Question
Starting from Coulomb's law, derive Gauss's law in differential form.
Answer :
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Coulomb’s law states that the electric field due to a point charge (q) located at the origin is [ \mathbf{E}=\frac{1}{4\pi\varepsilon_0}\frac{q}{r^2}\hat{\mathbf{r}} ] where (r) is the distance from the charge and (\hat{\mathbf{r}}) is the radial unit vector. The electric flux through a closed surface (S) surrounding the charge is [ \Phi_E=\oint_S \mathbf{E}\cdot d\mathbf{S} ] For a spherical surface of radius (r) centered on the charge, (\mathbf{E}) is everywhere radial
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