The electric field of a plane electromagnetic | vedclass

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

Question

(C) For an electromagnetic wave propagating in the $x$-direction,the electric field is in the $y$-direction $(\hat{j})$,so the magnetic field must be

Vedclass · Accepted Answer

$\overrightarrow{B} = E_{0} \sqrt{\mu_{0} \epsilon_{0}} \cos(kx) \hat{k}$

Vedclass · Answer

(C) For an electromagnetic wave propagating in the $x$-direction,the electric field is in the $y$-direction $(\hat{j})$,so the magnetic field must be in the $z$-direction $(\hat{k})$ because the direction of propagation is given by $\overrightarrow{E} 	imes \overrightarrow{B}$.Given $\overrightarrow{E} = E_{0} \cos(\omega t - kx) \hat{j}$.The amplitude of the magnetic field is $B_{0} = \frac{E_{0}}{c}$,where $c = \frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}$.Thus,$B_{0} = E_{0} \sqrt{\mu_{0} \epsilon_{0}}$.The magnetic field wave equation is $\overrightarrow{B} = B_{0} \cos(\omega t - kx) \hat{k}$.At $t = 0$,$\overrightarrow{B} = B_{0} \cos(-kx) \hat{k} = B_{0} \cos(kx) \hat{k}$.Substituting $B_{0}$,we get $\overrightarrow{B} = E_{0} \sqrt{\mu_{0} \epsilon_{0}} \cos(kx) \hat{k}$.

The electric field of a plane electromagnetic wave propagating along the $x$-direction in vacuum is $\overrightarrow{E} = E_{0} \hat{j} \cos(\omega t - kx)$. The magnetic field $\overrightarrow{B}$ at the moment $t = 0$ is:

Similar Questions

$A$ light wave traveling in air along the $x$-direction is given by $E_{y} = 540 \sin \pi \times 10^{4}(x - ct) \text{ Vm}^{-1}$. Then,the peak value of the magnetic field of the wave will be $\dots \times 10^{-7} \text{ T}$ (Given $c = 3 \times 10^{8} \text{ ms}^{-1}$)

The correct statement among the following is:

Which of the following is $NOT$ true for electromagnetic waves?

The electric field of a plane polarized electromagnetic wave in free space at time $t = 0$ is given by the expression $\vec E(x,z) = 10\hat j \cos(6x + 8z)$. The magnetic field $\vec B(x,z,t)$ is given by: ($c$ is the velocity of light)

If the amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is $270 \ nT$,the amplitude of the electric field part of the wave is: (in $NC^{-1}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module