Question

When a current $I$ is set up in a wire of radius $r$, the drift velocity is $v_d$. If the same current is set up through a wire of radius $2r$ of the same material, the drift velocity will be

• A. $4v_d$
• B. $2v_d$
• C. $v_d/2$
• D. $v_d/4$

Answer 1

The correct option is D $v_d/4$

Relation between current and drift velocity is given by

$I=nAe{v}_d$

From expression, we can see that

$v_d\propto \frac{1}{A}\Rightarrow v_d\propto \frac{1}{r^2}$

$\therefore \frac{v_{d_1}}{v_{d_2}}=\frac{r_2^2}{r_1^2}=\frac{(2r{)}^2}{r^2}=4$

$\Rightarrow v_{d_2}=\frac{v_{d_1}}{4}=\frac{v_d}{4}$

Hence, option $\left(d\right)$ is correct.