A plane electromagnetic wave having a frequen | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

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

Vedclass · Answer

(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?

Similar Questions

Write the standard equation for a plane electromagnetic wave traveling in the $x$-direction.

An electromagnetic wave propagating through a vacuum is described by $E = E_0 \sin(kx - \omega t)$ and $B = B_0 \sin(kx - \omega t)$. Which of the following equations is true?

An electromagnetic wave travelling in the $x-$ direction has a frequency of $2 \times 10^{14} \, Hz$ and an electric field amplitude of $27 \, Vm^{-1}$. From the options given below,which one describes the magnetic field for this wave?

The amplitude of the electric field in a parallel beam of plane electromagnetic waves of intensity $53.1 \ W \ m^{-2}$ is (Permittivity of free space $\epsilon_0 = 8.85 \times 10^{-12} \ C^2 \ N^{-1} \ m^{-2}$) (in $N \ C^{-1}$)

$A$ plane electromagnetic wave is incident on a material surface. If the wave delivers momentum $p$ and energy $E$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module