First slide

Drift velocity

Question

A current I flows through a uniform wire of diameter d when the mean electron drift velocity is v. The same current will flow through a wire of
diameter d/2 made of the same material if the mean drift velocity of the electron is

Easy

A

v/4
B

v/2
C

2v
D

4v

Solution

$\begin{array}{l} j = \frac{I}{A} {nev}_{d} \\ \frac{4 I}{{πd}^{2}} = nev . ... (i) \\ \frac{16 I}{{πd}^{2}} = nev' . ... (ii) \end{array}$
From equations (i) and (ii)
$\frac{4 I}{16 I} = \frac{v}{v'} \Rightarrow v' = 4 v$

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