# Integration of a solenoidal vector field over a volume

1. Feb 28, 2009

### 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

2. Mar 1, 2009

### 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?

3. Mar 1, 2009

### Phillips101

Thanks for that - everything now works.