The drift velocity of electrons in a copper wire of length \( 2 \) m under a potential difference of \( 200 \) V is \( 0.5\,\mathrm{m\,s^{-1}} \). The mobility (in \( \mathrm{m^{2}\,V^{-1}\,s^{-1}} \)) of electrons is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 5\times10^{-3} \)
Mobility is the drift speed per unit electric field, \( \mu = v_d/E \). The field inside a uniform wire is the potential difference divided by the length.
\( \displaystyle E = \frac{V}{l} = \frac{200\,\mathrm{V}}{2\,\mathrm{m}} = 100\,\mathrm{V\,m^{-1}} \)
\( \displaystyle \mu = \frac{v_d}{E} \)
\( \displaystyle \mu = \frac{0.5\,\mathrm{m\,s^{-1}}}{100\,\mathrm{V\,m^{-1}}} \)
\( \displaystyle \mu = 5\times10^{-3}\,\mathrm{m^{2}\,V^{-1}\,s^{-1}} \)
Note: A similar question was also asked in CUET (UG) 2023 on 13-06-2023 (Slot 1).