A plane electromagnetic wave propagating in x-direction is descri… - Vidyadip

MCQ

A plane electromagnetic wave propagating in $\mathrm{x}$-direction is described by

$\mathrm{E}_{\mathrm{y}}=\left(200\ \mathrm{Vm}^{-1}\right) \sin \left[1.5 \times 10^7 \mathrm{t}-0.05\ \mathrm{x}\right] \text {; }$

The intensity of the wave is :(Use $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

A
$35.4 \ \mathrm{Wm}^{-2}$
✓
$53.1 \ \mathrm{Wm}^{-2}$
C
$26.6 \ \mathrm{Wm}^{-2}$
D
$106.2 \ \mathrm{Wm}^{-2}$

✓

Answer

Correct option: B.

$53.1 \ \mathrm{Wm}^{-2}$

b
$ \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$

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