Integration of a solenoidal vector field over a volume

[Phillips101]

1. The problem statement, all variables and given/known data

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.



2. Relevant equations


3. 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.