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.