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The 'charges' (electrons, in the case of a metal conductor) are ALREADY distributed within the conductor. They are in a state of constant, haphazard, movement at just short of the speed of light. When a potential difference is applied across the conductor, there is a tendency for these electrons to move from the negative potential towards the positive potential. This tendency is VERY slow; for example, an individual electron is unlikely to pass through the filament of a flashlight during the lifetime of its battery!

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