A wire of length 4 m and cross-sectional area 1 mm ^2 carries a current of 2 A . Given that the material holds 10²⁹ free electrons per cubic metre, determine the average time required for an electron to traverse the entire length of the wire.

Step-by-step solution

The drift velocity of free electrons is given by the relation I = n e A v_d , which gives v_d = I n e A . The average time required for an electron to traverse the length L of the wire is t = L v_d = L n e A I . Substituting the given values: L = 4 m n = 10²⁹ m ⁻³ e = 1.6 10⁻¹⁹ C A = 1 mm ^2 = 10⁻⁶ m ^2 I = 2 A t = 4 10²⁹ 1.6 10⁻¹⁹ 10⁻⁶ 2 t = 6.4 10^4 2 t = 3.2 10^4 s