The equation that represents the magnetic field of a plane electromagnetic wave which is propagating along the $x$-direction with a wavelength of $10 \,mm$ and a maximum electric field of $60 \,Vm^{-1}$ in the $y$-direction is (where,$c$ is the speed of light):

If $\overrightarrow{E}$ and $\overrightarrow{B}$ represent electric and magnetic field vectors of an electromagnetic wave,the direction of propagation of the electromagnetic wave is along . . . . . . .

Identify the correct statements from the following descriptions of various properties of electromagnetic waves.
$A$. In a plane electromagnetic wave,the electric field and magnetic field must be perpendicular to each other,and the direction of propagation of the wave should be along the electric field or magnetic field.
$B$. The energy in an electromagnetic wave is divided equally between the electric and magnetic fields.
$C$. Both the electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of the wave.
$D$. The electric field,magnetic field,and direction of propagation of the wave must be mutually perpendicular to each other.
$E$. The ratio of the amplitude of the magnetic field $(B_0)$ to the amplitude of the electric field $(E_0)$ is equal to the reciprocal of the speed of light $(1/c)$.
Choose the most appropriate answer from the options given below:

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].

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 $2$.

Which of the following is not a property of light?