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## Homework Statement

Suppose a grounded spherical conducting shell of radius R surrounds a pointlike dipole at the center with [itex]\vec{p}=p\vec{k}[/itex] Find the potential [itex]V(r,\theta[/itex]) for r <= R. Hint: Use spherical harmonics regular at r=0 to satisfy the boundary condition.

## Homework Equations

General solution:

[itex]V(r,\theta)= \sum_{n=0}^\infty A_nr^nP_n(cos\theta) + \sum_{n=0}^\infty B_nr^{-(n+a)}P_n(cos\theta) [/itex]

##V_{dip}=\frac{kqdcos\theta}{r^2}##

## The Attempt at a Solution

So ##V(r,\theta)## ends up being the sum of the above general solution plus the potential due to the dipole.

I believe we can get rid of the whole ##B_n## term because the potential inside the sphere is finite and at r=0 the summation including ##B_n## would explode so ##B_n=0##. Result:

##V(r,\theta)= \frac{kqdcos\theta}{r^2} + \sum_{n=0}^\infty A_nr^nP_n(cos\theta)##

I have solved systems similar to this without the dipole, for example. I'm not sure how to go about solving this with that there. I did see a suggestion somewhere to notice that ##P_1(cos\theta)=cos\theta## but I am not sure how to utilize this fact.

Any suggestions? Thanks!