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Vectors and fields

  1. Apr 21, 2007 #1
    I am trying to show for a closed surface
    the integral n.curlF ds and
    the integral n^grad(phi) ds
    both equal zero.

    Any ideas? Do I need to use identities such as div curl F=0
    I can't seem to find a way to make the integrands equal zero.

  2. jcsd
  3. Apr 21, 2007 #2
    does ^ mean a cross product? If that is the case, then what do you mean by the integral of a vector being equal to zero? Do you mean the vector (0,0,0)?
  4. Apr 21, 2007 #3
    Siberius, I assume dS is actually a vector too, Tiggy just didn't put in the 'dot' to make it a scalar.

    Tiggy, Stokes Theorem is that for a nice surface/volume you have the relation

    [tex]\int_{V}d\eta = \int_{\partial V}\eta[/tex]

    You're asking to find [tex]\int_{S = \partial V}\eta[/tex] where [tex]\eta[/tex] is the integrands you've given. Can you work out their divergences? The first one is quite clearly zero by the identity you mention. The second one is zero by the fact [tex]a.(b \times a) = 0[/tex], even when [tex]a = \nabla[/tex] (proof by suffix notation).
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