Do the Electrons Rotate with a Superconducting Disk?

Question

In a superconductor the electrons can move with respect to the material they are part of without resistance, in a sense without friction. If I have a superconducting disk and I set it to rotating, do the electrons participate in the rotational motion? If so, how is the force transmitted to them?

Answer 1

The key to solving this problem is recognizing that the amount of current produced by even a small rotating disk where the free electrons aren't moving would be astounding. Suppose there was only one free superconducting electron per $100$ nucleons. In a superconductor with $0.01\operatorname{moles}$ of atoms in it, there will be about $6\times 10^{21}$ free electrons, giving a disk with about $10^5 \operatorname{C}$ of charge. Even a tiny rate of rotation would produce a staggering current.

Importantly, the process of accelerating the positively charged disk by an infinitesimal amount would produce a magnetic field of a rotating charged disk. That infinitesimal change in the magnetic field will produce an electric field of similar magnitude by one of Maxwell's equations: $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}.$$ Examining the direction of the electric field reveals that it points in precisely the direction needed to exert a torque on the free electrons, spinning them up with the disk.

This thought exercise is, of course, very nonphysical because it implicitly treats the speed of sound through the superconductor as infinite. Even so, it provides insight into the processes that keep the free electrons in a conductor moving in tandem with the underlying atoms.