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I'm having a bit of trouble understanding a pretty simple issue. Assuming I have 2 conducting spheres uniformly charged connected by a long fine line (as shows in the added photo) and im being asked about what will happened, how much charged will move from on spheres to the other.

I was told that the electric potential of these 2 spheres are: $k\frac{Q_1}{R_1}$ and $k\frac{Q_1}{R_1}$ The thing is, that I don't get why, I mean, $R_1$ and $R_2$ are the radiuses of the 2 spheres, these are not vectors or anything and they do not meet the same coordinates and this is what I should take when calculating the potential using integral the good way...

So, how can $k\frac{Q}{R}$ be the potential of the spheres?

enter image description here

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  • $\begingroup$ I don't understand what you mean by "The thing is, that I don't get why, I mean, $R_1$ and $R_2$ are the radiuses of the 2 spheres, these are not vectors or anything and they do not meet the same coordinates and this is what I should take when calculating the potential using integral the good way..." $\endgroup$
    – user42733
    Apr 9, 2014 at 17:50
  • $\begingroup$ are you asking about why electric potential goes like $\frac{1}{R}$? Otherwise I'm not sure what the question is $\endgroup$
    – Jim
    Apr 9, 2014 at 17:54
  • $\begingroup$ well yea, R1 and R2 are just sizes. $\endgroup$
    – user3921
    Apr 9, 2014 at 18:09
  • $\begingroup$ $k\frac{Q}{R}$ would be the potential (relative to $V=0$ at an infinite distance away) of one isolated sphere having charge $Q$. With another sphere present, that wouldn't be the case, so I don't understand why the statement would have been made. Unless it was stated in the original context that those values are the potentials of each sphere in isolation. Perhaps the original wording of the question would help. $\endgroup$
    – garyp
    Apr 9, 2014 at 18:26

1 Answer 1

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There is an important fact for this problem, namely that the spheres are very very far away. If they are close together, but connected by a long wire then it's a different issue.

In isolation a sphere of charge $Q$ and radius $R$ has a potential of $kQ/r$ relative to a zero potential at infinity, and so it's potential at $r=R$ is $V=kQ/R$. If the spheres are far from each other, neither has much of an effect on each other, so the potential is now approximately $kQ_1/R_1$ on the surface of the first sphere (what it would be in isolation), and the potential is now approximately $kQ_2/R_2$ on the surface of the second sphere (what it would be in isolation).

If you connect a long wire between the far away spheres, they will want to reach the same potential, and what they can do is exchange charge. So find out how much charge must be exchanged so that the total charge remains the same but the new distribution makes the spheres have the same potential.

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