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Q.

A copper wire of radius 1 mm contains 10²² free electrons per cubic metre. The drift velocity for free electrons when 10 A current flows through the wire will be (Given, charge on electron = $1.6 \times 10^{- 19} C) :$

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a

$\frac{6.25}{π} \times 10^{3} {ms}^{- 1}$

b

$\frac{6.25 \times 10^{4}}{π} {ms}^{- 1}$

c

$\frac{6.25}{π} {ms}^{- 1}$

d

$\frac{6.25 \times 10^{5}}{π} {ms}^{- 1}$

answer is B.

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Detailed Solution

Current (i) in a wire in terms of drift velocity
v_d is given by ____
i = neAv_d
n is no. of electrons per unit volume,
A = πr² = area of cross section
$\begin{array}{l} v_{d} = \frac{i}{n e A} = \frac{10}{10^{22} \times 1.6 \times 10^{- 19} π {(10^{- 3})}^{2}} \\ = \frac{10^{4}}{1.6 π} = \frac{6.25 \times 10^{3}}{π} {ms}^{- 1} \end{array}$

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