The number density of free electrons in a copper conductor estimated in Example 3.1 is 8.5 × 10²⁸ m⁻³. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 × 10⁻⁶ m² and it is carrying a current of 3.0 A.

Number density of free electrons in a copper conductor, n = 8.5 x 10²⁸ m^–3 Length of the copper wire, I = 3.0 m

Area of cross-section of the wire, A = 2.0 x 10^-6 m²

Current carried by the wire, I = 3.0 A, which is given by the relation, I = nAeVd Where, e = Electric charge = 1.6 x 10^-19 C

Vd= Drift Velocity = Length of the wire (l) /Time taken to cover l (t)

I = nAel/t => t = nAel/t

t = 3x 8.5 x 10²⁸ x 2 x 10^-6 x 1.6 x 10^-19 )/3.0

= 2.7 x 10⁴ s

Therefore, the time taken by an electron to drift from one end of the wire to the other is 2.7 x 10⁴ s.