Define drift velocity and relaxation time. Derive an expression for the drift velocity of free electrons in a conductor, and hence obtain I = neAv_d.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Define the terms. Drift velocity: the average velocity of free electrons in a conductor under an applied field. Relaxation time τ: the average time between two successive collisions.
2 · Write the acceleration. The force on an electron is −eE, so a = −eE/m.
3 · Average the velocities. Vᵢ = vᵢ − eEtᵢ/m. The average of vᵢ is zero and the average of tᵢ is τ, so v_d = −eEτ/m.
4 · Draw the diagram. [Wire of area A with a slice of length v_d Δt shaded; E arrow one way, electron drift arrow v_d the other way]
5 · Count the charge crossing A. In time Δt, the electrons in volume A v_d Δt cross A. Charge = neAv_d Δt, so I = neAv_d.
6 · Real life. In house wiring v_d is about a millimetre per second, yet bulbs light at once because the field spreads almost instantly.
7 · Close in one line. So, v_d = eEτ/m in magnitude and I = neAv_d.
Scoring tip: Keep the minus sign in v_d = −eEτ/m and say what it means: electrons drift opposite to E.
