8.Electromagnetic waves
hard

In a plane $EM$ wave, the electric field oscillates sinusoidally at a frequency of $5 \times 10^{10} \mathrm{~Hz}$ and an amplitude of $50 \mathrm{Vm}^{-1}$. The total average energy density of the electromagnetic field of the wave is :

[Use $\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$ ]

A

$1.106 \times 10^{-8} \mathrm{Jm}^{-3}$

B

$4.425 \times 10^{-8} \mathrm{Jm}^{-3}$

C

$2.212 \times 10^{-8} \mathrm{Jm}^{-3}$

D

$2.212 \times 10^{-10} \mathrm{Jm}^{-3}$

(JEE MAIN-2024)

Solution

$\mathrm{U}_{\mathrm{E}}=\frac{1}{2} \epsilon_0 \mathrm{E}^2$

$\mathrm{U}_{\mathrm{E}}=\frac{1}{2} \times 8.85 \times 10^{-12} \times(50)^2$

$=1.106 \times 10^{-8} \mathrm{~J} / \mathrm{m}^3$

Standard 12
Physics

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