A total of \( 5.0\times10^{16} \) electrons per second go through a conductor of area of cross-section \( 2\,\mathrm{mm^{2}} \). The current density will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 4\times10^{3}\,\mathrm{A\,m^{-2}} \)
The current is the charge passing per second, and the current density is the current per unit area of cross-section.
\( I = n e = 5.0\times10^{16}\,\mathrm{s^{-1}} \times 1.6\times10^{-19}\,\mathrm{C} = 8.0\times10^{-3}\,\mathrm{A} \)
\( A = 2\,\mathrm{mm^{2}} = 2\times10^{-6}\,\mathrm{m^{2}} \)
\( \displaystyle J = \frac{I}{A} = \frac{8.0\times10^{-3}\,\mathrm{A}}{2\times10^{-6}\,\mathrm{m^{2}}} = 4\times10^{3}\,\mathrm{A\,m^{-2}} \)