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I need help proving the following vector calculus identity:

$$ \oint_{\partial V} (\mathbf{\hat{n}} \times \mathbf{A}) \; \mathrm{d}S = \int_V (\nabla \times \mathbf{A}) \; \mathrm{d}V $$

the identity is also found on this link, under "Surface–volume integrals".

Thank you very much

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    It looks like a corollary to the Divergence Theorem, like applying it to the cross product of a vector field and a nonconstant vector. Do you know that theorem?2012-07-08

3 Answers 3