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Electrostatic potential on the surface of a conductor

  1. Dec 23, 2011 #1
    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
    E=-grad V

    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. jcsd
  3. Dec 23, 2011 #2
    Noone ? Does noone understand what I am saying or does noone know the anwer?
  4. Dec 23, 2011 #3


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    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.
  5. Dec 23, 2011 #4
    Cheers :D
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