Why work done by the electric field in moving a charge on a conducting surface is zero? What is the potential difference between two points along the surface of a charged conductor?

Question

Why work done by the electric field in moving a charge on a conducting surface is zero?  What is the potential difference between two points along the surface of a charged conductor?

turingtest · Answer

The potential difference between points on any charged surface of a conductor is zero (unless there is a current moving through it). If it was not, the charges would be moving.
I'm not sure about the work done by a field on the surface of a conductor with a current running though it being zero though, because electrons move through wires in this way, and the E-field does work in those cases.

anonymous · Answer

hey turing could you help me with my question, do you know anything about polarization of light?