A current of 15 A flows in a wire of cross-sectional area \( 5\,\mathrm{mm^2} \) with a drift velocity of \( 3 \times 10^{-3}\,\mathrm{m/s} \). The electron density in the wire will be
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 625 \times 10^{25}\,\mathrm{m^{-3}} \)
The current in a conductor is \( I = n e A v_{d} \), where \( n \) is the electron density, \( e \) the electron charge, \( A \) the area of cross-section and \( v_d \) the drift velocity.
\( \displaystyle n = \frac{I}{e\,A\,v_{d}} \)
\( A = 5\,\mathrm{mm^2} = 5\times10^{-6}\,\mathrm{m^2} \)
\( e = 1.6\times10^{-19}\,\mathrm{C} \)
\( \displaystyle e\,A\,v_{d} = 1.6\times10^{-19} \times 5\times10^{-6} \times 3\times10^{-3} = 2.4\times10^{-27}\,\mathrm{C\,m\,s^{-1}} \)
\( \displaystyle n = \frac{15}{2.4\times10^{-27}} = 6.25\times10^{27}\,\mathrm{m^{-3}} = 625\times10^{25}\,\mathrm{m^{-3}} \)