derives its name as, the Henry.71.251.179.218 (talk) 22:25, 3 February 2009 (UTC)

You Misinterpret What Feynman Said, Or Perhaps Feynman Said It Wrong

There are not two different phenomena, that is completely wrong and feynman is wrong to say it that way. There is only the change in flux but two different ways that flux can be changed, either by changing the flux without movement, for example changing the current in a transformer, and moving the two circuits in a number of different ways. The circuits can stay the same and be moved in space. The size of the cirucits can change. Finally there is a transformer effect due to moving the circuit in orientation. For example by rotationg one of the coils in a transformer relative to the other coil. This changes the flux but the coils are not actually being moved apart or closer together. This is called a variometer. Its action is modeled by the transformer effect. In all of the cases here, there is only one fundamental physical phenomenon, that is change in flux. There are two math models for that change, and that is what Feynman is saying. There is only one physical phenomenon, but there are two different ways of expressing it mathematically as particular cases of the general law being rewritten to describe the two different cases where flux is changing. You need to correct this problem that you dont understand the physics involved.72.84.64.59 (talk) 19:18, 2 February 2009 (UTC)

You believe that "change in flux" is the "physical phenomenon", while "two different ways that flux can be changed" are "two different ways of expressing it mathematically". Feynman believed the exact opposite, that "change in flux" is the single mathematical model, while "two different ways that flux can be changed" correspond to the two different physical phenomena. (In one physical phenomenon, an EMF appears because of an electric force; in the other physical phenomenon, an EMF appears because of a magnetic force.) I agree with Feynman, and you might too if you read his book. He goes on and on about this, and justifies this statement very explicitly. Griffiths also makes this point, and explains it just as clearly. --Steve (talk) 23:38, 2 February 2009 (UTC)

Feynman's book is wrong if he is saying what you are claiming to be what he really meant to say. What I said above is the correct statement of the problem.72.64.56.210 (talk) 00:29, 3 February 2009 (UTC)

72.64.56.210, It's not so much that Feynman was wrong as that he didn't understand the mechanism. I think that Feynman was merely poining out wat Maxwell and Einstein had already pointed out regarding two distinct manners in which the change in flux can be brought about. It seems to be forgotten that Maxwell had already treated this distinction in detail in his 1861 paper 'On Physical Lines of Force'.

It is there that we can get some insight into the commonality of the two aspects. You seem to be of the opinion that the two aspects are firmly united under the banner of change of flux. I think that Feynman would probably have agreed with you on that point. Maxwell gives us a clearer insight into the two different mechanisms whereby that change in flux can be brought about. In the time varying situation, Maxwell explains how a pressurized rotatory effect is transmitted through his vortex sea and discharged into a wire. In the motionally induced case, Maxwell considered how the moving wire induced a pressure in the vortex sea in front of the wire, which was then discharged at right angles into the wire due to the differential vorticity as between the front and the back of the moving wire.

I do think it is important to highlight these two distinct aspects of Faraday's law. David Tombe (talk) 04:32, 3 February 2009 (UTC)

Steve and 72.64.56.210, I was looking at your argument again. You are arguing over what Feynman thought. Ultimately, does it matter what Feynman thought? He was merely pointing to two distinct aspects of EM induction that had already been identified by Maxwell. That is all that matters. There are two distinct aspects and they share a degree of commonality. And just as 72.64.56.210 says, the two aspects arise in relation to the manner in which that commonality is invoked. In fact, as I read all this again, I think that all three of you are just saying the same thing in a different way. David Tombe (talk) 04:49, 3 February 2009 (UTC)

Tidying up the article

I would agree with alot of what anonymous 72.64.56.210 has been saying regarding the untidy state of this article. I believe that alot of it could simply be discarded. I was working on a strategy of getting the key points into a few sections at the top and then binning the rest. David Tombe (talk) 04:42, 3 February 2009 (UTC)

The Einstein Quote

Can anybody understand the point that Einstein is making in his quote? He mentions how there is an asymmetry in Maxwellian electrodynamics. Well yes, we all know that. It is the asymmetry associated with the two aspects under discussion. It's an asymetry in Faraday's law that predates Maxwell.

