# Charge distribution over different bodies

Two metal spheres (r2 = 2 X r1) have the same charge q on each of them separately. Now they are brought in contact. What will be the new charge distribution?
My extension : What are all the factors that determine the new charge distribution?
What if they are connected by a metallic rod?
What if these two are insulator material? We are all told in the beginning texts that when you bring a charged body (could insulator or conductor) in contact with another neutral body, they share the charge. But I have been bugged with several questions in this context. (When this distribution will be equal and when will it be unequal?) What factors determine the final charge distribution. I have been searching every where but I could not get the complete answer.

And I came across this question, in a book and am curious to know the answer of this and extrapolations of this question.

What if they have same polarity but different amounts of charge say Q1 and Q2?

What if one of them is a metal and the other one is an insulator?

Basically, is there a single expalnation or equation which will answer all these questions?

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The charges will look for an equilibrium position. In the case of two metal spheres this is on half on one sphere and the other half on the other sphere.
If sphere A has more charge than sphere B, the charges in sphere A will repel eachother; they will move to sphere B. Now, sphere B might have more charge, thus its charges will repel eachother to sphere A again. This keeps happening until equilibrium has been reached (which is quite obviously one half on sphere A and one half on sphere B).

In the case of insulators; charges cannot move in an insulator so afaik nothing will happen... Not 100% sure on that though :S

alphysicist
Homework Helper
The charges will look for an equilibrium position. In the case of two metal spheres this is on half on one sphere and the other half on the other sphere.
If sphere A has more charge than sphere B, the charges in sphere A will repel eachother; they will move to sphere B. Now, sphere B might have more charge, thus its charges will repel eachother to sphere A again. This keeps happening until equilibrium has been reached (which is quite obviously one half on sphere A and one half on sphere B).
Hi Nick89,

I don't think that's true for the case of unequally sized spheres. What sets the charge distribution is not that the charges are equal but that the potentials must be equal once the metal is in contact.