Define drift velocity. Derive an expression for it, and show how it gives the current in a wire.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Define. Drift velocity is the average velocity with which free electrons move through a conductor, against the applied field.
2 · Acceleration. The force on an electron is eE, so its acceleration is a = eE/m, opposite to E.
3 · Drift velocity. Over the average time τ between collisions: v_d = aτ = eEτ/m.
4 · Draw the figure. [A wire of cross-section A with a slice of length v_dΔt shaded; arrows E and I one way; arrow v_d for electrons the other way]
5 · Count the charge. In time Δt, the electrons in the volume Av_dΔt cross A: their charge is nAev_dΔt.
6 · Current. I = charge ÷ time = nAev_d.
7 · Close in one line. So the current in a wire is proportional to the tiny drift velocity of its free electrons.
Scoring tip: Mention the random motion first: with no field the average velocity is zero. It shows why the drift is an extra velocity on top of the random motion.
