During the propagation of electromagnetic waves in a medium,

The following travelling electromagnetic wave $E_x=0$,$E_y=E_0 \sin (kx + \omega t)$,$E_z=-2E_0 \sin (kx - \omega t)$ is:

$A$ plane electromagnetic wave of frequency $25 \text{ MHz}$ travels in free space along the $X$-direction. At a particular point in space and time, the electric field is $\vec{E} = 6.3 \hat{j} \text{ V m}^{-1}$. What is the magnetic field $\vec{B}$ at that point?

The velocity of an electromagnetic wave is in the direction of

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 $2$.

The electric field of a plane electromagnetic wave is given by: $E_y = 69 \sin[0.6 \times 10^3 x - 1.8 \times 10^{11} t] \text{ V/m}$. The expression for the magnetic field associated with this electromagnetic wave is . . . . . . $T$.