# Boundary conditions for charged cylinder

1. Sep 26, 2005

### bigplanet401

Hello,

Charge density $$\sigma(\phi) = k \sin 5\phi$$ (where k is a constant is glued over the surface of an infinite cylinder of radius R with axis along the z-direction. Find the potential inside and outside the cylinder.

Two things I'm having trouble with:

1. Is the potential of an infinite cylinder
$$V(\rho^\prime, \phi) = \sum_{m = 0}^{\infty} \, [A_m J_m (k\rho^\prime) + B_m N_m (k\rho^\prime)] [C_m \sin m\phi + D_m \cos m\phi] \; ?$$

Do you need to include Neuman functions in the full solution?

2. Whatare the boundary conditions for this problem? Not knowing the potential at rho^prime = R made me confused. How many conditions do you need? And does the charge density tell you in any way about the radial dependence of the potential?