We show how the electrical field inside the conductor changes as a function of the number of charged particles. We show that the nonvanishing electrical field is concentrated near the surface of the conductor, at a shallow depth on the same order of magnitude as the separation between charges. Our study has illustrated the effect of charge discretization on a fundamental emergent law of electrostatics.

It is often stated in introductory physics textbooks that the electrical field inside a conductor should be zero,1–5 but that can only be true if the charge is a continuous distribution. Consider a simple classical model (which is used in the famous Thomson problem6), in which the charge is made of identical point particles and the conductor is a confined volume in space that the charged particles can freely move around. If there is only a single charged particle, no matter where...

Supplementary Material

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