The electric field in an electromagnetic wave is given by $\overrightarrow{\mathrm{E}}=\hat{\mathrm{i}} 40 \cos \omega\left(\mathrm{t}-\frac{\mathrm{z}}{\mathrm{c}}\right) N \mathrm{NC}^{-1}$. The magnetic field induction of this wave is (in SI unit):
The electric field in an electromagnetic wave is given by $\overrightarrow{\mathrm{E}}=\hat{\mathrm{i}} 40 \cos \omega\left(\mathrm{t}-\frac{\mathrm{z}}{\mathrm{c}}\right) N \mathrm{NC}^{-1}$. The magnetic field induction of this wave is (in SI unit):
- [JEE MAIN 2024]
- A
$\overrightarrow{\mathrm{B}}=\hat{\mathrm{i}} \frac{40}{\mathrm{c}} \cos \omega\left(\mathrm{t}-\frac{\mathrm{z}}{\mathrm{c}}\right)$
- B
$\vec{B}=\hat{j} 40 \cos \omega\left(t-\frac{z}{c}\right)$
- C
$\overrightarrow{\mathrm{B}}=\hat{\mathrm{k}} \frac{40}{\mathrm{c}} \cos \omega\left(\mathrm{t}-\frac{\mathrm{z}}{\mathrm{c}}\right)$
- D
$\vec{B}=\hat{j} \frac{40}{c} \cos \omega\left(t-\frac{z}{c}\right)$
Similar Questions
Given below are two statements:
Statement $I$ : A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates $EM$ waves.
Statement $II$ : In a material medium. The $EM$ wave travels with speed $v =\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$.
In the light of the above statements, choose the correct answer from the options given below
Given below are two statements:
Statement $I$ : A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates $EM$ waves.
Statement $II$ : In a material medium. The $EM$ wave travels with speed $v =\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$.
In the light of the above statements, choose the correct answer from the options given below
- [JEE MAIN 2022]
The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to
The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to
A plane $EM$ wave travelling along $z-$ direction is described$\vec E = {E_0}\,\sin \,(kz - \omega t)\hat i$ and $\vec B = {B_0}\,\sin \,(kz - \omega t)\hat j$. Show that
$(i)$ The average energy density of the wave is given by $U_{av} = \frac{1}{4}{ \in _0}E_0^2 + \frac{1}{4}.\frac{{B_0^2}}{{{\mu _0}}}$
$(ii)$ The time averaged intensity of the wave is given by $ I_{av}= \frac{1}{2}c{ \in _0}E_0^2$ વડે આપવામાં આવે છે.
A plane $EM$ wave travelling along $z-$ direction is described$\vec E = {E_0}\,\sin \,(kz - \omega t)\hat i$ and $\vec B = {B_0}\,\sin \,(kz - \omega t)\hat j$. Show that
$(i)$ The average energy density of the wave is given by $U_{av} = \frac{1}{4}{ \in _0}E_0^2 + \frac{1}{4}.\frac{{B_0^2}}{{{\mu _0}}}$
$(ii)$ The time averaged intensity of the wave is given by $ I_{av}= \frac{1}{2}c{ \in _0}E_0^2$ વડે આપવામાં આવે છે.
During the propagation of electromagnetic waves in a medium
During the propagation of electromagnetic waves in a medium
- [JEE MAIN 2014]
The intensity of the light from a bulb incident on a surface is $0.22 \,W / m ^{2}$. The amplitude of the magnetic field in this light-wave is_______ $\times 10^{-9} \,T$. (Given : Permittivity of vacuum $\epsilon_{0}=8.85 \times 10^{-12} \,C ^{2} N ^{-1} m ^{-2}$, speed of light in vacuum $c =3 \times 10^{8} \,ms ^{-1}$ )
The intensity of the light from a bulb incident on a surface is $0.22 \,W / m ^{2}$. The amplitude of the magnetic field in this light-wave is_______ $\times 10^{-9} \,T$. (Given : Permittivity of vacuum $\epsilon_{0}=8.85 \times 10^{-12} \,C ^{2} N ^{-1} m ^{-2}$, speed of light in vacuum $c =3 \times 10^{8} \,ms ^{-1}$ )
- [JEE MAIN 2022]