Question

The drift velocity of free electrons in a conductor is $v$ when a current $I$ is flowing in it. If both the radius and current are doubled, then drift velocity will be

• A. v
• B. $\frac{v}{2}$
• C. $\frac{v}{4}$
• D. $\frac{v}{8}$

Answer 1

Answer: (B)

Given initial drift velocity $\left(v_{d_{1}}\right)=v$;
initial current $\left(I_{1}\right)=I,$
initial radius $\left(r_{1}\right)=r,$
final radius $\left(r_{2}\right)=2 r$
and final current $\left(I_{2}\right)=2 I$.
The drift velocity is given by
$v_{d}=\frac{I}{n e A}=\frac{I}{n e \times \pi r^{2}}$ i.e., $v_{d} \propto \frac{I}{r^{2}}$
Therefore, $\frac{v_{d_{1}}}{v_{d_{2}}}=\frac{I_{1}}{I_{2}} \times \frac{r_{2}^{2}}{r_{1}^{2}}=\frac{I}{2 I} \times \frac{(2 r)^{2}}{r^{2}}=2$
$\therefore v_{d_{2}}=\frac{v_{d_{1}}}{2}=\frac{v}{2}$