drift velocity

Drift velocity is the surprisingly slow, steady crawl of the charge carriers that make up a current. Here is the puzzle it answers: when you flip a switch, the light comes on instantly, so surely the electrons must be zooming along near the speed of light? In fact they inch along at a snail's pace. Think of a packed corridor of people jostling randomly in every direction, with only a gentle overall shuffle toward the exit. That slow shuffle is the drift.

Precisely, drift velocity v_d is the average velocity that charge carriers acquire along a wire because of the electric field, on top of their fast, random thermal motion which averages to zero. It links directly to the current by I = n A q v_d, where n is the number of carriers per unit volume, A is the cross-sectional area of the wire, and q is the charge on each carrier. Rearranged, v_d = I / (n A q). Because n is enormous in a metal (around 10^28 electrons per cubic metre), even a healthy current only needs a tiny drift, typically less than a millimetre per second.

So why does the light switch on at once? Because the electric field that nudges every electron is set up along the whole wire almost instantly, near the speed of light. Every electron everywhere starts drifting together the moment you close the switch, like water already filling a long hose starting to leave the nozzle the instant you open the tap, even though any single water molecule travels slowly. The signal is fast; the carriers themselves are slow.