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Gauß law for electrodynamics states that $$\nabla \vec{E}= \frac{\rho}{\varepsilon_0} $$ at any point and no matter by what the electric field $\vec{E}$ is produced. $\vec{E}$ here stands for the total electric field at a point produced by all sources that are present, not just any selected few. So the whole derivation is valid for any surface and any ...

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