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?


1 Answer 1


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.

  • $\begingroup$ Thanks for the answer. Yes, using $\text{C}$ was just for simplification purposes, but, in reality, it would be $\text{$\mu$C}$ instead. With regards to your description of the charge distribution, wouldn't the electrons already seek to do this on each sphere (the electrons would seek to maintain maximal separation from each other, since they're all negatively charged), regardless of contact between the two spheres? Then what difference does the spheres making contact make? $\endgroup$ May 10, 2022 at 22:19
  • $\begingroup$ Contact is required for exchange of charge. In absence of contact, 8C and 10C will be distributed on them. $\endgroup$ May 11, 2022 at 14:05
  • $\begingroup$ But why will the charges spread over the outside of each sphere? Why not the inside of the sphere as well? $\endgroup$ May 11, 2022 at 19:12
  • $\begingroup$ That is a separate question. It is a basic property of conductors under electrostatic conditions with an elegant proof. All excess charge resides on outer surface. I will try to give you an intuition. Imagine small similarly charged thermocol in a container. Ignore gravity. Can you visualise that all thermocol balls will spread on outside surface due to mutual repulsion? $\endgroup$ May 12, 2022 at 6:22
  • $\begingroup$ @SabatAnwar: What if the spheres are not identical, e.g. if one is smaller than the other? Intuitively I assume the larger one would end up with more of the excess charge, but even if that is indeed the case it's not clear to me how one would calculate exactly how the excess charge would be distributed between the two, as I can envision pitfalls with just going by the ratio of their volumes or areas (but maybe it ends up actually being that simple). $\endgroup$
    – Outis Nemo
    Feb 27 at 17:04

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