Boundary-Value Problems in Electrostatics: I — John David Jackson
Physics — E&M · gauss-theorem-conductors
Problem
Use Gauss's theorem [and (1.21) if necessary] to prove the following:
((a)) Any excess charge placed on a conductor must lie entirely on its surface. (A conductor by definition contains charges capable of moving freely under the action of applied electric fields.)
((b)) A closed, hollow conductor shields its interior from fields due to charges outside, but does not shield its exterior from the fields due to charges placed inside it.
((c)) The electric field at the surface of a conductor is normal to the surface and has a magnitude σ/ϵ0, where σ is the charge density per unit area on the surface.