How does divergence theorem holds good for electric field. How does this hold true-

$$\iiint\limits_{\mathcal{V}} (\vec{\nabla}\cdot\vec{E})\ \mbox{d}V=\mathop{{\int\!\!\!\!\!\int}\mkern-21mu \bigcirc}\limits_{\mathcal{S}} {}\vec{E}\cdot\hat{n}\ \mbox{d}A$$


For a formal proof of the divergence theorem in general, I refer you to any basic textbook that covers vector calculus (for instance, Adams' 'Calculus'). As for developing a physical intuition on why it applies in this context, see my answer to your previous question (which was essentially the same).

  • $\begingroup$ i meant the proof of gauss divergence theorem taking the vector as electric feild. ∫∫∫(divergence E)dV=∫∫E.dA $\endgroup$ – N.G.Tyson Sep 14 '13 at 8:45
  • $\begingroup$ Like I said, I refer you to Adams' book (or any number of websites which will undoubtably be easily found through google), for the proof itself is very tedious and not that enlightening, and I will not bother to reproduce it in full right here. $\endgroup$ – Danu Sep 14 '13 at 8:56

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