But then Einstein goes on to say that this asymmetry is not inherent in the phenomenon? What does he mean? Of course it's inherent in the phenomenon otherwise he wouldn't have been talking about it. Maxwell dealt with the two aspects in detail. We know there is an asymmetry, but why should that asymmetry be a problem? David Tombe (talk) 08:33, 3 February 2009 (UTC)

David, I think it unlikely that anyone actually understands the Einstein quotation, because it actually says nothing clearly. The experts disagree about what it means. J.A. Wheeler in "A Journey Into Spacetime" gives one opinion and A.I. Miller in "Albert Einstein's Special Theory Of Relativity " gives a completely different opinion. Since the experts don't agree on what this quotation is supposed to mean, it should be deleted. If the experts can't make sense of it, how is an the average reader supposed to be able to? 71.251.179.218 (talk) 22:13, 3 February 2009 (UTC)

If you don't understand what he means by the first sentence, try reading the next five sentences, where he explains exactly what he means very explicitly and with an example. He's saying the same thing as Feynman, Griffiths, Purcell, etc. have said. Anyway, even if not every reader understands every word of the quote, it should stay in because it's clearly a relevant quote, with important historical interest, and on-topic for that section. --Steve (talk) 22:42, 3 February 2009 (UTC)

Einstein states that there is an asymmetry in the Maxwell laws "as usually understood at the present time". His point is that there is no asymmetry. Maxwell's laws apply in any inertial frame. As he shows at the end of Section 6 in his paper, the Lorentz magnetic force is physically due to an electric field in the frame of the moving charge. One arrives at that E field by performing a lorentz transformation of the EM field as measured in the lab to the EM field in the conductor's frame. In this more accurate and modern view, electrons only respond to E fields in their rest frame. They don't respond to the magnetic field.

There is only one Faraday law, which, in an inertial frame, relates the circulation of the induced E field to the time rate of change of the B field. It can be expressed in differential or integral form.

If you wave a magnet past a test loop ("flip coil"), the voltage will be proportional to the flux change in the loop. If you wave the flip coil past the magnet, to do the calculation correctly you must transform the magnetic field to the rest frame of the loop. The time rate of change of the flux will be almost the same, and Faraday's law applies to that flux change and produces emf as usual. There will also be a small E field, which may result in a small additional emf corresponding to the lorentz force. When summed, we get the same result as in the first case.

The point is that the "Lorentz force" has nothing to do with Faraday's law. It's a convenience which allows us to do EM calculations without Lorentz transforms. Quoting Einstein:

We see that electromotive force [he's referring to the Lorentz force] plays in the developed theory merely the part of an auxiliary concept, which owes its introduction to the circumstance that electric and magnetic forces do not exist independently of the state of motion of the system of co-ordinates. Furthermore it is clear that the asymmetry mentioned in the introduction as arising when we consider the currents produced by the relative motion of a magnet and a conductor, now disappears. Moreover, questions as to the “seat” of electrodynamic electromotive forces (unipolar machines) now have no point.

In my view, if the discussion doesn't involve the time rate of change of magnetic flux, either in the magnet frame (so-called transformer EMF), or in the loop frame (relative motional EMF), then we are not discussing Faraday's law. There is much in the article that pertains to the Lorentz force that should be moved out and possibly combined with the several articles on that topic.

The article is at least twice as long as it should be, and contains material covered in depth in other locations, e.g. Maxwell's equations. There also appears to be a fair amount of OR regarding Maxwell's early concepts, which were superseded by Maxwell himself, Hertz, Heaviside, and Einstein, and which are IMO irrelevant to the main article.

We already have a Moving magnet and conductor problem article. The efforts being expended here on "dichotomy" could be taken there.

I'd recommend removing the section with the Feynman and Einstein quotes entirely at this point, even though I contributed to it.

