Using Green functions to solve potentials in electrostatics

TL;DR

This paper reviews the use of Green functions for solving electrostatic potential problems across different coordinate systems, providing derivations and examples for various geometries.

Contribution

It offers a comprehensive summary of Green function techniques applied to electrostatics, including derivations for multiple coordinate systems and example solutions.

Findings

Green functions enable solving electrostatic potentials for arbitrary charge distributions.

Explicit Green functions are derived for spherical, Cartesian, and cylindrical geometries.

The method simplifies calculating potentials in complex geometries.

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.