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Current from drift velocity

Short answer

Current I = n e v_d A = 10^24 × 1.6×10^−19 × 1.5×10^−2 × 10^−4 = 0.24 A.

A conductor material has a free electron density of 10^24 electrons per m³. When a voltage is applied a constant drift velocity of 1.5×10⁻² m/s is attained by the electrons. If the cross sectional area of the material is 1 cm², calculate the magnitude of the current.

Current in a conductor is the charge crossing a section per second: I = n e v_d A.

Data

  • n = 10²⁴ electrons/m³
  • e = 1.6 × 10⁻¹⁹ C
  • v_d = 1.5 × 10⁻² m/s
  • A = 1 cm² = 10⁻⁴ m²

Calculation

I = n e v_d A I = 10²⁴ × 1.6 × 10⁻¹⁹ × 1.5 × 10⁻² × 10⁻⁴ I = 1.6 × 10⁵ × 1.5 × 10⁻² × 10⁻⁴ I = 2400 × 10⁻⁴ = 0.24 A

Answer: I ≈ 0.24 A (240 mA)

✓ Answer checked by Claude Opus 5.5 (high effort)

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