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Integration of a solenoidal vector field over a volume

  1. Feb 28, 2009 #1
    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.

  2. jcsd
  3. Mar 1, 2009 #2


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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?
  4. Mar 1, 2009 #3
    Thanks for that - everything now works.
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