# Green's Fucntions in Cylindrical coordinates

1. Oct 10, 2007

### pfknapp

Hey everyone,
first time poster. I am looking for a general solution to poisson's equation in a cylindrical geometry for the electrostatic field. By general, I am thinking of two concentric, grounded, hollow cylinders of finite height, and the solution for the field using the green's function in between the two cylinders. With this kind of geometry one can take the limit as either the inner radius goes to zero or the outer radius goes to infinity and therby cover all your bases and have the solution everywhere. Let me know if you can help. I have general solutions for spherical and cartesian, but I can't seem to find one for cylindrical. Thanks everyone.

2. Oct 10, 2007

### GDogg

You can find it by solving the Laplace equation for the electric potential using separation of variables in cylindrical coordinates and then using a unit charge for the boundary conditions. The Green function should be a combination of Bessel functions for the radial coordinate and sines and cosines for the others.