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Metals are highly effective at screening electric fields. If we place two contacts reasonably far away from each other on a piece of metal and apply a voltage bias, the charge carriers in the section that is far enough from both the contacts should be unaffected by the electric field. Why then is the electrical resistance affected by the electric field between the contacts (through the electron mobility)? Why do we measure a voltage drop (e.g. in a four probe measurement) when there is no electric field, and the potential profile in the metal bulk should be flat?
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