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When we define Electrostatics we say that charges are at rest or they are stationary, but when we put a conductor in electric field (assuming Electrostatics) and say that all charge resides on it's surface so that the conductor has net electric field zero in it's bulk we are saying that net force on any small charge is zero. So, how are we claiming that the charges are in rest by sending whole charge on surface (I mean, zero force and rest are two different things) ?

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I'm not quite sure what you're getting at but

  1. The individual electrons are indeed moving around due to thermal excitation. But statistically there should be an equal number moving left as moving right, so the net movement of charge is 0.

  2. If the charge is mainly located near the surface of the metal, and not (in net) moving, that's a case of charge not moving, so we can analyze it as an electrostatic situation.

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