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Homework Help: Boundary conditions for charged cylinder

  1. Sep 26, 2005 #1
    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?
     
  2. jcsd
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