Magnetic field inside a cylinder which is rotating in a non-constant angular velocity

cadmus

1. The problem statement, all variables and given/known data

A hollow cylinder of length L and radius R, is madeout of a non-conducting material, is charged with a constant surface charge [itex]\sigma[/itex], and is rotating, along its axis of symmetry, with an angular velocity w(t) = [itex]\alpha[/itex]t.

2. Relevant equations



3. The attempt at a solution

The answer in the manual is B = [itex]\mu[/itex][itex]\alpha[/itex]tR[itex]\sigma[/itex]

Where [itex]\mu[/itex] is ofcurse [itex]\mu[/itex] zero. [ the magnetic constant ].

The manual's solution makes perfect sense if I knew that the circular electric field which is induced by the fact that the magnetic field is changing in time is constant.

because then i could say that that the displacement current density is zero.

Q: How can derive that the circular electric field, induced by the changing -in-time magnetic field, is not changing with time?


Thanks in advance
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution