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Drift velocity of electrons in copper

Short answer

Electron density n = (ρ_m/M)N_A ≈ 8.48×10²⁸ m⁻³. Drift velocity v_d = I/(nAe) ≈ 1.47×10⁻⁴ m/s ≈ 0.15 mm/s.

Assuming that each atom of copper contributes one free electron, calculate the drift velocity of free electrons in a copper conductor of cross sectional area 10⁻⁴ m² carrying a current of 200A. Given: Atomic weight of copper = 63.5 g/mol, Density of copper = 8.94×10³ kg/m³, Charge of an electron = 1.6×10⁻¹⁹ C

With one free electron per atom, n = (ρ_m/M) N_A, and v_d = I/(nAe).

Given: A = 10⁻⁴ m², I = 200 A, M = 63.5 g/mol = 63.5×10⁻³ kg/mol, density = 8.94×10³ kg/m³, e = 1.6×10⁻¹⁹ C, N_A = 6.022×10²³ mol⁻¹.

n = (8.94×10³ / 63.5×10⁻³) × 6.022×10²³
  = 1.408×10⁵ mol/m³ × 6.022×10²³
  = 8.48×10²⁸ m⁻³

v_d = I / (n A e)
    = 200 / (8.48×10²⁸ × 10⁻⁴ × 1.6×10⁻¹⁹)
    = 200 / (1.357×10⁶)
    = 1.47×10⁻⁴ m/s

Answer: v_d ≈ 1.5×10⁻⁴ m/s = 0.15 mm/s

✓ Answer checked by Claude Opus 5.5 (high effort)

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