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

A sphere of radius [itex] a[/itex] carries a uniform charge density [itex] \rho_0 [/itex] in one hemisphere and the opposite charge density [itex] -\rho_0 [/itex] in the other hemisphere. The charged sphere produces an electric potential [itex]\Phi (r,\theta,\phi)[/itex]. For [itex] r>>a[/itex], the potential to leading order is of the form,

[tex]

\Phi(r,\theta,\phi) \approx \frac{g_n(\theta,\phi)}{r^n}

[/tex]

Find [itex] g_n(\theta,\phi)[/itex] and the numerical value for n.

2. Relevant equations

??

I presume the multiple expansion could be used, but this was a test question so I think I could do it without having the expansion memorized.

Any ideas?

Thanks!

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# Electric Dipole - Oppositely charged hemispheres

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