Question

The number density of free electrons in a copper conductor estimated is $8.5\times {10}^{28}{m}^{-3}$ . How long does an electron take to drift from one end of a wire 3.0m long to its other end? The area of a cross-section of the wire is $2.0\times {10}^{-6}{m}^2$ and it is carrying a current of 3.0A.

Answer 1

The relation between current through conductor and drift velocity of electorn is :

$i=neA{V}_d$ (n=number density of electorns, e=charge of electrons , A=area of cross sections)

given: $i=3A,n=8.5\times {10}^{28}{m}^{-3},A=2\times {10}^{-6}{m}^2$

$\Rightarrow V_d=\frac{3}{8.5\times {10}^{28}\times 1.6\times {10}^{-19}\times 2.0\times {10}^{-6}}m{s}^{-1}$

$\Rightarrow V_d=1.10\times {10}^{-4}m/s$

Now length of conductor$\left(l\right)=3m$

So time required for electorn to drift to other end is :

$t=\frac{1}{V_d}=\frac{3}{1.10\times {10}^{-4}}sec$

$\Rightarrow t=2.72\times {10}^{4}sec$