Model

Microscopic model

I = n q v_{d} A

Statement

Links the current to the number of carriers per volume n, their charge q, drift speed v_d and the wire's cross-section A.

Symbols and units

$n$	charge carriers per unit volume	m⁻³
$q$	charge per carrier	C
$v_{d}$	drift speed	m/s
$A$	cross-sectional area	m²
$I$	current	A

When it applies

One kind of carrier, uniform cross-section, steady flow.

Don't use when

Assumes a single kind of carrier, uniform cross-section, and steady flow — a semiconductor with both electron and hole carriers needs a combined treatment.

Derivation

In a time Δt, a carrier moving at the drift speed covers

Δ x = v_{d} Δ t

So every carrier inside a cylinder of that length gets through. Its volume is:

V = A v_{d} Δ t

Multiply by the carrier density and the charge each carries:

Δ Q = n q (A v_{d} Δ t)

Divide by Δt:

I = \frac{Δ Q}{Δ t} = n q v_{d} A

Worked examples

Drift speed in a household wire

Copper, n = 8.5 × 10²⁸ m⁻³, I = 10 A, A = 2.0 mm²:

v_{d} = \frac{I}{n q A} \approx 3.7 \times 1 0^{- 4} m/s

About 1.3 m per hour, while the signal travels at nearly the speed of light.

Watch out for

The drift speed is startlingly slow — under a millimetre per second — while the signal travels near light speed. The field carries the message, not the electrons.

Connects to

Current Current density Classical model