Kbk (talk) 23:18, 3 February 2009 (UTC)

Hi Kbk, you seem to be in the Griffiths/Feynman/etc. school of that that "Faraday's law" should properly refer to the specific law $\nabla \times E=-\partial B/\partial t$. I learned it that way too, and I'm very sympathetic. However, there's no denying that lots of textbook refer to "EMF = -d(flux)/dt" as "Faraday's law" (Griffiths/Feynman call this one "the flux rule", and you're right that it incorporates the Lorentz force into it). My opinion (and this point is made in a number of textbooks) is that these are two different (albeit closely-related) laws of physics that are both, ambiguously, called "Faraday's law" by physicists, and it's a shame that the article doesn't say so. The current state of things is a sort of incoherent compromise settled months ago between David Tombe, myself, and a couple others. I'm not thrilled about this state of affairs, and I would be very happy to have you making major edits to the article. Good luck getting consensus though.... :-) --Steve (talk) 00:06, 4 February 2009 (UTC)

Kbk, There are asymetries in electromagnetic induction and so I don't understand how Einstein can say otherwise. These asymetries arise because the phenomenon has got two distinct aspects. Maxwell dealt with these two distinct aspects in detail. One of these aspects is the vXB force. Are you suggesting that we take all references to the vXB force out of the article?

The vXB force is an integral part of the flux rule, and many textbooks call the flux rule 'Faraday's law'. Maxwell already recognised the vXB force in EM induction long before Lorentz. It would appear that Heaviside dropped the vXB factor when he modernised Maxwell's equations, and that it returned again with the Lorentz transformations. But from then on it sat outside Maxwell's equations, as opposed to inside where it had once been in the distant past. David Tombe (talk) 07:26, 4 February 2009 (UTC)

What Einstein said is that depending on the FR (frame of reference) one have a differente result. The problem raise when you move the coil but not the magnet. As you see in reference frame (FR) of the coil there is no vxB (no v), BUT B' (in the coil RF) is time depending, How is that? B which is space depending, or B(x,y,z), became B'(x',y',z') but the coil is moving so x'(x,t), or for that matter x'(x',t'), so B'(x',y',z',t'). Finally what Einstein did, was to find the transformations which made all consistent-I think important to add some explanation in these sense in the text. What we usually try to do is $\nabla \times E'=-\partial B/\partial t$ which is wrong because E is in coil FR so E is E' after all, forcing us to use the ' FR of reference for the formula then $\nabla \times E'=-\partial B'/\partial t'$. The wonderful thing is that you don't need the vxB term if your in the appropiated FR. I found this link about the same http://www.nationmaster.com/encyclopedia/Moving-magnet-and-conductor-problem#Transformation_of_fields_as_predicted_by_Newtonian_mechanics Am I right? Felipe Blin —Preceding unsigned comment added by 164.77.255.226 (talk) 19:45, 12 February 2009 (UTC)

I don't see how you can get rid of the vXB term. Consider that $\mathbf {E}$ is,

$\mathbf {E} =-({\frac {\partial \mathbf {A} }{\partial t}}-\mathbf {v} \times \mathbf {B} )$

Then taking the curl, we get,

$\nabla \times \mathbf {E} =-({\frac {\partial \mathbf {B} }{\partial t}}+({\mathbf {v} \cdot \nabla })\mathbf {B} )=-{{d\mathbf {B} } \over dt}$

Maxwell used a different physical explanation for the two effects. It would look very much as if Einstein (or Lorentz) had been trying to paper over cracks for a problem which didn't exist in the first place. David Tombe (talk) 11:24, 15 February 2009 (UTC)

David May I ask from where you get v when you stand in coil frame of reference-notice that in this case v = 0 (!). Anyway I am not saying that we should use vxB It is just that we should consider his origin. May I dare to recommend "Principles of Electrodynamics" by Melvin Schwartz (Nobel prize 1988). —Preceding unsigned comment added by 164.77.255.226 (talk) 12:31, 16 February 2009 (UTC)

164.77.255.226 The v term implies a preferred frame of reference. Maxwell eliminated the v term when he derived the EM wave equation, because he considered the wave to be propagating in his vortex sea (the preferred frame of reference).

Later erroneous statements by Einstein to the extent that Maxwell's equations are equally valid in all frames of reference indicated that Einstein had no knowledge of what was in Maxwell's original papers. Einstein claimed to have been working from the Maxwell-Hertz equations. Well, whatever those equations were, or wherever they appeared, they were not Maxwell's equations. David Tombe (talk) 15:05, 16 February 2009 (UTC)

Is it then a question of terminologies?

