First slide

Electromagnetic waves and its nature

Question

The energy contained in a small volume through which an electromagnetic wave is passing oscillates with

Moderate

A

double the frequency of the wave
B

Zero frequency
C

The frequency of the wave
D

Half the frequency of the wave

Solution

Energy contained per unit volume through which electromagnetic wave is propagating is sum of energy of electric field and energy of magnetic field.
$U = U_{E} + U_{B} = \frac{1}{2} \in o_{} E^{2} + \frac{1}{2} \frac{B^{2}}{μ_{0}}$
Where E and B are Sinusoidal function
$E = E_{0} \sin ω (t - \frac{X}{C})$
& $B = B_{o} \sin ω (t - \frac{X}{C})$
$\Rightarrow U_{E} = \frac{1}{2} \in_{0} E^{2} = \frac{1}{2} E_{_{0}}^{2} \sin^{2} ω (t - \frac{X}{C})$
$\Rightarrow U_{E} = \frac{1}{2} \times E_{0}^{2} [\frac{1 - \cos 2 ω (t - \frac{X}{C})}{2}]$
Hence the frequency of $U_{E}$ is double than that of electromagnetic wave. Similarly the frequency of $U_{B}$ is double than that of electromagnetic wave.

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