circulation of a 3d vector field

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)

Re: circulation of a 3d vector field

If the component of the curl in the z direction is constant on the plane $\displaystyle z=z_0$, then the circulation will be just the area times that value. You probably learned how to calculate the curl - here we just want the component in the z direction. You should get something that depends on z only so when you plug in $\displaystyle z=z_0$, you get a constant.

That should get you going in the right direction - let us know if you have any trouble finishing the problem.

- Hollywood

Re: circulation of a 3d vector field

I'm struggling with the same question, can you explain it a little more?

Re: circulation of a 3d vector field

The circulation is just the surface integral of the curl. Without knowing what you've done already, it's hard to help you. Do you know how to find the curl of a vector field?

- Hollywood