Surface area and line integral

  • Thread starter rbwang1225
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  • #1
rbwang1225
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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
GarageDweller
104
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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.
 
Last edited:
  • #3
DonAntonio
606
1
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
GarageDweller
104
0
Oops
 
  • #5
chiro
Science Advisor
4,815
134
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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