A cylindrical conductor of length 2 m and area of cross section 0.2 mm² carries current of 1.6 A when connected to a 2 V battery. Find mobility of electrons.

Solution:

Resistance:

R = V/I = 2/1.6 = 1.25Ω

Resistivity:

ρ = RA/L

Area:

A = 0.2 × 10^-6 m²

ρ = (1.25 × 0.2 × 10^-6)/2

ρ = 1.25 × 10^-7 Ωm

Conductivity:

σ = 1/ρ = 8 × 10⁶

Using:

σ = neμ

Assuming electron density:

n = 8 × 10²⁸ m^-3

μ = σ/(ne)

μ = (8 × 10⁶)/(8 × 10²⁸ × 1.6 × 10^-19)

μ = 6.25 × 10^-4 m²/Vs

Answer: 6.25 × 10^-4 m²/Vs