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 $\left(r_2\right)=2r$
and final current $\left(I_2\right)=2I$.
The drift velocity is given by
$v_d=\frac{I}{neA}=\frac{I}{ne\times \pi r^2}$ i.e., $v_d\propto \frac{I}{r^2}$
Therefore, $\frac{v_{d_1}}{v_{d_2}}=\frac{I_1}{I_2}\times \frac{r_2^2}{r_1^2}=\frac{I}{2I}\times \frac{(2r{)}^2}{r^2}=2$
$\therefore v_{d_2}=\frac{v_{d_1}}{2}=\frac{v}{2}$