Using Green functions to solve potentials in electrostatics

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.