Circulation of a 3d vector field

[cummings12332]

Homework Statement

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)

The Attempt at a Solution

i know it is simple,but i don't know how to star it. should i parameterize the curve c ? but how? could someone give me some details hints?

 

[Dick]

Homework Statement

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)

The Attempt at a Solution

i know it is simple,but i don't know how to star it. should i parameterize the curve c ? but how? could someone give me some details hints?

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?