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Divergence theorem

  1. Feb 17, 2004 #1
    I need help evaluating both sides of the divergence theorem if V=xi+yj+zk and the surface S is the sphere x^2+y^2+z^2=1, and so verify the divergence theorem for this case.

    Is the divergence theorem the triple integral over V (div V) dxdydz= the double integral over S (V dot normal)dS? If so I would I evaluate it for the above problem?
  2. jcsd
  3. Feb 18, 2004 #2

    matt grime

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    Try looking these things up, (Wolfram/mathworld). And yes, verify means evaluate both sides of the equality.
  4. Feb 18, 2004 #3


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    Note that, in this problem, div V is very simple so the integration over the volume is trivial. Integrating V.n dS on the surface is a bit more challenging but if you "project" the surface into the xy-plane and then use polar coordinates, it should be easy. (Don't forget to do both the part of the sphere above the xy-plane and the part below!)
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