Question

A potential difference of 5 V is applied across a conductor of length 10 cm. If drift velocity of electrons is $2.5\times {10}^{-4}m/s,$ then electron mobility will be

• A. $5\times {10}^{-4}{m}^2{V}^{-1}{s}^{-1}$
• B. $5\times {10}^{-6}{m}^2{V}^{-1}{s}^{-1}$
• C. $5\times {10}^{-2}{m}^2{V}^{-1}{s}^{-1}$
• D. Zero

Answer 1

The correct option is B $5\times {10}^{-6}{m}^2{V}^{-1}{s}^{-1}$

We know,

$E=\frac{V}{d}$

Given,

$V=5v$

$d=10cm=0.1m$

$\begin{array}{c}{V}_d=2.5\times {10}^{-2}cm{s}^{-1}=2.5\times {10}^{-4}m{s}^{-1}\\ \therefore E=\frac{5}{0.1}=50V{m}^{-1}\end{array}$

Mobility of an electron is it's drift velocity per unit electric field.

$\begin{array}{c}\therefore \mu =\frac{V_d}{E}\\ \mu =\frac{2.5\times {10}^{-4}}{50}\\ =5\times {10}^{-6}{m}^2{V}^{-1}{s}^{-1}\end{array}$

$\therefore$ Option $B$ is correct.