What is the potential at the center of a sphere with given boundary conditions?

[rolandas9999]

Homework Statement

Given potential r=2m on the surface of the sphere which meets the Laplasian equation (triangle)u=0 and is u(2,theta,psi)=5sin(theta)sin(0.25psi). I need to find the potential of sphere center. Can anyone help me?

Homework Equations

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The Attempt at a Solution

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[jambaugh]

Write Laplace's equation in spherical coordinates, plug in your boundary condition and solve.

Note that the angular component has solutions which you can expand in terms of http://en.wikipedia.org/wiki/Spherical_harmonics" . You should first match the angular component with the boundary condition. Then it is a simple matter of solving the radial ODE for the boundary conditions... noting you must have non-singular solutions only at r=0.