Integration of a solenoidal vector field over a volume

[Phillips101]

Homework Statement

div(J)=0 in volume V, and J.n=0 on surface S enclosing V, where n is the normal vector to the surface.

Show that the integral over V of J dV is zero.

Homework Equations

The Attempt at a Solution

I can't get anywhere with it! The divergence theorem doesn't seem to help, as I just go round in circles. Any help at all will really be useful.

Thanks

 

[gabbagabbahey]

Try applying the divergence theorem to the vector field $$\lambda\vec{J}$$ What happens if you choose $\lambda$ such that $$\vec{\nabla}\lambda$$ is a constant vector?

 

[Phillips101]

Thanks for that - everything now works.