Stoke's theorem

  • Thread starter wesleyad
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Hi ive got this question that ive been stuck on a while now.. im sure its really obvious but i cant see to get it:
Q: with the help of stokes's theorem, show that F(r) is conservative provided that nabla X F = 0.
nabla X F is the same as curl F?
Cheers.
 

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  • #2
Galileo
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[itex]curl F[/itex] is sometimes written as [itex]rot F[/itex] or [itex]\nabla \times F[/itex]. It's the same thing.

You either have to show that [itex]\int F \cdot dr[/itex] is independent of path,
or that F(r) can be written as the gradient of a function. (Depending on your definition).

Hint: Independance of path is the same is [itex]\oint F \cdot dr=0[/itex] for any closed path.
 
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