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Excess charge placed on a conductor distributes itself on the surface of a conductor. But why isn't the force which confines the charge to remain there, modelled in some way?

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It is modelled in some way: by Maxwell's equations in fact! Have a look at for a good discussion of this. – John Rennie May 15 '12 at 18:32

It is an electrostatic force, and it is actually the force by which atom cores of the materials drag electrons back to the material. In terms of potential, one could think as if atom cores make a potential well, which is so deep that electrons cannot escape it without huge energy provided from the outside.

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