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

Actually, this is not truly a homework, I'm just ineterested in how to solve problems, like the one below.

So, we have two conductive spheres, at a distance R from each other, the radii are r1 and r2 (r1 and r2 are comperable in size, while R is significantly larger than either of them), both speheres are insulated, and they have a net charge of Q1 and Q2, respectevly.

What is the force acting between them (up to the first order term)?

2. Relevant equations

We were to solve these kind of exercises when studying multipole expansion, so I guess, we could use the formulae of that.

http://en.wikipedia.org/wiki/Spherical_multipole_moments#General_spherical_multipole_moments

(Sorry, this is my first post, I don't really know how to write equations properly yet.)

3. The attempt at a solution

Well, I'm quite confused about it rigth now, though probably it was meant to be an easy problem, because the configuration has azimuthal symmetry (by taking the z axis to be parallel with the vector pointing from the center of one of the spheres to center of the other). Therefore, we could use the Legendre polynomials for the expansion, instead of the spherical harmonics, I presume. Also, it seems to me, that the part with importance gonna be the dipole moment, because the azimuthally symmetric effect of the other sphere.

Even if we know the formulae for the expansion and the multipole moments, I find the situation quite confusing, because both spheres are affecting the other.

One more thing that might be used during the solution is that inside the conductive sphere the electric field is 0 and the potential is constant.

Thanks!

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# Homework Help: Force acting between bodies - using multipole expansion

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