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Homework Help: Peculiar problem

  1. Mar 12, 2007 #1
    1. The problem statement, all variables and given/known data

    Can anyone say if this can at all be evaluated?
    closed integral{F dS} using divrgence theorem/any of its corollary?
    here F is a vector and dS is a scalar and there is no dot sign between them.

    2. Relevant equations



    3. The attempt at a solution

    I do not want to evaluate this.I just want to know if it is done.And how?
     
  2. jcsd
  3. Mar 12, 2007 #2

    Dick

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    I don't think so, unless F has some special relation with the normal vector n. Is it a cross product with n, as in a problem you posted before?
     
  4. Mar 12, 2007 #3
    OK,there is no cross product.This actually appeared in the exam I appeared yesterday.
     
  5. Mar 13, 2007 #4

    Dick

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    I'll think about this, but let me know what the answer is when you find out.
     
  6. Mar 13, 2007 #5
    I misread the question and worked as int{F.dS}...it's easy.
    This observation may yield something-
    Note that FdS=F(n dot dS).Using triple product rules, we have nx(FxdS)=F(n dot dS)-dS(n dot F) => FdS=F(n dot dS)=nx(FxdS)+dS(n dot F).
     
  7. Mar 13, 2007 #6

    Dick

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    Hmm. Ok. I'll keep thinking about it. But I'm having trouble thinking about dS as a vector separate from n.
     
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