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There is a nice example in Griffiths where he calculated magnetic field of a spherical shell/sphere for uniform surface charge $\sigma$.

The argument was, since the surface current is $K= \sigma r \omega$, the rotation of the sphere/shell will give the surface current density. That surface current density will give the vector potential and eventually the magnetic field we want.

My question is, what if the the sphere is not conducting, like it's a dielectric how would we approach this problem?

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Related post : Vector Potential of a rotating Spherical Shell

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Are you sure it is given that the sphere is conducting? What you are describing is how you would solve this problem if the sphere were not a conductor. If it is a conductor, the Lorentz force due to the induced magnetic field will apply a force on the charges and cause them to redistribute. This complicates the problem, as the charge density will no longer be uniform.

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  • $\begingroup$ Puk, he did not mention that if the charged sphere is conducting sphere or not. I have updated the question. $\endgroup$ – user193422 Jul 31 at 21:33
  • $\begingroup$ Then it is safe to say he assumes the sphere is not conducting, because otherwise the charge density would not remain uniform. $\endgroup$ – Puk Jul 31 at 21:37
  • $\begingroup$ What kind of materials he assumed then? And why did not he mention that in that? Could you elaborate that in terms of the question please? $\endgroup$ – user193422 Jul 31 at 21:39
  • $\begingroup$ Based on the answer, he assumes a dielectric (zero electrical conductivity). The remaining material properties don't matter if the material is infinitesimally thin, as the question seems to assume. $\endgroup$ – Puk Jul 31 at 21:48

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