babuliaam

2022-09-22

A metal pipe is held vertically, and a bar magnet is dropped into it What do the electric field lines in the pipe look like as the magnet falls through it?

garnboernl

The approaching bar magnet generates a dipole-like magnetic field, with closed field lines that leave the north, circle around, and enter into the south.
With the bar magnet falling vertically inside the conducting cylinder, the magnetic field lines are such that, at every surface element of the cylinder, we visualize that the magnetic field vector can be decomposed into two components: one that points parallel to the surface and another that points in the radial direction with respect to the cylinder's axis.
Now, if we instead view the problem in the bar's reference frame, the cylinder is moving with the bar at rest in its center. In that case, any free positive charges q that are at any surface element of the cylinder will feel a magnetic force given by $q\stackrel{\to }{v}×\stackrel{\to }{B}$. Thus, only the aforementioned radial components of $\stackrel{\to }{B}$ contribute to the magnetic force (because the parallel ones are also parallel to $\stackrel{\to }{v}$), and, consequently, the field lines of the magnetic force field generated around the cylinder surface are circles.
As a result, we clearly see that these magnetic force field lines seen by the bar magnet are actually electric force field lines when seen by the cylinder. Hence, the electric field lines are circles.

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