Question

An electric current of $16A$ exists in a metal wire of cross section ${10}^{-6}{m}^2$ and length $1m$. Assuming one free electron per atom. The drift speed of the free electrons in the wire will be:
(Density of metal $=5\times {10}^{}kg/m^3$, atomic weight $=60$)

• A. $5\times {10}^{-3}m/s$
• B. $2\times {10}^{-3}m/s$
• C. $4\times {10}^{-3}m/s$
• D. $7.5\times {10}^{-3}m/s$

Answer 1

The correct option is B $2\times {10}^{-3}m/s$

We know,

$I=neA{v}_d$

where n=electron density,

e=electronic charge

A= cross section area

$v_d$=drift velocity

But, $n=\frac{\rho }{Atm.Wt}\times N_A$

And $v_d=\frac{I}{neA}$

So, $v_d=\frac{16\times 60}{5\times {10}^4\times N_A\times 1.6\times {10}^{-19}\times {10}^{-6}}$

Taking $N_A=6\times {10}^{23}$

$v_d=\frac{120\times {10}^{-2}}{6}=2\times {10}^{-3}$