Steve, from what you say above, it would appear that you understand the fundamental interlinkage between all the relationships involved. But there seems to be a disagreement over terminologies. Yourself, anonymous 71.251.179.218, and Kbk all seem to think that the vXB force should not accurately be discussed in connection with Faraday's law, and that it is a separate law. Have I ascertained this correctly?

I would fully agree with Feynman's statement, providing that we equate the flux rule with Faraday's law, as I believe Faraday's law was originally understood. That's perhaps where the disagreement lies. I don't want that Feynman statement removed. I usually disapprove of the cult of quoting Feynman, but on this occasion, he has made a very accurate point in a very concise and easy readable manner.

So I'm not quite clear on how you would like to proceed. I cannot go along with the idea that there are two Faraday's laws. There is only one Faraday's law, but I am fully aware that the version which we see in the modern Maxwell's equations only caters for the time varying aspect.

I still think that the best way forward is to emphasize the two aspects early on in the article and then proceed to discuss the two aspects in separate sections.

We should not overlook the fact that Maxwell dealt with these two aspects clearly and concisely in 1861, and we should not overlook the fact that Maxwell used the vXB term to cater for the motionally induced EMF, long before Lorentz ever produced that expression, and that he treated it as a crucial aspect of electromagnetic induction. We cannot ignore Maxwell's important role in all of this. I don't know what Einstein's problem was regarding asymetry. There is absolutely no doubt that there is asymetry in electromagnetism. This is clear from the Faraday paradox, and the asymetry is due to the very two aspects in question, as per Feynman's quote. Why should the asymetry have been such a big problem for Einstein, that he felt the need to fix it? There was nothing broken that needed fixed. The two aspects both sit perfectly inside the total time derivative version of Faraday's law.

My view would be to begin by emphasizing the two aspects. Then treat the two aspects separately. Point out that they both sit comfortably inside the general flux rule, and bin the rest of the article.

When we have a basic structure agreed, then we could perhaps do some kind of appendix on terminologies. David Tombe (talk) 04:18, 4 February 2009 (UTC)

David, I think your discussion here makes some important points. I will say that very recently when my attention was directed to this article and the current discussion I was surprised that the article was full of such basic mistakes. You still failed to acknowledge that you dont state Faraday's law correctly. The problem here is that this article is really not about Faraday's Law but about the Maxwell equation commonly called Faraday's law. This is the reason for the intoduction of the two different interpretations, since they arise from how Maxwell uses the equations. It doesnt arise from anything Faraday or Henry did. They derived empirical rules. The Faraday Law is not actually valid in general as it doesnt apply in all cases, the reason is that it is an empirical rule. The Maxwell equation on the other hand is a theoretical law. So you need to decide if this is about Maxwells equations or simply the empirically derived Faraday Law. This confusion is of course perpetuated in the textbooks and this explains the problem.

As far as I can tell there are three topics not separated in this article. They are Faradays empirical Law of induction, electromagnetic induction in general, and Maxwell's equation known as Faraday's law. They need to be separated out as this is the point of confusion. Now the following is the case. Faraday and Henry discovered electromagnetic induction. But they were not the same idea. Faraday introduced the notion later to become the Faraday Law which relates the negative of the rate of change of magnetic flux to a supposed induced emf. Henry had a different idea and his line of study led to wireless telegraphy. Maxwell working from the Faraday viewpoint developed a theory of electromagnetism that is not exactly the current theory as it employed an aether. Faraday later discovered that his law was not always as it seemed to be and this has been the source of difficulty and controversy regarding what his empirical law means. The bottom line is that all of this confusion has not been adaquately resolved in modern electromagnetic theory. The current article mixes up a lot of the confusion and that is the difficulty in understanding it.72.64.33.173 (talk) 16:35, 4 February 2009 (UTC)

