- #1
bigplanet401
- 104
- 0
Hello,
Charge density [tex] \sigma(\phi) = k \sin 5\phi[/tex] (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
[tex]
\begin{equation}
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] \; ?
\end{equation}
[/tex]
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?
Charge density [tex] \sigma(\phi) = k \sin 5\phi[/tex] (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
[tex]
\begin{equation}
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] \; ?
\end{equation}
[/tex]
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?