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Here are two common statements about the charge distribution in a solid conductor:

  1. There is no net charge inside the conductor, "because if we think of charges as balls repelling each other they will congregate at the boundary".

  2. The charge will distribute on the boundary in such a way that the potential inside the conductor is constant.

I am confused by these two statements, as follows:

  1. if I imagine balls repelling each other in a given domain I'd guess that they would end up in a lattice-like configuration over the entire conductor

  2. if the potential from a charge scales like 1/R where R is the distance from the charge, it seems like any charge distribution confined to the surface of the body necessarily induces a electric potential that tends to infinity close to (at least parts of) that boundary. Hence it cannot be constant (it'd have to be constant infinity).

If the electrons-as-charged-balls analogy is not valid, is there some other valid analogy that explains the physical truth?

My original motivation is that I want to compute how a given amount q of charge distributes in a given conductor. (For example, I want to verify the common wisdom that curved parts of the surface receives more charge.)

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Don't start with the charge in the conductor. Start with the field around the conductor.

The field lines only end when they meet a charge (speaking in crude terms. To be physics-y-er we could restate it in terms of the gradient of the field). So if there is charge inside the conductor, then there must be field penetrating the conductor for the lines to terminate on those charges. But if there is field inside the conductor, then the charge will move under the influence of that field, until it gets to a boundary it can't cross. Which is the boundary between the conductor and surrounding dielectric.

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