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What is divergence theorem in electrostatics?

  1. Jul 30, 2011 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jul 30, 2011 #2
    What do you mean :S

    The divergence theorem just states:

    [tex] \int_{\mathcal{V}}(\mathbf\nabla\cdot\mathbf{v})d{\tau} = \oint_{\mathcal{S}} \mathbf{v}\cdot d{\mathbf{a}} [/tex]

    This can be applied in electrostatics by:

    [tex] \int_{\mathcal{V}} (\mathbf\nabla\cdot\mathbf{E})d{\tau} = \oint_{\mathcal{S}} \mathbf{E}\cdot d{\mathbf{a}} = \frac{1}{{\epsilon}_{0}}\int_{\mathcal{V}} {\rho} d\tau = \frac{1}{{\epsilon}_{0}} Q_{enc}[/tex]
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