Consider a wire o

8.9 hours

Given,

Number of free electron per unit volume, n=10²⁹

Area of cross-section, A=1 mm²=10^-6 m²

Length of wire, l= 4m

Current through the wire, I=2A

Formula used

We know that the expression for drift velocity, V_d of ‘n’ free electrons through a wire of cross-sectional area A, for a current ‘i' is

Where e is the charge of 1 electron= 1.6×10^-19 C

V_d can be expressed in terms of the travel length, l and travel time, t as,

Combining the above two expressions, we can write as,

Or,

Solution,

Substituting the given values in eqn.1, we get the time taken by the free electrons to cross the length as,

So the average time taken by an electron to cross the length of the wire is approximately 8.9 hours.