# Gauss's / Divergence theorem in Classical electrodynamics for the Electric field [duplicate]

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Can somebody explain the proof of Gauss's theorem / divergence theorem taking the vector as electric field

$$\iiint(\nabla\cdot\vec E)\mbox{ d} V=\iint \vec E \cdot\hat{n} \mbox{ d} A?$$

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## marked as duplicate by Qmechanic♦Sep 14 '13 at 9:09

Gauss's/Divergence theorem states that $\iiint(\nabla\cdot\vec f)\mbox{ d} V=\iint \left(\vec \nabla\cdot\vec f\right)\cdot\hat{n} \mbox{ d} A$ for all vector fields $\vec f$. Therefore, since $\vec E$ is a vector field, the statement holds true for the Electric field too.