Surface area and line integral

  • Thread starter rbwang1225
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  • #1
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Main Question or Discussion Point

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!
 

Answers and Replies

  • #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:
  • #3
606
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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.

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

DonAntonio
 
  • #4
Oops
 
  • #5
chiro
Science Advisor
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Strokes Theorem is what we get sometimes from our loved ones. Stokes Theorem is, perhaps, what you mean.

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

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