The frequency of an electromagnetic wave is $3 \, MHz$. If the refractive index of the medium is $n = 4$,what happens to the wavelength and frequency when it passes through the medium?

$A$ plane $EM$ wave travelling in vacuum along $z$-direction is given by $\vec E = E_0 \sin(kz - \omega t) \hat i$ and $\vec B = B_0 \sin(kz - \omega t) \hat j$.
$(i)$ Evaluate $\int \vec E \cdot d\vec l$ over the rectangular loop $1234$ shown in the figure.
$(ii)$ Evaluate $\int \vec B \cdot d\vec s$ over the surface bounded by loop $1234$.
$(iii)$ Use $\int \vec E \cdot d\vec l = -\frac{d\phi_E}{dt}$ to prove $\frac{E_0}{B_0} = c$.
$(iv)$ By using a similar process and the equation $\int \vec B \cdot d\vec l = \mu_0 I + \mu_0 \epsilon_0 \frac{d\phi_E}{dt}$,prove that $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$.

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 electric field of a plane electromagnetic wave propagating along the $x$-direction in vacuum is $\overrightarrow{E} = E_{0} \hat{j} \cos(\omega t - kx)$. The magnetic field $\overrightarrow{B}$ at the moment $t = 0$ is:

$A$ cube of unit volume contains $35 \times 10^7$ photons of frequency $10^{15} \text{ Hz}$. If the energy of all the photons is viewed as the average energy being contained in the electromagnetic waves within the same volume,then the amplitude of the magnetic field is $\alpha \times 10^{-9} \text{ T}$. Taking permeability of free space $\mu_0 = 4\pi \times 10^{-7} \text{ Tm/A}$,Planck's constant $h = 6 \times 10^{-34} \text{ Js}$ and $\pi = \frac{22}{7}$,the value of $\alpha$ is $.....$

If $\vec E$ and $\vec B$ represent the electric and magnetic field vectors of an electromagnetic wave,then the direction of propagation of the electromagnetic wave is in the direction of