Question

A wire of length 2 m, cross-sectional area \( 4\ \text{mm}^2 \), and current 1.6 A has electron drift time \( 40 \times 10^{-3} \ \text{s} \). Find electron number density.

• A. \( 8 \times 10^{28}\ \text{m}^{-3} \)
• B. \( 6 \times 10^{28}\ \text{m}^{-3} \)
• C. \( 4 \times 10^{28}\ \text{m}^{-3} \)
• D. \( 5 \times 10^{28}\ \text{m}^{-3} \)

Hint:

Use \( I = n A e v_d \), and convert area to \( \text{m}^2 \) properly.

Answer 1

The Correct Option is D

Drift velocity \( v_d = \frac{L}{t} = \frac{2}{40 \times 10^{-3}} = 50\ \text{m/s} \)
Use \( I = nAe v_d \Rightarrow n = \frac{I}{Ae v_d} \)
\[ A = 4 \times 10^{-6}\ \text{m}^2,\quad e = 1.6 \times 10^{-19},\quad I = 1.6\ \text{A} \] \[ n = \frac{1.6}{4 \times 10^{-6} \cdot 1.6 \times 10^{-19} \cdot 50} = 5 \times 10^{28}\ \text{m}^{-3} \]