The electric field component of a monochromat | vedclass

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

Question

Given, Electric field component of monochromatic radiation,

$(\overrightarrow{\mathrm{E}})=2 \mathrm{E}_{0} \hat{\mathrm{i}} \cos \mathrm{kz} \cos

Vedclass · Accepted Answer

$\frac{{2{E_0}}}{c}\hat j\,\sin\, kz\,\sin\, \omega t$

Vedclass · Answer

Given, Electric field component of monochromatic radiation,

$(\overrightarrow{\mathrm{E}})=2 \mathrm{E}_{0} \hat{\mathrm{i}} \cos \mathrm{kz} \cos \omega \mathrm{t}$

We know that, $\frac{d E}{d z}=-\frac{d B}{d t}$

$\frac{\mathrm{dE}}{\mathrm{dz}}=-2 \mathrm{E}_{0} \mathrm{k} \sin \mathrm{kz} \cos \omega \mathrm{t}=-\frac{\mathrm{dB}}{\mathrm{dt}}$

$\mathrm{dB}=+2 \mathrm{E}_{0} \mathrm{k} \,\sin \mathrm{kz} \cos\, \omega \mathrm{td}\, \mathrm{t}$ .... $(i)$

Integrating $eq^n$. $(i)$, we have

$B=+2 E_{0} k \sin k z \int \cos \omega t d t$

Magnetic field is given by,

$=+2 \mathrm{E}_{0} \frac{\mathrm{k}}{\omega} \sin \mathrm{kz} \sin \,\omega \mathrm{t}$

We also know that,

$\frac{E_{0}}{B_{0}}=\frac{\omega}{k}=c$

Magnetic field vector,

$\overrightarrow{\mathrm{B}}=\frac{2 \mathrm{E}_{0}}{\mathrm{c}} \hat{\mathrm{j}} \sin \mathrm{kz} \sin \omega \mathrm{t}$

The electric field component of a monochromatic radiation is given by

$\vec E = 2{E_0}\,\hat i\,\cos\, kz\,\cos\, \omega t$

Its magnetic field $\vec B$ is then given by

Similar Questions

The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to

Ratio of electric field and magnetic field gives which physical quantity ?

A plane electromagnetic wave propagating in the direction of the unit vector $\hat{ n }$ with a speed $c$ is described by electric and magnetic field vectors $E$ and $B$, respectively. Which of the following relations (in $SI$ units) between $E$ and $B$ can be ruled out on dimensional grounds alone?

The oscillating magnetic field in a plane electromagnetic wave is given by $B _{ y }=5 \times 10^{-6} \sin$ $1000\,\pi\left(5 x -4 \times 10^{8} t \right) T$. The amplitude of electric field will be.

Consider an electromagnetic wave propagating in vacuum . Choose the correct statement