Hello, I've been working my way through Griffiths' "Introduction to Electrodynamics" book, and I'm slightly confused by Problem 3.20. For those of you with out a copy of this book, given a conducting sphere of radius R and charge Q in a uniform electric field of strength E0, what is the potential outside the sphere?(adsbygoogle = window.adsbygoogle || []).push({});

Intuitively, this is virtually identical to example 3.8, which solved the problem for an uncharged sphere. The sphere is an equipotential which can be defined to be zero when r = R. Far away from the sphere, the field is just E0 in, say, the z direction, so the potential is -E0 z there. After playing games with separation of variables, you end up with V(r, theta) = -E0 (r - R^3/r^2) cos(theta).

In this problem, I can still say that the sphere is an equipotential zero and field is the same as above when we get far from the sphere. If we are to add a charge Q to an equipotential sphere so that it remains an equipotential, the charge must be uniform over the surface of the sphere. Therefore, the charged solution is V(r, theta) = -E0 (r - R^3/r^2) cos(theta) - Q/(4 pi e0 r).

I'm not happy with this solution though. Am I missing some way of setting up the problem and solving it directly without frantically waving my hands over the important bits?

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# Charged conducting sphere in a uniform electric field?

Can you offer guidance or do you also need help?

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