- #1

kreil

Gold Member

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## Homework Statement

Electric charges are distributed on a spherical surface of radius a so as to produce the potential

[tex] \Phi(\vec r)=A(x^2-y^2)+Bx[/tex]

in the region r<a. Find the potential in the region r>a (hint: use the table of spherical harmonics).

## Homework Equations

I am unsure, but I think I should start with the following general potential expression (solution to laplace's eqn in terms of the spherical harmonics Y).

[tex] \Phi(r, \theta, \phi)= \sum_{l=0}^{\infty} \sum_{m=-l}^l \left[ A_{lm}r^l+B_{lm}r^{-(l+1)} \right] Y_l^m(\theta, \phi)[/tex]

## The Attempt at a Solution

If I am to use the above potential eqn, I need to utilize boundary conditions to find the coefficients A and B, but the surface potential is not specified so I'm not sure where to start...can someone point me in the right direction?

Thanks for your comments.