Your vector field has a z component, but it doesn't depend on z. So F is the same for z=0 as z=whatever on the surface of the torus. I think there's a factor for the area that changes, too, but it ends up being the same thing. If you break up the integral into components, you should see the z terms drop out.

If you still have trouble, post your integral here and we'll work through it.

- Hollywood