JEE Main 2023 — Current Electricity Question with Solution

The drift velocity $v_d$ can be found using the formula for current $I$ in a conductor:

$I=nqA{v}_d$,

where:

• $n$ is the number density of free electrons (number of free electrons per unit volume),
• $q$ is the charge of an electron,
• $A$ is the cross-sectional area of the conductor, and
• $v_d$ is the drift velocity of the electrons.

We can rearrange the above formula to solve for $v_d$:

$v_d=\frac{I}{nqA}$.

Given that $I=2\text{A}$, $n=2.0\times 10^{28}{\text{m}}^{-3}$, $q=1.6\times 10^{-19}\text{C}$, and $A=25.0{\text{mm}}^2=25.0\times 10^{-6}{\text{m}}^2$, we can substitute these values into the formula to find $v_d$:

$v_d=\frac{2}{(2.0\times 10^{28})(1.6\times 10^{-19})(25.0\times 10^{-6})}$

$v_d=25\times 10^{-6}{\text{ms}}^{-1}$.

Therefore, the drift velocity of the electrons is $25\times 10^{-6}{\text{ms}}^{-1}$.