haidara
Nov22-10, 02:44 AM
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_{}ncos(n\Phi)+D_{}nsin(n\ Phi)r^{-n}]+A_{}0ln(r)+C_{}0.
take C_{0}=0 inside the cylinder
3. The attempt at a solution
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_{}ncos(n\Phi)+D_{}nsin(n\ Phi)r^{-n}]+A_{}0ln(r)+C_{}0.
take C_{0}=0 inside the cylinder
3. The attempt at a solution