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About Dirichlet problem of Laplacian equation in 3D sperical coordinates

  1. Oct 8, 2011 #1
    i wanted to solve an electrostatic problem that includes an infinite conical conductor whose vertex is the origin of the spherical coordinates,
    and i knew that the general solution of laplacian equation in spherical coordinates is:
    u(r,θ)=Ʃ(An*rn+Bn*r-n-1), n>=0
    however, the boundary conditions on the cone prevents me from getting an overall analytical solution.

    the boundary conditions are that:
    u(+∞,θ)=0.
    u(r,θ0)=u0, where θ0 is the angle of the cone and u0 is the conductor's potential, which is a constant.

    anyone has some advice on solving this Dirichlet problem?
    thx.
     
  2. jcsd
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