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 same material, the drift velocity will be

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

Answer 1

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

We know the relation between current and drift velocity given by,
$I=neA{v}_d$
where $n=$ number of electrons per unit volume.
$e=$ charge on electron
$A=$ Area
$\begin{array}{}\Rightarrow v_d=\frac{I}{neA}& \text{(1)}\end{array}$
For wire with radius $2r$, area $A_f=\pi (2r{)}^2=4\pi r^2=4A$
Hence for wire of radius $2r$ drift velocity, $v_{d_f}\frac{I}{ne{A}_f}=\frac{I}{ne\left(4A\right)}=\frac{v_d}{4}$