On the electrostatic equilibrium of charges and cavities in a conductor
  We consider a charged conductor of arbitrary shape, in electrostatic equilibrium, with one or more cavities inside it, and with fixed charges placed outside the conductors and inside the cavities. The field inside a particular cavity is then only due to charges within that cavity itself and to the surface charge induced on the surface of the same cavity. A similar statement holds for the exterior of the conductor. Although this is an elementary property of conductors, it is not a trivial statement, as explained in this article. Undergraduate texts in electrodynamics do not discuss at length or provide a complete argument for an important problem such as this. Two simple and complete proofs are provided in this note with the help of the standard electrostatic uniqueness theorems. 
Aritro Pathak
physics.gen-ph