# Electrostatic potential on the surface of a conductor

1. Dec 23, 2011

### rbnphlp

1. The problem statement, all variables and given/known data

At the surface of a conductor the potential is constant .. I cant get my head around this ..

2. Relevant equations

3. The attempt at a solution

The only reason I can think about this is Electric field is perpendicular at the surface , hence no work is done when moving a point charge around the surface , hence potential is constant ..

But if V is constant , the surely E=-grad (V)-> E=0 , which is not the case since there are charges on the surface of the conductor, so surely must provide a E field normal to the surface ..

Thanks for any help

Last edited: Dec 23, 2011
2. Dec 23, 2011

### rbnphlp

Noone ? Does noone understand what I am saying or does noone know the anwer?

3. Dec 23, 2011

### vela

Staff Emeritus
Say the surface lies in the xy-plane, for example. You'd have V(x,y,0)=V0 so that ∂V/∂x=∂V/∂y=0, but that doesn't imply that ∂V/∂z=0.

4. Dec 23, 2011

Cheers :D