Question

A current of $2A$ is passing through a metal wire of cross sectional area $2\times {10}^{-6}{m}^2$. If the number density of free electrons in the wire is $5\times {10}^{26}{m}^{-3}$, the drift speed of electrons is (given $e=1.6\times {10}^{-19}C$)

• A. $\frac{1}{16}m{s}^{-1}$
• B. $\frac{1}{40}m{s}^{-1}$
• C. $\frac{1}{80}m{s}^{-1}$
• D. $\frac{1}{32}m{s}^{-1}$

Answer 1

Answer: (C)

$\frac{1}{80}m{s}^{-1}$

Given : $I=2$ A

$A=2\times {10}^{-6}{m}^2$

$n=5\times {10}^{26}$ $m^{-3}$

Drift velocity of electrons $v_d=\frac{I}{Ane}$

$\therefore$ $v_d=\frac{2}{(2\times {10}^{-6})(5\times {10}^{26})(1.6\times {10}^{-19})}=\frac{1}{80}$ $m/s$