Question:

An electromagnetic wave of frequency \(1\times10^{14}\) hertz is propagating along z-axis. The amplitude of electric field is 4 V/m. If \(\varepsilon_0=8.8\times10^{-12}\ \mathrm{C^2/N\text{-}m^2}\), then average energy density of electric field will be:

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Average of \(\sin^2\) is 1/2, so \(u_E=\frac14\varepsilon_0E_0^2\).
Updated On: Nov 11, 2026
  • \(35.2\times10^{-10}\ \mathrm{J/m^3}\)
  • \(35.2\times10^{-11}\ \mathrm{J/m^3}\)
  • \(35.2\times10^{-12}\ \mathrm{J/m^3}\)
  • \(35.2\times10^{-13}\ \mathrm{J/m^3}\)
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The Correct Option is C

Solution and Explanation

Average electric energy density of an EM wave: \(u_E=\frac12\varepsilon_0E_{rms}^2=\frac12\varepsilon_0\frac{E_0^2}{2}=\frac14\varepsilon_0E_0^2\).
\(u_E=\frac14\times8.8\times10^{-12}\times16=35.2\times10^{-12}\ \mathrm{J/m^3}\).
The frequency is not needed.
Answer: (3) \(35.2\times10^{-12}\ \mathrm{J/m^3}\)
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