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A law in classical electromagnetism and Newtonian gravity which relates (charge) density to the divergence of a field, or alternatively the charge in a volume to the flux through the bounding surface.
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Gauss' Law Applied to a Charged Sphere
If I were to apply Gauss' law $$\nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0}$$ to a charged sphere of radius $R$, which I believe should have an (exterior) electric field given by:
$$\vec{E}(r) = …