I note that in looking at the lead statement it says to refer to Maxwell's equations, so I conclude from that this article is solely about the empirical Faraday Law. That being the case, the Feynman and Einstein quotations have no place in this article, as they refer to the theoretical relation between electricity and magnetism and not to the empirical Faraday law used by electrical enginers and the designers of electrical machines. 72.64.33.173 (talk) 17:17, 4 February 2009 (UTC)

If I can jump in, anon 72, I disagree with you on which is the more general equation. Faraday's induction law covers all situations where the magnetic flux changes - (1) moving conductor in a magnetic field, (2) moving magnet and a stationary conductor, (3) and a time-varying magnetic field. The Maxwell-Faraday equation found in the modern presentation of EM theory implicitly assumes non-moving bodies, and so the moving conductor situation is not explained by that.

That said, I don't think we need a terminology appendix, but rather a better intro and better organization of the material. The fact that Faraday's induction law covers two phenomena is already addressed in the intro (motional and transformer EMF), though this could be fleshed out. Additionally, this would be the best place to quickly state that the Maxwell-Faraday equation is a special case of the induction law for non-moving conductors, explaining the behavior in situations 2 & 3. The next section should probably be the history section, covering:

• Faraday's initial experiments and his qualitative formulation of a general induction law (the cutting of magnetic lines of force)
• Lenz' contribution for the direction of the EMF (Lenz was aware of Faraday's observations was unaware that Faraday come up with a general induction law)
• Perhaps touch on the initial attempts to explain EM induction, but without using Faraday's paradigm (this was done by Neumann and Weber)
• Maxwell's 1855 quantitative law based on the idea of tubes of force which gets us to the general form we see today (Thomson actually preceded Maxwell a bit, giving a quantitative law of Faraday's induction, but only for a specific case)
• Not necessary, but perhaps getting from that original flux law to today's field equations and force law

Darrigol's Electrodynamics from Ampere to Einstein and Whittaker's A History of the Theories of Aether and Electricity are probably good references for this section.

The next sections should cover the basic three situations. If the Feynmann and Einstein quotes stay in, they should go at the end as, at least in my opinion, it doesn't make sense to begin the slightly philosophical two phenomena discussion without first describing the different phenomena - remember we've already stated stated the two phenomena idea in the intro. Thoughts on this type of reorganization? --FyzixFighter (talk) 18:06, 4 February 2009 (UTC)

FyzixFighter, you are saying more or less what I had been saying up until now. The flux law caters for all the situations, and it is known as Faraday's law in many textbooks. But now that I think more about it, there may actually be some merit to what Steve Byrnes and anonymous 72 are saying. They are casting some doubt on whether or not the vXB effect was originally a Faraday's law effect. I had assumed that it was. At High school, I learned that Faraday's law catered for both effects. But at university, we only did the restricted Faraday's law that contains partial time derivatives and is found in Maxwell's equations. Maxwell's 1861 paper doesn't actually have a Faraday's law as such. Equation (54) is a curl equation which corresponds to the so-called Maxwell-Faraday equation in this article, but it uses total time derivative symbols. I have disregarded these symbols however, and tried to ascertain from the context whether they mean total or partial time derivatives. I am inclined to believe that he only had partial in mind. He then goes on to deal with two distinct aspects of EM induction. The motional kind is then covered for by E = vXB. He adds the results together in equation (77), with equation (54) included in an integral form with the A vector, which he calls the electrotonic state. Equation (77) carries to equation (D) of the original 8 in his 1865 paper, and that caters for all EM induction. There is no Faraday's law as such in Maxwell's original 8. Heaviside seems to have grabbed hold of equation (54) and written it unequivocally in modern format with partial derivatives, and that equation is now called Faraday's law in Heaviside's set of 4. Heaviside meanwhile lost the vXB term. It may well be that Faraday never had this vXB term in mind, but I'm just not sure about that matter. I'd need to see more original Faraday sources. The evidence is now certainly confirming that both the partial time derivative curl equation known as the Maxwell-Faraday equation and also the vXB terms are both Maxwell's equations. Within the context of Maxwell's equations, one is known as Faraday's law and the other is known as the Lorentz Force (a bit of a misnomer, but Lorentz did come up with it again later after Heaviside lost it for a few years) and the latter now sits outside in the hall and not inside with the other 4. The question that needs to be addressed is what exactly was the form of the original Faraday's law and what effects did it cater for? Quite frankly, I don't know. I am only assuming it is what is in the introduction, because that form would be typical of what one would find in high school books such as Abbot, or Nelkon & Parker. But certainly I am now beginning to see that there is indeed some merit to what Steve Byrnes and anon 72 are saying. Meanwhile, it would also seem that since Einstein used Heavisides equations, that he didn't know about the vXB term, and that's why he thought there was a problem with matching the theory with the practice. vXB came back with the Lorentz transformations and so some people think it is a relativistic effect. David Tombe (talk) 20:42, 4 February 2009 (UTC)

