Poisson Equation for Electrostatic Potential

Live Script that solves the Poisson equation to find the electrostatic potential surrounding charge near a conductor in two dimensions.

The electrostatic potential V associated with a static charge density ρ is governed by Poisson's equation which follows from Gauss's Law in differential form. This Live Script illustrates how to use the 2nd order central difference approximation for the Laplacian on a square grid to represent Poisson's equation as a matrix equation. The potential values are found by matrix inversion. The example illustrated here is a single line charge inside a cylindrical hole in a conductor.

This script may interest students and instructors of physics. 'Try this' suggestions and coding 'Challenges' are included for further exploration. Alternative methods of solving two-dimensional electrostatics problems are explored in Ref[1-2].