(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a) Find the potential of an axial quadrupole: point charges q, -2q, and q placed on the z-axis at distances L, 0, and -L from the origin.

b) Find the potential only at distances r>>L.

c) Show that this potential is proportional to one of the zonal harmonics.

2. Relevant equations

3. The attempt at a solution

Ok I am not entirely sure of where to start. I am thinking I need to do an expansion of |r-r'|^(-1) (spherical coordinates) to get to the quadrupole term. Was figuring on having to do a taylor expansion (possibly binomial)? I am not sure however if this is the right approach, and if it is, I am not sure whether to expand with respect to r or r'. It is possible that I have to involve tensors, but I hope not to as we just started talking about them in my Vector and Tensor Analysis class and haven't gone very far with them.

As far as zonal harmonics are concerned, I believe I just have to show it is proportional to one of the legendre polynomials.

I don't want anyone to flat out give me answers, just some guidance :D

Thanks guys

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# Homework Help: Potential of Finite Quadrupole and Zonal Harmonics

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