Electrostatic Potential and Field of a Charged Sphere: Spherical Harmonics Approach

Abstract:
The electrostatic potential and field produced throughout space by a charged spherical surface are derived by employing the spherical harmonics expansion of $\frac{1}{|\pmb{\mathbf{r}}-\pmb{\mathbf{r}}'|}$, a term proportional to the Green function of the three-dimensional Laplacian.