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

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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 $\sigma$, and is rotating, along its axis of symmetry, with an angular velocity w(t) = $\alpha$t.

2. Relevant equations

3. The attempt at a solution

The answer in the manual is B = $\mu$$\alpha$tR$\sigma$

Where $\mu$ is ofcurse $\mu$ 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?

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

2. Relevant equations

3. The attempt at a solution