i wanted to solve an electrostatic problem that includes an infinite conical conductor whose vertex is the origin of the spherical coordinates,(adsbygoogle = window.adsbygoogle || []).push({});

and i knew that the general solution of laplacian equation in spherical coordinates is:

u(r,θ)=Ʃ(An*r^{n}+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,θ_{0})=u_{0}, where θ_{0}is the angle of the cone and u_{0}is the conductor's potential, which is a constant.

anyone has some advice on solving this Dirichlet problem?

thx.

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# About Dirichlet problem of Laplacian equation in 3D sperical coordinates

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