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

  1. 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
     
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