What is a false statement? the electric field strength on the surface of a charged conductor depends on the surface charge density. the net charge of the interior of a charged conductor is zero. the potential on the surface of a charged conductor is constant. the potential on the surface of a conductor is always zero. the electric field strength decreases as you move farther away from a charged conductor.

"The potential on the surface of a conductor is always zero."

This statement is false. A good number of times we define a point's potential to be the amount of work that must be done to move 1 coulomb of charge from infinitely far away to that point. So if, let's say, the conductor had a net positive charge, then you would need to do a net positive amount of work to move 1 coulomb of charge from infinitely far away to any point on the conductor's surface. We have just provided a case for which the potential on the surface of the conductor is not 0.