Integration of a solenoidal vector field over a volume

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

Homework Helper
Gold Member
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Try applying the divergence theorem to the vector field [tex]\lambda\vec{J}[/tex] What happens if you choose [itex]\lambda[/itex] such that [tex]\vec{\nabla}\lambda[/tex] is a constant vector?
 
Thanks for that - everything now works.
 

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