Consider a hollow conducting spherical shell S1 inside an irregularly shaped conducting wall S2 (in the figure). The sphere S1 is somehow given a charge +Q.
Will the charge distribution on S1 be uniform or not?
Here's what I've deduced till now:
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On the inner surface of S2, charge -Q will be induced (of course, non uniform).
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On the outer surface of S2, for its electrical neutrality, charge +Q appears.
This is all I've come up with so far, and what's confusing me is whether or not the induced charges on the inner surface of S2 will play a role in determining the charge distribution on S1.
Please provide a detailed explanation, and help me understand what's going on. I'm quite familiar with Electrodynamics (and physics as a whole), so place no restriction on the tools being used to explain. Not to mention, more of physics and less of math is always interesting to read!
Thanks a lot.
P.S.
Points A, B and C in the diagram have no relation with my question – do not get confused.
Best Answer
Your points 1. and 2. are correct. But the surface charge distributions on S1 and S2 will be non-uniform. Only if S2 was a concentric conducting sphere then the surface charge distributions both on S1 and S2 would be uniform. The reason is that for a uniform surface charge you need a constant normal surface electric field both on the surface of S1 and on the inner surface of S2. Such a constant normal surface electric field on closed conducting shells can only exist when you have a spherical symmetric solution of the Laplace equation for the potential and thus the electric field between the conductors. Due to the irregular shape of the outer conducting shell this is not possible.