Question

A current of $16A$ is made to pass through a conductor in which the number density of free electrons is $4\times {10}^{28}{m}^{-3}$ and its area of cross section is ${10}^{-5}{m}^2$. The average drift velocity of free electrons in the conductor is:

• A. $2.5\times {10}^{-4}{ms}^{-1}$
• B. $3.2\times {10}^{-4}{ms}^{-1}$
• C. $6.4\times {10}^{-4}{ms}^{-1}$
• D. $1.6\times {10}^{-4}{ms}^{-1}$

Answer 1

The correct option is A $2.5\times {10}^{-4}{ms}^{-1}$

in a small time interval $dt$, the number of electrons leaving a cross section is $(4\times {10}^{28})\left({10}^{-5}\right)vdt$.

Therefore, charge crossing in time $dt$ is :

$dq=(1.6\times {10}^{-19})(4\times {10}^{28})\left({10}^{-5}\right)vdt$

Hence, $I=\frac{dq}{dt}=6.4\times {10}^{4}v=16$

This gives: $v=2.5\times {10}^{-4}m/s$