JEE MAIN - Physics (2024 - 27th January Morning Shift - No. 16)
A plane electromagnetic wave propagating in $$\mathrm{x}$$-direction is described by
$$E_y=\left(200 \mathrm{Vm}^{-1}\right) \sin \left[1.5 \times 10^7 t-0.05 x\right] \text {; }$$
The intensity of the wave is :
(Use $$\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$$)
$$35.4 \mathrm{~Wm}^{-2}$$
$$53.1 \mathrm{~Wm}^{-2}$$
$$26.6 \mathrm{~Wm}^{-2}$$
$$106.2 \mathrm{~Wm}^{-2}$$
Explanation
$$\begin{aligned}
& \mathrm{I}=\frac{1}{2} \varepsilon_0 \mathrm{E}_0^2 \times \mathrm{c} \\
& \mathrm{I}=\frac{1}{2} \times 8.85 \times 10^{-12} \times 4 \times 10^4 \times 3 \times 10^8 \\
& \mathrm{I}=53.1 \mathrm{~W} / \mathrm{m}^2
\end{aligned}$$
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