Electrostatic potential on the surface of a conductor

[rbnphlp]

Homework Statement

At the surface of a conductor the potential is constant .. I can't get my head around this ..

Homework Equations

E=-grad V

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

 

[rbnphlp]

Noone ? Does no one understand what I am saying or does no one know the anwer?

 

[vela]

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.

 

[rbnphlp]

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.

Cheers :D