The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by $\vec{E}=30(2 \hat{x}+\hat{y}) \sin \left[2 \pi\left(5 \times 10^{14} t-\frac{10^7}{3} z\right)\right] \mathrm{V} \mathrm{m}^{-1}$. Which of the following option($s$) is(are) correct?

[Given: The speed of light in vacuum, $c=3 \times 10^8 \mathrm{~ms}^{-1}$ ]

($A$) $B_x=-2 \times 10^{-7} \sin \left[2 \pi\left(5 \times 10^{14} t-\frac{10^7}{3} z\right)\right] \mathrm{Wbm}^{-2}$.

($B$) $B_y=2 \times 10^{-7} \sin \left[2 \pi\left(5 \times 10^{14} t-\frac{10^7}{3} z\right)\right] \mathrm{Wbm}^{-2}$

($C$) The wave is polarized in the $x y$-plane with polarization angle $30^{\circ}$ with respect to the $x$-axis.

($D$) The refractive index of the medium is $2$ .

The ratio of contributions made by the electric field and magnetic filed components to the intensity of an electromagnetic wave is

Show that average value of radiant flux density $'S'$ over a single period $'T'$ is given by $S = \frac{1}{{2c{\mu _0}}}E_0^2$.

A point source of electromagnetic radiation has an average power output of $800\, W.$ The maximum value of electric field at a distance $4.0 \,m$ from the source is....$V/m$

Intensity of sunlight is observed as $0.092\, {Wm}^{-2}$ at a point in free space. What will be the peak value of magnetic field at that point? $\left(\sigma_{0}=8.85 \times 10^{-12}\, {C}^{2} \,{N}^{-1} \,{m}^{-2}\right.$ )

There exists a uniform magnetic and electric field of magnitude $1\, T$ and $1\, V/m$ respectively along positive $y-$ axis. A charged particle of mass $1\,kg$ and of charge $1\, C$ is having velocity $1\, m/sec$ along $x-$ axis and is at origin at $t = 0.$ Then the co-ordinates of particle at time $\pi$ seconds will be :-