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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
