Cornell Note — Drift Velocity and Current Density — Notes | NoteTube

Cue	Notes
Why is vd so small?	Electrons collide frequently with lattice ions; random motion (10^{5} m/s) overwhelms drift
Why is current instantaneous?	Electric field propagates at ~c; all electrons drift simultaneously
How does vd relate to area?	vd = I/(neA) → vd ∝ 1/A for constant I
What is relaxation time τ?	Average time between successive collisions; [T]; τ ∝ 1/T for metals
What is current density?	J = I/A = nevd = σE; units: A/ $m^{2}$
Microscopic Ohm's law?	J = σE (vector form); σ = $ne^{2}$ τ/m
How are ρ and τ related?	ρ = m/( $ne^{2}$ τ); higher τ → lower ρ → better conductor

Summary Box: The microscopic picture: electrons drift slowly (vd ~10^{-4} m/s) because of frequent collisions (τ ~10^{-14} s). Yet current is instantaneous because the field, not the electrons, propagates at the speed of light. The key formula chain: E → vd = eEτ/m → J = nevd → I = JA.