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(C) The electromagnetic wave propagates in the $+z$ direction,so the wave equation must be of the form $B = B_0 \sin(kz - \omega t)$.The amplitude of

Vedclass · Accepted Answer

$\vec B = 2 	imes 10^{-7} \sin(0.5 	imes 10^3 z - 1.5 	imes 10^{11} t) \hat i$

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(C) The electromagnetic wave propagates in the $+z$ direction,so the wave equation must be of the form $B = B_0 \sin(kz - \omega t)$.The amplitude of the magnetic field is $B_0 = \frac{E_0}{c} = \frac{60}{3 	imes 10^8} = 2 	imes 10^{-7} \, T$.The angular frequency is $\omega = 2\pi n = 2 	imes 3.14 	imes 23.9 	imes 10^9 \approx 1.5 	imes 10^{11} \, rad/s$.The wave number is $k = \frac{\omega}{c} = \frac{1.5 	imes 10^{11}}{3 	imes 10^8} = 0.5 	imes 10^3 \, m^{-1}$.Since the wave propagates in the $+z$ direction and the electric field is typically in the $x$ or $y$ direction,the magnetic field must be perpendicular to both the direction of propagation $(z)$ and the electric field. Thus,for an electric field in the $y$ direction,the magnetic field is in the $x$ direction. The correct form is $\vec B = 2 	imes 10^{-7} \sin(0.5 	imes 10^3 z - 1.5 	imes 10^{11} t) \hat i$.

$A$ plane electromagnetic wave having a frequency $n = 23.9\, GHz$ propagates along the positive $z-$ direction in free space. The peak value of the electric field is $60\, V/m$. Which among the following is the acceptable magnetic field component in the electromagnetic wave?

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