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I understand how, when a neutral conductor is charged, the charges will repel each other and after the relaxation time will all be distributed in the surface of the conductor.

My question is: after that period, the electric field inside the conductor will be zero, so if another charge is put inside the conductor, how will it get to the surface? It must get to the surface somehow, because the charge inside the conductor must be zero, but how is it going to do so if the electric field is zero?

I came out with one idea of how it could work, but couldn't base it on textbooks. Even though in the beginning the electric field is zero in the inside, since the electric field caused on the outside charges by the inside charge isn't zero, these ones would get "pushed" and the distribution would be "messed", momentaneously, causing an electric field in the inside, that would finally "push" the inside charge to the outside. After that, the distribution outside would be one that allows us to say the electric field in the inside is zero again. The problem here is (appart from the fact that this doesn't base itself on any textbooks) if the charge is placed perfectly in the middle of the (let's consider a sphere for simplicity's sake) sphere then the inside charge won't be able to unbalance the distribution on the outside, because the electric field caused on the outside charges won't have a tangetial component, but only one that is perperdicular to the surface.

I am very curious about this and I am eager to clarify any points that might be unclear in the question. I looked up many physics books but couldn't find anything about this specific case I made up. Maybe it is physically impossible to place that charge in the inside after static equilibrium has been reached, or maybe it is possible and there is indeed a mechanism for the charge to be directed to the surface of the conductor. Anyway, I just wanted a well based answer, because mine are just guesses.

Thank you very much

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    \$\begingroup\$ Your 3rd paragraph describes what would happen. It is not in textbook probably because the problem set up and solution are far too complicated (probably too complicated to have a closed form). If a single charge is perfectly in the center, then ideally it is indeed an acceptable, metastable solution. But it can stay that way probably only at absolute zero temperature, which is impossible. \$\endgroup\$
    – rioraxe
    Jul 20, 2015 at 6:14
  • \$\begingroup\$ Thanks you very much for the reply. I didn't really have too much confidence on the answer I thought of. \$\endgroup\$ Jul 20, 2015 at 11:38

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I suspect that you're over-thinking this.

Each charge has an electric field associated with it.

The charges end up on the surface of the conductor because of the mutual repulsion among them, and the surface of the object is as far away as they can get from each other. This happens regardless of any pre-existing charge on the conductive object.

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  • \$\begingroup\$ I probably am over-thinking, you are right. I was just wondering how the charge got to the surface when there is pre-existing charge. I do understand it will end up there, and the final state does make sense to me, otherwise it would disrespect Gauss' Law. I was just thinking about what happened in the relaxation time. \$\endgroup\$ Jul 20, 2015 at 11:42

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