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Jul 2, 2018 at 16:34 comment added Global I am completely excluding any fringe electric fields here. For this particular Griffiths's problem that is not required. Now having said that do you think there could be an electric field well inside a "conductor" if the applied electric field is very low? Why do you think so? en.wikipedia.org/wiki/Skin_effect. And what about the Uniqueness theorems? en.wikipedia.org/wiki/Electromagnetism_uniqueness_theorem
Jul 2, 2018 at 15:35 comment added gj255 I would like to know how you go from $\rho = 0$ to $E = 0$. In general there can be an electric field even in regions where there is no charge density, such as in the vicinity of stationary point charge, or in the presence of an electromagnetic wave. One has to be careful when reasoning that there is no field inside a conductor.
Jul 2, 2018 at 5:55 history answered Global CC BY-SA 4.0