An electromagnetic wave of frequency $45 \text{ MHz}$ travels in free space along the $X$-axis. At some point and at some instant, the electric field has a maximum value of $750 \text{ NC}^{-1}$ along the $Y$-axis. The magnetic field at this position and time is

The electric and magnetic fields associated with an electromagnetic wave propagating along the $Z$-axis can be represented by:

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 $2$.

If an electromagnetic wave propagating through vacuum is described by $E_y = E_0 \sin(kx - \omega t)$ and $B_z = B_0 \sin(kx - \omega t)$,then:

If an optical medium possesses a relative permeability of $\frac{10}{\pi}$ and relative permittivity of $\frac{1}{0.0885}$,then the velocity of light is greater in vacuum than that in this medium by . . . . . . times. $\left(\mu_0=4 \pi \times 10^{-7} \ H/m, \varepsilon_0=8.85 \times 10^{-12} \ F/m, c=3 \times 10^8 \ m/s\right)$

$X$-rays,gamma rays and microwaves travelling in vacuum have