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]
- A
$1.66 \times 10^{-16} \hat{\mathrm{i}} \;\mathrm{V} / \mathrm{m}$
- B
$15 \hat{\mathrm{i}}\; \mathrm{V} / \mathrm{m}$
- C
$-1.66 \times 10^{-16} \hat{i} \;\mathrm{V} / \mathrm{m}$
- D
$-15 \hat{\mathrm{i}}\; \mathrm{V} / \mathrm{m}$
Similar Questions
In an apparatus, the electric field was found to oscillate with an amplitude of $18 V/m. $ The magnitude of the oscillating magnetic field will be
In an apparatus, the electric field was found to oscillate with an amplitude of $18 V/m. $ The magnitude of the oscillating magnetic field will be
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]
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.
The speed of electromagnetic wave in a medium (whose dielectric constant is $2.25$ and relative permeability is $4$ ) is equal to .......... $\times 10^8 \,m / s$
The speed of electromagnetic wave in a medium (whose dielectric constant is $2.25$ and relative permeability is $4$ ) is equal to .......... $\times 10^8 \,m / s$
When $EM$ wave propagates through vacuum then
When $EM$ wave propagates through vacuum then