The potential of a charged conductor
The two properties of an isolated charged conductor are
· The electric field is zero in its interior.
· The charge resides on the outer surface of the conductor
A third important property of a charged conductor results from considering its electric potential.
Suppose we have a conductor of arbitrary shape, to which we transfer a net charge. The charges are free to move and will quickly distribute themselves on the outer surface of the conductor until they are in equilibrium. In effect, the charges of the same sign repel one another until they reach a distribution in which the average distance between them is as large as possible, so that the potential energy of the arrangement of charges reaches a minimum value.
If the charges are in equilibrium on the surface of the conductor, then its surface must be an equipotential. If this were not so, some parts of the surface would be at higher or lower potential than other parts. Positive charges would then migrate towards region of high potential and negative charges towards region of high potential. However, this contradicts our assertion that the charges are in equilibrium, and therefore the surface must be an equipotential.