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Surface area and line integral

  1. Aug 26, 2012 #1
    I met a proof problem that is as follows.
    ##\bf a = ∫_S d \bf a##, where S is the surface and ##\bf a ##is the vector area of it.
    Please proof that ##\bf a = \frac{1}2\oint \! \bf r \times d\bf l##, where integration is around the boundary line.

    Any help would be very appreciated!
     
  2. jcsd
  3. Aug 26, 2012 #2
    Strokes theorem?

    hmmm

    Well say you perform a surface integral, if the vector field in question is the normal vector of the surface, then the only thing left in the integrand is dA (scalar).

    So I guess using strokes theorem, you have to find a vector field who's curl is the normal vector of the surface.
     
    Last edited: Aug 26, 2012
  4. Aug 26, 2012 #3

    Strokes Theorem is what we get sometimes from our loved ones. Stokes Theorem is, perhaps, what you mean.

    DonAntonio
     
  5. Aug 26, 2012 #4
  6. Aug 26, 2012 #5

    chiro

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    Science Advisor

    What's this new theorem and who proved it lover boy?
     
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