A copper wire with a cross-section of 1.0 mm ^2 carries a current of 1.0 A . Determine the drift speed of the free electrons in the wire, assuming there is one free electron per atom. The density of copper is 9000 kg m ⁻³ .

Step-by-step solution

The number density of free electrons is equal to the number density of copper atoms, given by: n = N_A d M Substituting the standard values for copper ( N_A 6.02 10²³ mol ⁻¹ , M 63.5 g mol ⁻¹ = 63.5 10⁻³ kg mol ⁻¹ ): n = 6.02 10²³ 9000 63.5 10⁻³ 8.5 10²⁸ m ⁻³ The drift speed v_d is given by the relation: I = n e A v_d Rearranging for v_d : v_d = I n e A Substituting the given values ( I = 1.0 A , e = 1.6 10⁻¹⁹ C , A = 1.0 10⁻⁶ m ^2 ): v_d = 1.0 8.5 10²⁸ 1.6 10⁻¹⁹ 1.0 10⁻⁶ v_d 1.0 13.6 10^3 m s ⁻¹ 0.074 10⁻³ m s ⁻¹