David, I want to say that you just gave a very good discussion of the situation, and I think it correct. If wikipedia were to correctly resolve this difficulty they would be doing EM students a great service in clarifying the confusion that exists. When I was in school, like you, I first learned the flux rule, which is negative rate of change, and then in college was taught to use vXB to calculate the emf per unit length for a moving wire. This was said to be the Lorentz force on the electrons in the wire. I think that to be a false statement and incorrect physics. The vxB rule works because it is a calculation of flux change through the circuit. The Lorentz law vxB is more correctly applied to free electrons and is the calculation of the transformation of the electric field of the free charge into a magnetic field which is then subject to the magnetic field force. This force was already derived by Heaviside and I also think J.J. Tompson if I recall correctly. Einstein made this already known phenomenon into a relativity effect, but that seems to not be the case at all as it can be derived from classical principles. So I think it is not a relativity effect at all. You show that Maxwell had already derived this in his early papers, so I think that makes it pretty clearly not a relativistic effect that Einstein should be given the credit for. My view of it is that the student should be warned that the vxB rule is just that and that it does not imply any actual force exerted upon the free electrons inside the wire as that doesnt seem to really be true, but rather the actual situation is described by the Faraday Law flux rule.72.64.43.28 (talk) 19:52, 5 February 2009 (UTC)

72.64.43.28 Well yes, it amazes me that the vXB term can be treated in detail in Maxwell's 1861 paper, and that we then read in modern textbooks that it is a relativistic term introduced by either Einstein or Lorentz to patch up some asymmetries in Maxwell's electrodynamics. It does rather look as if Einstein was only working from secondary sources and that he had no knowledge of what was in Maxwell's original papers.

Having said that, the vXB term does actually sit perfectly within a total time derivative Faraday's law. Watch this derivation. I'll go now to the gravitomagnetism article to copy and paste it.

Consider that $\mathbf {E}$ is,

$\mathbf {E} =-({\frac {\partial \mathbf {A} }{\partial t}}-\mathbf {v} \times \mathbf {B} )$

Then taking the curl, we get,

$\nabla \times \mathbf {E} =-({\frac {\partial \mathbf {B} }{\partial t}}+({\mathbf {v} \cdot \nabla })\mathbf {B} )=-{{d\mathbf {B} } \over dt}$

The problem for those gravitomagnetism guys who tried to use Faraday's law in gravity is that Faraday's law is already in gravity in the form of Kepler's second law. And the curl of g in that case is zero. I don't know how the gravitomagnetism guys are intending to beef that zero up to a $\nabla \times \mathbf {g} =-{{d\mathbf {B} _{g}} \over dt}$

David Tombe (talk) 14:12, 6 February 2009 (UTC)

New section for "Parasitic induction and waste heating"

I've just added a new section with citations discussing parasitic induction and waste heating. I see there is no article for Parasitic induction (other than the redirect I just created pointing here)..

Since this article is already getting rather long, I may move the new material over to the redirect and just have a short reference to the new article in this one.

DMahalko (talk) 11:30, 26 February 2009 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Faraday's law of induction/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

I have a doubt. A very minor thing for those who know. The delta phi in the formula is 'change of flux'. I want to know whether this means 'initial value minus final value' or vise-versa? Will someone please clarify. A.C. Huria <achuria@gmail.com> Change in a quantity is pretty universally the final value minus the initial value.

Last edited at 16:00, 4 April 2007 (UTC). Substituted at 20:33, 2 May 2016 (UTC)