An electron beam has an aperture 2 mm2. A total of 6.0 × 1015 electrons pass through any perpendicular cross-section area per second. The current density of the beam is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4.8 × 102 Am-2
Current density is current per unit cross-sectional area, \( J = I/A \). The current is the charge passing per second: the number of electrons per second times the electronic charge.
\( \displaystyle I = (6.0\times10^{15}\,\mathrm{s^{-1}}) \times (1.6\times10^{-19}\,\mathrm{C}) = 9.6\times10^{-4}\,\mathrm{A} \)
\( \displaystyle A = 2\,\mathrm{mm^{2}} = 2\times10^{-6}\,\mathrm{m^{2}} \)
\( \displaystyle J = \frac{I}{A} = \frac{9.6\times10^{-4}\,\mathrm{A}}{2\times10^{-6}\,\mathrm{m^{2}}} \)
\( \displaystyle J = 4.8\times10^{2}\,\mathrm{A\,m^{-2}} \)