The common explanation for the electric field inside a conductor being zero goes something like this: Suppose a perfect conductor is placed in an electric field, the external field causes the free charges to redistribute in such a way, that the resulting internal field exactly cancels off the external field, inside the body of the conductor. I understand that a perfect conductor has unlimited supply of free electrons. But, my question is, how do i prove that there always exists a distribution of charges inside a conductor, which produces the internal electric field required to cancel off ANY external electric field. In other words, is it always possible to find such a distribution, for ANY external field, for ANY perfect conductor? How do i prove that?