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Homework Help: Proving a vector Identity

  1. Apr 29, 2008 #1
    1. The problem statement, all variables and given/known data
    Let the domain D be bounded by the surface S as in the divergence theorem, and assume that all fields satisfy the appropriate differentiability conditions.
    Suppose that:
    [tex]\nabla\cdot\vec{V}=0[/tex]
    [tex]\vec{W}=\nabla\phi with \phi = 0 on S[/tex]
    prove:
    [tex]\int\int\int_{D}\vec{V}\cdot\vec{W}dV=0[/tex]

    This problem is in the Laplace's, Poisson's and Greens Formulas section. Truthfully I'm not sure where to even get started here. If anyone could give me a push in the right direction I would appreciate it greatly.
     
  2. jcsd
  3. Apr 29, 2008 #2
    nevermind; got it!
     
  4. May 1, 2008 #3
    I used a vector identity, but can someone please help me do this one without an identity. This is in a greens identities section, but none of the greens identities look like they would work. Is it right of me to say that
    [tex] \vec{V} = curl \vec{G}[/tex]

    where g i ssome vector potential? or would this not help me at all?
     
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