First slide

Average energy density of electromagnetic wave

Question

In an electromagnetic wave, the amplitude of electric field is 1 V/m and the frequency of wave is $5 \times 10^{14} Hz$ . The wave is propagating along z-axis. The average energy density of electric field, in J/m³, will be

Moderate

A

$1.1 \times 10^{- 11}$
B

$2.2 \times 10^{- 12}$
C

$3.3 \times 10^{- 13}$
D

$4.4 \times 10^{- 44}$

Solution

Average energy density of electric field is given by
$U_{e} = \frac{1}{2} ε_{0} E^{2} = \frac{1}{2} ε_{0} {(\frac{E_{0}}{\sqrt{2}})}^{2} = \frac{1}{4} ε_{0} E_{0}^{2}$
$= \frac{1}{4} \times 8.85 \times 10^{- 12} \times (1)^{2} = 2.2 \times 10^{- 12} J / m^{3}$

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