Gauss' law is also useful in proving a number of results involving charges on isolated conductors in electrostatic equilibrium.
Charges placed on an isolated conductor always reside on the surface.
For a solid conductor, this is proven by choosing a Gaussian surface just below the actual surface. If the conductor has a cavity, one can similarly show that the inner surface should have no net charge. Charges on the surface of a conductor, even though leading to no net E-field inside, will lead to a field outside. In general, the surface charge density will not be uniform. However, the field and charge density are related to each other.