Find the drift velocity of electrons in a metal conductor having density of conduction electrons \( 9\times10^{28}\,\mathrm{m^{-3}} \) of cross sectional area \( 2\times10^{-7}\,\mathrm{m^{2}} \) carrying 2 A current:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.7 mm/s
The current in a conductor is carried by the drift of free electrons: \( I = nAev_d \), where n is the number of conduction electrons per unit volume, A the area of cross-section and e the electronic charge.
\( \displaystyle v_d = \frac{I}{nAe} \)
\( \displaystyle v_d = \frac{2\,\mathrm{A}}{(9\times10^{28}\,\mathrm{m^{-3}})(2\times10^{-7}\,\mathrm{m^{2}})(1.6\times10^{-19}\,\mathrm{C})} \)
\( \displaystyle v_d = \frac{2}{28.8\times10^{2}}\,\mathrm{m\,s^{-1}} = 6.9\times10^{-4}\,\mathrm{m\,s^{-1}} \approx 0.7\,\mathrm{mm\,s^{-1}} \)
Note: NTA picked this question from an NCERT (2026-27) example and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27):
Drift of Electrons and the Origin of Resistivity – “… Example 3.1 (a) Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 1.0 × 10–7 m2 carrying a current of 1.5 A. Assume that each copper atom contributes roughly one conduction electron. The density of copper is 9.0 × 103 kg/m3, and its atomic mass is 63.5 u.”