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Surface integral

  1. Dec 30, 2016 #1
    1. The problem statement, all variables and given/known data
    Is the solution provided by the author wrong ? Stokes theorem is used to calculate the line integral of vector filed , am i right ?



    2. Relevant equations


    3. The attempt at a solution
    To find the surface integral of many different planes in a solid , we need to use Gauss theorem , right ?
     

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  2. jcsd
  3. Dec 30, 2016 #2

    Charles Link

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    The author doesn't seem to specify what surface integral he is asking for. If he wants ## \int F \cdot dA ##, Gauss' law works for the surface enclosing a volume, and wouldn't apply here. If he wants you to evaluate ## \int \nabla \times F \cdot \, dA ##, you can use Stokes theorem and alternatively compute the line integral of ## \oint F \cdot \, ds ## around the perimeter. ## \\ ## editing... If the author wants you to evaluate ## \int F \cdot \, dA ##, there are no shortcuts that I know of=neither Gauss' law or Stokes theorem will apply. You simply need to crank it out the long way... And none of us are infallible=it is my guess the author made a mistake.
     
    Last edited: Dec 30, 2016
  4. Jan 1, 2017 #3
    Do you mean that the author maybe mean find the line integral and not find surface integral in this question ?
     
  5. Jan 1, 2017 #4

    LCKurtz

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    Frequently in such problems the author wants you to demonstrate Stokes' theorem by working it both ways. It's a learning thing.
     
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