The magnetic field in a plane electromagnetic | vedclass

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Question

(C) The general equation for a plane electromagnetic wave is $B = B_0 \sin(kx + \omega t)$.Comparing this with the given equation $B = 2 	imes 10^{-7

Vedclass · Accepted Answer

Microwave

Vedclass · Answer

(C) The general equation for a plane electromagnetic wave is $B = B_0 \sin(kx + \omega t)$.Comparing this with the given equation $B = 2 	imes 10^{-7} \sin(0.5 	imes 10^3 x + 1.5 	imes 10^{11} t)$,we get:Angular frequency $\omega = 1.5 	imes 10^{11} \, 	ext{rad/s}$ and wave number $k = 0.5 	imes 10^3 \, 	ext{m}^{-1}$.The frequency $f$ is given by $f = \frac{\omega}{2\pi} = \frac{1.5 	imes 10^{11}}{2 	imes 3.14} \approx 2.39 	imes 10^{10} \, 	ext{Hz}$.The wavelength $\lambda$ is given by $\lambda = \frac{2\pi}{k} = \frac{2 	imes 3.14}{0.5 	imes 10^3} \approx 1.25 	imes 10^{-2} \, 	ext{m} = 1.25 \, 	ext{cm}$.Electromagnetic waves with wavelengths in the range of $1 \, 	ext{mm}$ to $1 \, 	ext{m}$ (or frequencies between $300 \, 	ext{MHz}$ and $300 \, 	ext{GHz}$) are classified as microwaves.Therefore,the correct option is $C$.

Part of the electromagnetic spectrum	Applications
$P$. Microwave	$I$. For purifying the water
$Q$. $UV$ rays	$II$. For warming the food
$R$. Gamma rays	$III$. For $AM$ and $FM$ communication systems
$S$. Radio wave	$IV$. For treating the cancer cells

The magnetic field in a plane electromagnetic wave is given by $B = 2 \times 10^{-7} \sin(0.5 \times 10^3 x + 1.5 \times 10^{11} t)$. This electromagnetic wave is .........

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