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Past exam question about electrostatic field and potential

  1. May 15, 2013 #1
    1. The problem statement, all variables and given/known data

    Using Stoke’s theorem and the identities given, ∇x∇(Scalar)=0 deduce the relationship between electrostatic field E and potential ψ at a point in space, show that E = -∇ψ


    2. Relevant equations



    3. The attempt at a solution

    Does this question mean show a derivation which uses Stoke’s theorem and mathematical identities to obtain E = -∇ψ ?

    Or is something else required since it states, "∇x∇(Scalar)=0 deduce the relationship between electrostatic field E and potential ψ at a point in space". I wasn't sure if by a derivation arriving at E = -∇ψ then in effect this would be illustrated.

    Thanks
     
  2. jcsd
  3. May 16, 2013 #2

    rude man

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    Can't read your question. What is ∇x∇(Scalar)=0 ?
     
  4. May 16, 2013 #3
    That's exactly the way its typed on the past exam paper ie ∇x∇(Scalar)=0
     
  5. May 16, 2013 #4
    Isn't that just the vector calculus identity that the curl of a gradient is zero?
     
  6. May 16, 2013 #5
    Yes, this is an identity.
     
  7. May 16, 2013 #6

    rude man

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    OK, I can't read the del sign in your posts. But OK, no problem now.

    Start with the circulation integral: ∫E*ds = 0. This is a fundamental experimental observation. Then invoke Stokes' theorem to show that the curl of E must always be zero since the theorem applies to all possible closed paths.

    Then invoke the fact that, in consequencxe of curl E = 0 there exists a potential function V such that E = - grad V.
     
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