laplace's equation in two dimensions_clyindrical coordinates


by haidara
Tags: coordinates, equation, laplace
haidara
haidara is offline
#1
Nov22-10, 02:44 AM
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

[tex]\sigma[/tex]=[tex]\sigma_{1}[/tex]sin(2[tex]\Phi[/tex])+[tex]\sigma_{2}[/tex]cos([tex]\Phi[/tex]).
what are the four boundary conditions for this problem?
using the four boundary conditions and the identification of the coefficients of sin(n[tex]\Phi[/tex])and cos(n[tex]\Phi[/tex])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,[tex]\Phi[/tex])=[tex]\sum^{n=1}_{\infty}[/tex][[tex]A_{n}[/tex]cos(n[tex]\Phi[/tex])+
[tex]B_{n}[/tex]sin(n[tex]\Phi[/tex]))r[tex]^{n}[/tex]+(C[tex]_{}n[/tex]cos(n[tex]\Phi[/tex])+D[tex]_{}n[/tex]sin(n[tex]\Phi[/tex])r[tex]^{-n}[/tex]]+A[tex]_{}0[/tex]ln(r)+C[tex]_{}0[/tex].
take C[tex]_{0}[/tex]=0 inside the cylinder
3. The attempt at a solution
Phys.Org News Partner Science news on Phys.org
Simplicity is key to co-operative robots
Chemical vapor deposition used to grow atomic layer materials on top of each other
Earliest ancestor of land herbivores discovered

Register to reply

Related Discussions
Hom. heat equation in cylindrical coordinates using Fourier & Laplace transforms Differential Equations 1
Laplace solution in polar coordinates Calculus & Beyond Homework 2
Laplace equation in cylindrical coordinates Differential Equations 9
New Problem about solving a Laplace Equation in cylinder coordinates Advanced Physics Homework 6
The Laplace Equation in Polar Coordinates Calculus & Beyond Homework 2