Drift Velocity

Also called Drift speed

Drift velocity is the slow average velocity that charge carriers acquire along a conductor when a potential difference is applied, typically well under a millimetre per second even while the current itself appears instantly.

Electrons in a metal move fast and randomly all the time. Applying a potential difference barely changes that, but it does add a tiny average drift along the wire, and that average is the whole of the current.

AP Physics C: Electricity and Magnetism states it at EK 11.1.A.1.i: current within a conductor consists of charge carriers traveling through the conductor with an average drift velocity. The CED gives the relevant equation as

I = nqv_d A

where $n$ is the number of carriers per unit volume, $q$ the charge on each, $v_d$ the drift velocity and $A$ the cross-sectional area.

It is a CED equation, not a sheet equation. The printed C: E&M table of information carries $I = dq/dt$ , $I = \int \vec{J} \cdot d\vec{A}$ and $\vec{E} = \rho \vec{J}$ , and none of them contains $v_d$ . Neither does any other AP Physics sheet. So this relation has to be reconstructed rather than looked up.

The signal is not the carriers. A drift velocity of well under a millimetre per second sits behind a lamp that lights the instant you flip the switch, because the field that drives every carrier is established through the circuit at close to the speed of light. Nothing has to travel from the switch to the lamp.

Current density is the same idea per unit area, and the two share the same $nq v_d$ factor.

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