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I'm having trouble understating the following example in section 3.2 of electricity and magnetism by M.Purcell: enter image description here

In paragraph 2 of the solution, it states that "The combination of these charges produces no field in the material of the conductor". I understand that it produces no net flux because of Gausses law, but why can't the -q and +q charges produce a net e field anywhere inside the conductor?

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    $\begingroup$ Of course such an arrangement would still make the total charge zero, and even in a charged "ideal" metal internally there exists a temporally and spatially very fast varying electric and magnetic field. We model these fields by averaging them in time and space over zillions of temporal and spatial cycles that gives us a macroscopically homogeneous description. In this model, when in a steady stationary state, all free charges accumulate on the surface and we can say this because we assume resistance free behavior. This is an average model of reality that is good enough for every day life. $\endgroup$
    – hyportnex
    Mar 26 at 15:20

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Conductors, by definition, have electrons that are able to adjust themselves to any electric field present, i.e. the electrons in a conductor respond with motion whenever they encounter an electric field. This is the reason that conductors are able to carry an electric current. As a consequence of this, when the electrons in a conductor experience an external electric field, they rapidly arrange themselves in a way that results in equilibrium; once the equilibrium state is reached no more current flows in the conductor and the there is no potential difference anywhere in the conducting medium. Since the electric field requires the existence of a potential gradient, no electric field exists in a conductor at a constant potential. It is the ability of a conductor's electrons to freely move in response to an external electric field that allows for this effect of zero electric field within the conductor. If this were not the case, then electric fields would be present as they are in dielectrics, where the dielectric's charge carriers are not free to move under the influence of an electric field.

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