Drift Speed of Electrons
Fast random motion, slow steady drift.
Lesson at a glanceShow the key points
- Free electrons move randomly and collide with the lattice; no net flow without a field.
- In a field they drift against it: v_d = eτE/2m = kE (32.4).
- i = nAev_d, j = nev_d (32.5); typical v_d ≈ 0.1 mm/s.
- The field, not the electrons, travels round a circuit almost at light speed.
Electrons inside a metal rush about at hundreds of kilometres a second, yet carry a current by creeping along at a fraction of a millimetre per second.
Free electrons and the lattice
A metal contains many loosely bound free (conduction) electrons moving among heavy positive ions, the lattice, which vibrate about fixed positions (more strongly when hotter). Every so often an electron collides with the lattice and sets off in a new random direction with a new random speed, so it follows a zig-zag path. With so many electrons moving at random, as many cross any area one way as the other: no current.
Drift in a field
Apply a field E. Between collisions each electron feels a force eE against the field and picks up extra velocity in that direction, growing steadily until the next collision wipes it out. The random part averages to nothing, but the extra part doesn’t: the electrons slowly drift opposite to the field. If the time between collisions is τ, the extra distance gained per interval is
For a given material at a given temperature τ is fixed, so we can picture the electrons as at rest with no field and moving at a steady drift velocity proportional to E when there is one:
Current and drift speed
Take a wire of cross-section A with n free electrons per unit volume. In time Δt the electrons in a length vdΔt, i.e. nAvdΔt of them, cross a given section, carrying charge nAvdΔt · e. Dividing by Δt:
A copper wire of cross-section 1.5 mm² carries 3.0 A. Copper has 8.5 × 10²⁸ free electrons per m³. Find the drift speed.
A wire of cross-section 0.50 mm² carries 1.0 A and has 8.0 × 10²⁸ free electrons per m³. Find the current density and drift speed.
- 1Free electrons move randomly and collide with the vibrating lattice; no field, no net flow.
- 2In a field they drift against it: v_d = (eτ/2m)E = kE (32.4).
- 3i = nAev_d and j = nev_d (32.5); drift speeds are tiny (≈ 0.1 mm/s).
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