Question

Do charges move to the outer surface of a conductor to minimize the potential energy?

Answer 1

there is any net charge inside the bulk of the conductor Gauss's law guarantees that there is some electric field lines with directions towards the outside of that region.

Any such electric field inside moves charges around inside, so it will only stop when there is no way the charges can move any. That guarantees zero electric field inside, and charges on the surface distributed so the tangential electric fields must be zero. Only fields perpendicular to the surface can survive.

Answer 2

Any such electric field inside movescharges around inside, so it will only stop when there is no way the chargescan move any. That guarantees zero electric field inside, and charges on thesurface distributed so the tangential electric fields must be zero.