Question

A metallic wire of cross sectional area $ 4 \, mm^{2} $ carries a current of $ 3.2 \, A $ . If $ 5 \times 10^{26} $ charge carriers flow across the wire per unit volume, then their drift velocity in $ m \,s^{-1} $ is

• A. $ 1 $
• B. $ 0.1 $
• C. $ 0.01 $
• D. $ 10 $

Answer 1

Answer: (C)

Here,
Cross-sectional area of the wire,
$A=4\,mm^{2}=4\times 10^{-6}\,m^{2}$
Current flowing through the wire , $I=3.2\,A$
Number of charge carriers per unit volume of the wire (number density), $n=5\times 10^{26}\,m^{-3}$ The drift velocity is
$v_{d}=\frac{I}{neA}=\frac{\left(3.2 A\right)}{\left(5\times10^{26} m^{-3}\right)\left(1.6\times10^{-19}C\right)\left(4\times10^{-6} m^{2}\right)}$
$=0.01\,m\, s^{-1}$