Microscopic view of current — I = nAvq

5 minAS Level9.1.4

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can derive I = nAvq, calculate drift velocity, and explain why drift speed is tiny while current starts instantly.

From macro to micro

We know $I = Q/t$ . Now zoom in on a wire of cross-sectional area $A$ . Charge carriers (electrons in a metal) have number density $n$ (carriers per m³) and each carries charge $q$ . In time $t$ , carriers drift a distance $v t$ where $v$ is the drift velocity.

Volume that passes a point in time $t$ : $A \times v t$ . Number of carriers in that volume: $n A v t$ . Total charge: $Q = n A v t \times q$ . Current: $I = Q/t = n A v q$ .

This is the microscopic current equation.

Definition

Drift velocity (v)

The average velocity of charge carriers in the direction of current. In metals, typically ~10⁻⁴ m/s (fractions of a mm/s).

Definition

Number density (n)

Number of charge carriers per unit volume (m⁻³). For copper, n ≈ 8.5 × 10²⁸ m⁻³.

Worked example: Drift velocity in a copper wire

A copper wire (cross-section 1.0 mm²) carries a current of 2.0 A. Number density of conduction electrons in copper is 8.5 × 10²⁸ m⁻³. Find the drift velocity.

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