The use of Gauss' law to examine the electric field of a charged sphere shows that the electric field environment outside the sphere is identical to that of a point charge. Therefore the potential is the same as that of a point charge:

The electric field inside a conducting sphere is zero, so the potential remains constant at the value it reaches at the surface:

Since the electric field is equal to the rate of change of potential, this implies that the voltage inside a conductor at equilibrium is constrained to be constant at the value it reaches at the surface of the conductor. A good example is the charged conducting sphere, but the principle applies to all conductors at equilibrium.