The problem: Find the potential between 2 concentric spheres, of radii a & b, where the potential of the spheres are held at Ca*P3(cos(t)) & Cb*P5(cos(t)), where P3 & P5 are the 3rd & 5th Legendre functions, t is theta & Ca & Cb are constants.(adsbygoogle = window.adsbygoogle || []).push({});

The general solution to Laplace with azimuthal symetry:

V = sum over l of (Al*(r^l)+Bl*r^(-(l+1)))*Pl(cos(t))

I can use the orthoganality of the Legendre functions to elimimate all but one of the series terms when I plug in the boundry conditions, giving:

V(a,t) = (A*a^3 + B*a^(-4))P3(cos(t)) = Ca*P3(cos(t))

V(b,t) = (C*b^5 + D*b^(-6))P5(cos(t)) = Ca*P5(cos(t))

The solution should be a combination of these, but I'm a bit stumped about how to find the constants when I can't use r=zero or r=infinity to zero one of them (as is done in single shell problems). I have a feeling this may become obvious after a good sleep, but I'd be grateful for a nudge in the right direction.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Potential between 2 concentric spheres

**Physics Forums | Science Articles, Homework Help, Discussion**