Question

A potential difference of $5V$ is applied across a conductor of length $10cm$. 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 $5\times {10}^{-6}{m}^2{V}^{-1}{s}^1$

A potential difference $=5V$

length $=10cm$

drift velocity of electrons $=2.5\times {10}^{-4}m/s$

The electron mobility $E=\frac{V}{d}$

Given, $V=5d$, $d=10cm=0.1m$

$V_d=2.5\times {10}^{-2}{cms}^{-1}$

$=2.5\times {10}^{-4}m/s$

$E=\frac{5}{0.1}=50V/m$

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

$\therefore$ $\mu =\frac{V_d}{E}$

$=\frac{2.5\times {10}^{-4}}{50}$

$=5\times {10}^{-6}{m}^2{V}^{-1}{S}^{-1}$