Electrons rush about at huge random speeds, but drift slowly along the wire. I = n A e vd
Current I0 A
Drift velocity vd0 mm/s
Charges crossing the ring0 /s
Compared with A = 1 mm²—
I = n A e vd ⇒ vd = I / (n A e) Same battery: the field E sets the drift speed (vd = μE). A thicker wire carries more electrons, so I grows with A, but vd stays the same. Drift velocity does not depend on area. Same current: if I is kept fixed, a thicker wire or more electrons per m³ means each electron drifts slower: vd ∝ 1/A and vd ∝ 1/n.
The gold electron leaves a trail: a zigzag of collisions with the ions, with a tiny net drift. In copper (n = 8.5 × 10²⁸ m⁻³), vd is only a fraction of a mm per second, while the random speed is about 10⁶ m/s.
Kamran Afsar Khan · Professor of PhysicsElectric Current