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I am not seeing the "big picture" here. If I have two conducting spheres separated by a long conducting wire, why would the spheres share the same electric potential?

I think of the spheres as point charges, what does the conducting wire do? The $E$ field inside the conducting wire is 0, so what is it really doing?

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The sphere should be conductible, or you may face 1/0. – puresky Jan 6 '12 at 3:53
Hi @puresky - it looks like you may have intended to comment on the question, so I converted your post into a comment. – David Zaslavsky♦ Jan 6 '12 at 4:39

2 Answers

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Because electrons flow when there is potential difference. So only when every point has the same potential will the system reach electrostatic equilibrium.

The above holds only if everything is conductor.

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But what does the electron flowing have to do with the potential differences? – lam Jan 6 '12 at 3:59
potentials are caused because of excess or deficiency of electrons. Now when there exist a pot. difference, a current flows which is flow of electrons. Now, this will happen till there is a pot. difference. So, when current flow stops, you have two equipotential spheres. – Vineet Menon Jan 6 '12 at 5:11
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you mean "till there is NO potential difference" – ThePopMachine Jan 6 '12 at 5:21
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Opposite charges attract, electrons are moving charges. A conducting wire is the perfect way for electrons to move until the charge of the two ends is equal, and this happens very quickly.

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