# Laplace's equation in two dimensions_clyindrical coordinates

by haidara
Tags: coordinates, equation, laplace
 P: 1 1. The problem statement, all variables and given/known data an infinitely long thin conducting cylindrical shell(radius R) of surface charge density $$\sigma$$=$$\sigma_{1}$$sin(2$$\Phi$$)+$$\sigma_{2}$$cos($$\Phi$$). what are the four boundary conditions for this problem? using the four boundary conditions and the identification of the coefficients of sin(n$$\Phi$$)and cos(n$$\Phi$$)find the expression of the potential inside and outside the cylindrical shell. 2. Relevant equations the general solution of laplace's equation in this case can be written: V(r,$$\Phi$$)=$$\sum^{n=1}_{\infty}$$[$$A_{n}$$cos(n$$\Phi$$)+ $$B_{n}$$sin(n$$\Phi$$))r$$^{n}$$+(C$$_{}n$$cos(n$$\Phi$$)+D$$_{}n$$sin(n$$\Phi$$)r$$^{-n}$$]+A$$_{}0$$ln(r)+C$$_{}0$$. take C$$_{0}$$=0 inside the cylinder 3. The attempt at a solution