I have the following thought experiment. Assume that we have two conducting spheres. Sphere A has a charge of $+ 10 \ \text{C}$ and sphere B has a charge of $+ 8 \ \text{C}$. Now assume that we place them together so that they make contact. The question is as follows: what happens to the distribution of the charges on the spheres?
I am told that the charges will spread over the outside of both spheres in such a way as to maximise the distances between them. My first thought was that, assuming both spheres have the same number of protons, electrons from the more negatively charged sphere (sphere B) would flow to the more positively charged sphere (sphere A), until the spheres both have equal charge, $\dfrac{(+ 10 \ \text{C}) + (+ 8 \ \text{C})}{2} = 9 \ \text{C}$.
What, exactly, is meant by "the charges will spread over the outside of both spheres in such a way as to maximise the distances between them"? And why does this happen?
Also, would my first thought about what would happen be correct (aside from the provided description), or is it incorrect? If it is incorrect, then why?
Best Answer
I will try to help you visualize what is happening.
Assuming that spheres are identical, you are correct in saying that they will have equal charge of 9C each. (by symmetry)
(It is a different issue that 9C is huge charge. It is more likely to be 9$\mu C$)
Charges are free to move on conductors. Imagine as if this excess charge is floating on both spheres in fluid form. They will repel each other. All the charge wants to get away from all other charge. Problem is they cannot get out of sphere. So they will spread on surface of charge while maintaining as much distance from each other as possible.