Drift Velocity

With no electric field applied, a conductor's free electrons undergo a purely random zig-zag motion, repeatedly colliding with the lattice's positive ions; on average, exactly as many electrons travel in any one direction as travel in the opposite direction, so there is no net flow and no current, exactly as described in section 2.1. Once a battery is connected and a potential difference is set up across the conductor, an electric field $\vec E$ appears inside it. This field exerts a force on every free electron, and because the electron's charge is negative, the resulting acceleration $\vec a$ points opposite to $\vec E$:

Between one collision and the next, each electron accelerates in this direction; the mean free time $\tau$ is the average time interval between successive collisions. Averaging over very many electrons and collisions, the electric field superimposes a slow, steady net motion on top of the electrons' underlying random zig-zag -- this net average velocity is called the drift velocity, $\vec v_d = \vec a\,\tau$, i.e.

which is conventionally written as $\vec v_d = -\mu \vec E$ (2.5), where $\mu = e\tau/m$ is called the mobility of the electron -- defined as the magnitude of the drift velocity produced per unit applied electric field, $\mu = v_d/E$ (2.6). The SI unit of mobility is $\text{m}^2\text{V}^{-1}\text{s}^{-1}$. …