Q. Current is flowing with a current density $J = 480{Acm}^{- 2}$ in a copper wire. Assuming that each copper atom contributes one free electron and given that Avogadro number=$6.0 \times 10^{23}atoms\ {mol}^{- 1}$ Density of copper=$9.0g\ {cm}^{- 3}$ Atomic weight of copper =64 $g\ {mol}^{- 1}$ The drift velocity of electrons is
A) $1\ mm\ s^{- 1}$
B) 2$\ mm\ s^{- 1}$
C) 0.5$\ mm\ s^{- 1}$
D) 0.36$\ mm\ s^{- 1}$
Explanation
(d) Drift velocity is given by
$v_{d} = \frac{I}{nqA}$
Where $I$ is current, n the number of electrons, A the area, q the charge. Given
$\frac{I}{A} = \frac{480A}{cm^{2}},\ q = 1.6 \times 10^{- 19}C$
$n = \frac{6 \times 10^{23} \times 9}{64}\ $
$\therefore v_{d} = 480 \times \frac{64}{6 \times 10^{23} \times 9 \times 1.6 \times 10^{- 19}}$
$\Longrightarrow v_{d} = \frac{480 \times 64}{6 \times 9 \times 1.6 \times 10000}cms^{- 1}$
$\Longrightarrow v_{d} = \frac{32}{900}cms^{- 1}$
$= \frac{32 \times 10}{900}mms^{- 1}$
$= 0.36mms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.