I have a lot of records in EM, and I know all about charge induction and Gauss's theorem for systems of conductors, nonetheless I still have a problem that I cannot face without feeling uncomfortable.
Suppose to have a hollow conducting sphere, with a pointlike charge $q$ inside, placed at a point not at the centre of the sphere. That induces an asymmetrical (but axisymmetrical) charge distribution on the inner surface of the hollow sphere; but also, a perfectly homogeneous charge distribution on the external surface. Why is this?
This is something I can understand could happen, but I miss some actual proof that it must happen. It must reside in something related to the particular symmetry of the sphere, but for me it is not enough to say that "this happens due to the spherical symmetry". Is there something that clearly forces things to happen like this?
Best Answer
The metal of the conductor 'shields' the outer surface charges from the inner ones, because no macroscopic electrostatic field can exist inside the metal of the conductor.As such, the outer charges have no information about the presence of inner charges. So, the charges must exist in the form so as to make the conductor surface an equipotential(since this is the lowest energy configuration). For a sphere, this is simply uniform due to homegeneity of space. It may not be uniform for another random shape, but it always MUST be an equipotential.