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Past exam question about electrostatic field and potential

  • Thread starter ZedCar
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Homework Statement



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


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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
 

Answers and Replies

  • #2
rude man
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Can't read your question. What is ∇x∇(Scalar)=0 ?
 
  • #3
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Can't read your question. What is ∇x∇(Scalar)=0 ?
That's exactly the way its typed on the past exam paper ie ∇x∇(Scalar)=0
 
  • #4
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Can't read your question. What is ∇x∇(Scalar)=0 ?
Isn't that just the vector calculus identity that the curl of a gradient is zero?
 
  • #5
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Isn't that just the vector calculus identity that the curl of a gradient is zero?
Yes, this is an identity.
 
  • #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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