Which one of the following is the property of a monochromatic, plane electromagnetic wave in free space?

Which one of the following is the property of a monochromatic, plane electromagnetic wave in free space?
  1. Electric and magnetic fields have a phase difference of $\frac{\pi}{2}$
  2. The energy contributions of both electric and magnetic fields are equal
  3. The direction of propagations is in the direction of $\mathbf{B} \times \mathbf{E}$
  4. The pressure exerted by the wave is the product of its speed and energy density

Solution

The average electric energy density of EM wave in free space, $\mu_E=\frac{1}{2} \varepsilon_0 E^2$
$=\frac{1}{2} \varepsilon_0\left[\frac{E_0}{\sqrt{2}}\right]^2$
$=\frac{1}{4} \varepsilon_0 E_0^2...(i)$
Average magnetic energy density of EM wave in free space,
$\begin{aligned}
\mu_B & =\frac{1}{2 \mu_0} \frac{B^2}{2}=\frac{1}{2}\left(\frac{B_0}{\sqrt{2}}\right)^2 \frac{1}{\mu_0} \\
& =\frac{B_0^2}{4 \mu_0}...(ii))
\end{aligned}$
Using relation, $E_0=c B_0=\frac{B_0}{\sqrt{\mu_0 \varepsilon_0}}...(iii)$
From Eqs. (i), (ii) and (iii), we get
$u_E=u_B$
Hence, energy contributions of both electric and magnetic fields are equal.

Asked in: AP EAMCET 2021 (25 Aug Shift 1)

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