The magnetic field of an $\text{E.M.}$ wave is given by $\overrightarrow{ B }=\left(\frac{\sqrt{3}}{2} \hat{ i }+\frac{1}{2} \hat{ j }\right) 30 \sin \left[\omega\left( t -\frac{ z }{ c }\right)\right]$ ($\text{S.I.}$ units). The corresponding electric field in $\text{S.I.}$ units is:
- A$\overrightarrow{ E }=\left(\frac{1}{2} \hat{ i }-\frac{\sqrt{3}}{2} \hat{ j }\right) 30 c \sin \left[\omega\left( t -\frac{ z }{ c }\right)\right]$
- B$\overrightarrow{ E }=\left(\frac{3}{4} \hat{ i }+\frac{1}{4} \hat{ j }\right) 30 c \cos \left[\omega\left( t -\frac{ z }{ c }\right)\right]$
- C$\overrightarrow{ E }=\left(\frac{1}{2} \hat{ i }+\frac{\sqrt{3}}{2} \hat{ j }\right) 30 c \sin \left[\omega\left( t +\frac{ z }{ c }\right)\right]$
- D$\overrightarrow{ E }=\left(\frac{\sqrt{3}}{2} \hat{ i }-\frac{1}{2} \hat{ j }\right) 30 c \sin \left[\omega\left( t +\frac{ z }{ c }\right)\right]$
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The radiation energy emitted per second by a point source is $100 \,W$. If the efficiency of the source is $4 \%$, then the rms value of the electric field at a distance of $2 \,m$ is [use $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9$ in $SI$ units].
An electromagnetic wave travels in free space along the $x$-direction. At a particular point in space and time, $\vec{B} = 2 \times 10^{-7} \hat{j} \text{ T}$ is associated with this wave. The value of corresponding electric field $\vec{E}$ at this point is . . . . . . $V$/m. (in $\hat{k}$)
The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by $\vec{E} = 30(2 \hat{x} + \hat{y}) \sin \left[2 \pi \left(5 \times 10^{14} t - \frac{10^7}{3} z\right)\right] \text{V m}^{-1}$. Which of the following option$(s)$ is(are) correct?
[Given: The speed of light in vacuum,$c = 3 \times 10^8 \text{ m s}^{-1}$]
$(A)$ $B_x = -2 \times 10^{-7} \sin \left[2 \pi \left(5 \times 10^{14} t - \frac{10^7}{3} z\right)\right] \text{Wb m}^{-2}$.
$(B)$ $B_y = 2 \times 10^{-7} \sin \left[2 \pi \left(5 \times 10^{14} t - \frac{10^7}{3} z\right)\right] \text{Wb m}^{-2}$.
$(C)$ The wave is polarized in the $xy$-plane with a polarization angle $\theta = \tan^{-1}(0.5)$ with respect to the $x$-axis.
$(D)$ The refractive index of the medium is $2$.
[Given: The speed of light in vacuum,$c = 3 \times 10^8 \text{ m s}^{-1}$]
$(A)$ $B_x = -2 \times 10^{-7} \sin \left[2 \pi \left(5 \times 10^{14} t - \frac{10^7}{3} z\right)\right] \text{Wb m}^{-2}$.
$(B)$ $B_y = 2 \times 10^{-7} \sin \left[2 \pi \left(5 \times 10^{14} t - \frac{10^7}{3} z\right)\right] \text{Wb m}^{-2}$.
$(C)$ The wave is polarized in the $xy$-plane with a polarization angle $\theta = \tan^{-1}(0.5)$ with respect to the $x$-axis.
$(D)$ The refractive index of the medium is $2$.
If the amplitude of the magnetic field in a travelling plane electromagnetic wave is $2.2 \times 10^{-4} \ T$,then the intensity of the wave is nearly
$A$ plane electromagnetic wave travels in vacuum along the $z$-direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is $30 \; MHz$,what is its wavelength in $m$?
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