Poisson Equation PDE Model Explorer

Live Script exploring solutions to electrostatics problems using a PDE model.

This Live Script explores solutions to Poisson's equation governing the electrostatic potential in a region defined by conducting surfaces and containing a charge density distribution in two dimensions. It shows how to define a nonconstant charge density for a PDE model and illustrates how to customize geometry creation functions like circleg to create simple geometries with nonstandard parameter values. The script compares numerical results for the potential to an analytic form for a cylinder of uniform volume charge density (a rod) contained within and concentric with a conducting cylindrical surface.

This script may interest students and instructors of physics and related fields. Background information, 'Try this' suggestions, coding 'Challenges,' and hyperlinks to documentation are included for further exploration. Interactive methods of setting up and solving electrostatic problems with complex geometries are illustrated in Ref [1]. Alternative direct numerical methods are explored in Ref[2-4]. PDE toolbox use is detailed and applied in Ref[5].