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It is a basic result in electrostatics that a charge $q$ in an arbitrary cavity of an ideal conductor will generate a total charge $-q$ on the surface of the cavity in such a way that the electric field is cancelled outside the the cavity (but only within the conductor). However, if the charge $q$ is the charge of an electron, and therefore the fundamental quantum of charge, how can opposing charge arrange itself in a symmetric way? Is the field cancelling nature of ideal conductors only valid when the amount of charge in play is large enough that quantization of charge is negligible?

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  • $\begingroup$ What kind of conductor with small amount of free charges are you thinking about? Note that electric field in the bulk of the conductor is subject to lattice-period oscillations anyway, so as the amount of free charge goes down, the concept of the mean electric field inside the conductor becomes less meaningful to the point of unusefulness. $\endgroup$ – Ruslan Jul 10 at 16:43
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You are asking if the charge is an electron, how can an opposing charge arrange itself in a symmetric way?

In a simple atom, the electron field that exists around the proton as per QM, arranges itself in a symmetric way so, that the atom itself is EM neutral.

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