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 $2r,$ the drift velocity will be

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

Answer 1

The correct option is D $\frac{v_d}{4}$

We know that $I=neA{v}_a$, Here $I$ is the same in both cases. $n$ will also be the same in both cases because the material is the same. The value of $n$ depends upon the nature of material only and not on the dimensions.

$I=nAe{v}_d\Rightarrow v_d\propto \frac{1}{\pi r^2}$
$(v_d{)}_2\propto \frac{1}{\pi (2r{)}^2}$
$(v_d{)}_1\propto \frac{1}{\pi r^2}$
Hence , $\frac{(v_d{)}_2}{(v_d{)}_1}=\frac{1}{4}$