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Yes it does. Classically, the current density in a conductor is given by $\vec j = e \vec v_D \cdot n$, where $n$ is the concentration of charge carriers, $e$ is the charge of the charge carriers and $\vec v_D$ is the drift velocity (this is part of the Drude theory). The drift velocity is the average velocity of the charge carriers, the idea is, that they ...

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