A plane electromagnetic wave is propagating along the direction $\frac{\hat{i}+\hat{j}}{\sqrt{2}},$ with its polarization along the direction $\hat{\mathrm{k}}$. The correct form of the magnetic field of the wave would be (here $\mathrm{B}_{0}$ is an appropriate constant)
A plane electromagnetic wave is propagating along the direction $\frac{\hat{i}+\hat{j}}{\sqrt{2}},$ with its polarization along the direction $\hat{\mathrm{k}}$. The correct form of the magnetic field of the wave would be (here $\mathrm{B}_{0}$ is an appropriate constant)
- [JEE MAIN 2020]
- A
$\mathrm{B}_{0} \frac{\hat{\mathrm{i}}-\hat{\mathrm{j}}}{\sqrt{2}} \cos \left(\omega \mathrm{t}-\mathrm{k} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}\right)$
- B
$\mathrm{B}_{0} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}} \cos \left(\omega \mathrm{t}-\mathrm{k} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}\right)$
- C
$\mathrm{B}_{0} \hat{\mathrm{k}} \cos \left(\omega \mathrm{t}-\mathrm{k} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}\right)$
- D
$\mathrm{B}_{0} \frac{\hat{\mathrm{j}}-\hat{\mathrm{i}}}{\sqrt{2}} \cos \left(\omega \mathrm{t}+\mathrm{k} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}\right)$
Similar Questions
Identify the correct statements from the following descriptions of various properties of electromagnetic waves.
$A$. In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field.
$B.$ The energy in electromagnetic wave is divided equally between electric and magnetic fields.
$C.$ Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave.
$D.$ The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other.
$E.$ The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light.
Choose the most appropriate answer from the options given below:
Identify the correct statements from the following descriptions of various properties of electromagnetic waves.
$A$. In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field.
$B.$ The energy in electromagnetic wave is divided equally between electric and magnetic fields.
$C.$ Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave.
$D.$ The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other.
$E.$ The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light.
Choose the most appropriate answer from the options given below:
- [JEE MAIN 2022]
A plane electromagnetic wave of frequency $25\; \mathrm{GHz}$ is propagating in vacuum along the $z-$direction. At a particular point in space and time, the magnetic field is given by $\overrightarrow{\mathrm{B}}=5 \times 10^{-8} \hat{\mathrm{j}}\; \mathrm{T}$. The corresponding electric field $\overrightarrow{\mathrm{E}}$ is (speed of light $\mathrm{c}=3 \times 10^{8}\; \mathrm{ms}^{-1})$
A plane electromagnetic wave of frequency $25\; \mathrm{GHz}$ is propagating in vacuum along the $z-$direction. At a particular point in space and time, the magnetic field is given by $\overrightarrow{\mathrm{B}}=5 \times 10^{-8} \hat{\mathrm{j}}\; \mathrm{T}$. The corresponding electric field $\overrightarrow{\mathrm{E}}$ is (speed of light $\mathrm{c}=3 \times 10^{8}\; \mathrm{ms}^{-1})$
- [JEE MAIN 2020]
Given below are two statements:
Statement $I$ : Electromagnetic waves are not deflected by electric and magnetic field.
Statement $II$ : The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as $E _0=\sqrt{\frac{\mu_0}{\varepsilon_0}} B_0$
In the light of the above statements, choose the correct answer from the options given below:
Given below are two statements:
Statement $I$ : Electromagnetic waves are not deflected by electric and magnetic field.
Statement $II$ : The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as $E _0=\sqrt{\frac{\mu_0}{\varepsilon_0}} B_0$
In the light of the above statements, choose the correct answer from the options given below:
- [JEE MAIN 2023]
The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by
$E _{ x }= E _0 \sin ( kz -\omega t )$
$B _{ y }= B _0 \sin ( kz -\omega t )$
Then the correct relation between $E_0$ and $B_0$ is given by
The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by
$E _{ x }= E _0 \sin ( kz -\omega t )$
$B _{ y }= B _0 \sin ( kz -\omega t )$
Then the correct relation between $E_0$ and $B_0$ is given by
- [JEE MAIN 2023]
An electromagnetic wave is represented by the electric field $\vec E = {E_0}\hat n\,\sin \,\left[ {\omega t + \left( {6y - 8z} \right)} \right]$. Taking unit vectors in $x, y$ and $z$ directions to be $\hat i,\hat j,\hat k$ ,the direction of propogation $\hat s$, is
An electromagnetic wave is represented by the electric field $\vec E = {E_0}\hat n\,\sin \,\left[ {\omega t + \left( {6y - 8z} \right)} \right]$. Taking unit vectors in $x, y$ and $z$ directions to be $\hat i,\hat j,\hat k$ ,the direction of propogation $\hat s$, is
- [JEE MAIN 2019]