Spherically symmetric charge distribution ($\rho (\mathbf{r})=\rho (|\mathbf{r}|)$)

A charge distribution invariant under rotations about one center. For its spherically symmetric potential, Gauss's law gives the radial electric field $\mathbf{E}=Q(r){\mathbf{e}}_r/(4\pi {ϵ}_0{r}^2)$, where $Q(r)$ is the enclosed electric charge.