Electron drift in a metal – drift speed, mobility and resistivity
PhysicsElectricity & CircuitsAges 16–17
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Free electrons in a metal wire move randomly at about 10⁵ m/s and collide with the vibrating lattice ions; a current adds a slow drift opposite to the field. Set the current, cross-section, metal and temperature to read the drift speed v_d = I/(neA), the field E = ρJ, the mean time between collisions τ and the mobility μ = v_d/E, and see why a hotter metal has a higher resistivity ρ = m/(ne²τ).
Lesson: Current in metals: drift velocity, I = nAv_d e, mobility, relaxation time and resistivity
What it shows
In a metal, about one electron per atom is free to move through the lattice of positive ions. These electrons dash about randomly at around 10⁵ m/s and keep colliding with the vibrating ions, so with no field there is no overall motion. A potential difference sets up a field E in the wire; between collisions each electron is pushed opposite to E, giving a slow drift of a fraction of a millimetre per second. The current is I = nAv_d e. Hotter ions vibrate more, collisions come sooner, τ falls and the resistivity ρ = m/(ne²τ) rises.
How to use
Choose a Metal and set Current I, Cross-section A, Temperature T and Wire length L. Watch the orange electron zig-zag and slowly drift against the field, and count the electrons crossing the dashed section. Read the drift speed, field, collision time and mobility below the picture, and press Record to add a row to the table. The graph shows how resistivity and τ change with temperature.
Parameters you can change
- Metal Copper, Silver, Gold, Aluminium
- Current I 0–20 A
- Cross-sectional area A 0.1–10 mm²
- Temperature T 100–600 K
- Wire length L 0.1–10 m
- Follow one electron
Questions to explore
- Why is the drift speed of electrons so small even though they move randomly at about 10⁵ m/s?
- If the same current flows through a thinner wire, what happens to the drift speed and why?
- Why does the resistance of a copper wire rise when it gets hotter?
