English: Alfvén's theorem states that in a fluid with infinite electrical conductivity the magnetic flux through an arbitrary open surface ${\displaystyle S_{1}}$ advected by a macroscopic, space- and time-dependent velocity field ${\displaystyle \mathbf {v} }$ in a time ${\displaystyle \delta t}$ to the surface ${\displaystyle S_{2}}$ is constant. One way to prove Alfvén's theorem requires the line element ${\displaystyle d\mathbf {l} }$ of the boundary around ${\displaystyle S_{1}}$ to construct a third surface ${\displaystyle S_{3}}$ with ${\displaystyle d\mathbf {S} _{3}=d\mathbf {l} \times \mathbf {v} \delta t}$. The three surfaces (with the sense of ${\displaystyle S_{1}}$ reversed) form a single closed through which the total magnetic flux must be zero according to Gauss' theorem.