Question
Download Solution PDFAn electron beam with cross-section area 1.0 mm2 has 6 × 1016 electrons (q = 1.6 × 10-19 C) passing per second perpendicular to any section. The current density (ampere per metre2) in the beam is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Number of electrons \(n=6\times10^{16}\ electrons\)
Charge of electron beam \(q=1.6\times10^{-19}C\)
Area \(A=1mm^2=10^{-6}m^2\)
Time \(t=1 \ sec\)
Concept:
The total charge crossing a perpendicular cross-section in one second is
- q=ne
- Current \(I=\frac{q}{t}\)
- Current density, \(J=\frac{I}{A}\)
Explanation:
The total charge crossing a perpendicular cross-section in one second is
q=ne\(\implies q=6\times10^{16}\times1.6\times10^{-19}=9.6\times10^{-3}C\)
\(I=\frac{q}{t}\implies I=\frac{9.6\times10^{-3}}{1}=9.6\times10^{-3}A\)
\(J=\frac{I}{A}\)\(\implies J=\frac{9.6\times10^{-3}}{10^{-6}}=9.6\times10^3A/m^2\)
Hence, the correct answer is \(J=9.6\times10^3A/m^2\).
Last updated on May 26, 2025
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