November 2, 2013

Is this an electromagnetic paradox?

Because of relative motion of sources of B (regardless of how one imagines their source), there should be an E field near the poles of magnets spinning around their polar axes. (Compare to separate magnets held in a rotating cylinder and their relative motions.) It would be a similar configuration to the B field from a solenoid (even more so if we used a hollow cylindrical magnet to isolate magnetization as close to the rim.) It seems rather obscure.

  This seems rather prosaic until you start thinking about "sources of E" in terms of what projects potential and magnetic vector potential A. The usual view of sourcing E is to write, such as from Feynamn Lectures II:
E = -Del phi - dA/dt,
and the source of phi is retarded 1/r^2 from dV of rho, and source of A is 1/r projection from current density j.

   There is a problem here
  1. Because this is a stable configuration there can't be a continuing dA/dt, and
  2. magnets aren't really current loops (most of the B comes from axial electron quantum spin, not orbital motion anyway) so there isn't really a shifting of current density to project the changed phi.
We need to treat the spinning magnet poles as actual "pole currents" since it is misleading to pretend there are actual little loops with increased relativistically altered current densities in them. Yeah, amazing this wouldn't have been hashed out before, but there it is. Your thoughts?