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Circulation of a 3d vector field

  1. Oct 31, 2012 #1
    1. The problem statement, all variables and given/known data
    consider the vector field v(x,y,z)=(-h(z)y,h(z)x,g(z)) wherer h:R->R and g:R—>R are differentiable .Let C be a closed curve in the horizontal plane z=z0.show that the circulation of v around C depends only on the area of the reion enclosed by C in the given plane and h(Z0)


    3. The attempt at a solution
    i know it is simple,but i dont know how to star it. should i parameterize the curve c ? but how? could someone give me some details hints????
     
  2. jcsd
  3. Oct 31, 2012 #2

    Dick

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    Parameterize any way you like, say [x(t),y(t),z0], for t in [0,1]. Write down the line integral that defines "circulation" around your curve. Factor out constants. Do you recognize a formula for area in what's left?
     
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