Finding Potential Inside a Conducting Sphere

Void123
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Homework Statement



If I wanted to find the potential inside a sphere, would I be looking for the general solution (in terms of Bessel's expression) for the helmholtz equation, in spherical polar coordinates?

Also, does a 'conducting' sphere imply that there is no potential outside the sphere?



Homework Equations



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The Attempt at a Solution



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Can no one verify this for me? Have I been too ambiguous?
 
It's not really a math problem is it? Try physics.
 
Well, it is a topic addressed in the mathematical literature. But I will try your suggestion anyways. Thanks.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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