Drift speed of electrons, 20 A

Drift speed comes from I = n A e v_d, so v_d = I/(nAe).

Given: I = 20 A, A = 1 mm² = 1×10⁻⁶ m², n = 10²⁸ m⁻³, e = 1.602×10⁻¹⁹ C.

v_d = 20 / (10²⁸ × 1×10⁻⁶ × 1.602×10⁻¹⁹)
    = 20 / (1.602×10³)
    = 1.25×10⁻² m/s

Answer: v_d ≈ 1.25×10⁻² m/s = 12.5 mm/s

The drift speed is very small compared with the random thermal speed (~10⁶ m/s). The bulb lights at once because the electric field travels through the wire at nearly the speed of light, not because electrons rush from the switch.