Question

Find the drift velocity in Cu wire if it has 1A current through 2 mm cross-section. Free electron density is $8.5\times {10}^{22}$ cm${}^{-3}$

• A. $0.36$ mms${}^{-1}$
• B. $0.36$ cms${}^{-1}$
• C. $0.036$ mms${}^{-1}$
• D. $0.036$ cms${}^{-1}$

Answer 1

The correct option is C $0.036$ mms${}^{-1}$

Given
$I=1A$
$A=2$ mm${}^2=2\times {10}^{-6}$ m${}^2$
${\mu }_e=8.5\times {10}^{22}$ cm${}^{-3}=8.5\times {10}^{28}$ m${}^{-3}$
The current flowing through the $Cu$ wire is
$I={\mu }_e.e.A.v_d$
where, e is the charge on electron and $v_d$ is the drift velocity of electrons.
$\therefore v_d=\frac{I}{{\mu }_e.e.A}$
$\therefore v_d=\frac{1}{(8.5\times {10}^{28})(1.6\times {10}^{-19})(2\times {10}^{-6})}$
$\therefore v_d=\frac{1}{27.2\times {10}^3}$

$\therefore v_d=0.03676\times {10}^{-3}$ ms${}^{-1}$

$\therefore v_d\approx 0.036$ mms${}^{-1}$