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Stoke's theorem

  1. Jan 14, 2005 #1
    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.
     
  2. jcsd
  3. Jan 14, 2005 #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.
     
    Last edited: Jan 14, 2005
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