Using Green functions to solve potentials in electrostatics

Abstract: In this paper, we summarize the technique of using Green functions to solve electrostatic problems. We start by deriving the electric potential in terms of a Green function and a charge distribution. We then provide a variety of example problems in spherical, Cartesian, and cylindrical coordinates. For a given coordinate system, we derive the corresponding Green function for some geometries, and then place an arbitrary charge distribution in the region; we then calculate the corresponding electric potential.