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

1. Oct 8, 2011

### caoyuan9642

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.