# Solving Laplace's equation in a circular annulus

• October 3rd 2013, 06:14 PM
temaire
Solving Laplace's equation in a circular annulus
Problem Statement:

http://i43.tinypic.com/1eoviw.png

General solution:
http://i43.tinypic.com/1z23h4z.png

Fourier series:
http://i43.tinypic.com/2md14k1.png

where $r_{1}=a$, $r_{2}=b$, $f_{1}(\theta)=sin(\theta)$, and $f_{2}(\theta)=2sin(\theta)cos(\theta)$.

By evaluating the Fourier series shown above, I determined that $a_{o}=b_{o}=a_{n}=b_{n}=c_{n}=d_{n}=0$.

Is this correct?