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.

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it