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 $2$ .

Electromagnetic waves travel in a medium which has relative permeability $1.3$ and relative permittivity $2.14$. Then the speed of the electromagnetic wave in the medium will be

A plane electromagnetic wave travelling along the $X$-direction has a wavelength of $3\ mm$ . The variation in the electric field occurs in the $Y$-direction with an amplitude $66\  Vm^{-1}$. The equations for the electric and magnetic fields as a function of $x$ and $t$ are respectively :-

The mean intensity of radiation on the surface of the Sun is about $10^{8}\,W/m^2.$ The $rms$ value of the corresponding magnetic field is closet to

The electric field in a plane electromagnetic wave is given by

$\overrightarrow{{E}}=200 \cos \left[\left(\frac{0.5 \times 10^{3}}{{m}}\right) {x}-\left(1.5 \times 10^{11} \frac{{rad}}{{s}} \times {t}\right)\right] \frac{{V}}{{m}} \hat{{j}}$

If this wave falls normally on a perfectly reflecting surface having an area of $100 \;{cm}^{2}$. If the radiation pressure exerted by the $E.M.$ wave on the surface during a $10\, minute$ exposure is $\frac{{x}}{10^{9}} \frac{{N}}{{m}^{2}}$. Find the value of ${x}$.

Radiations of intensity $0.5\,\,W/{m^2}$ are striking a metal plate. The pressure on the plate is