Identify the correct statements from the following descriptions of various properties of electromagnetic waves.

$A$. In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field.

$B.$ The energy in electromagnetic wave is divided equally between electric and magnetic fields.

$C.$ Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave.

$D.$ The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other.

$E.$ The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light.

Choose the most appropriate answer from the options given below:

If ${\varepsilon _0}$ and ${\mu _0}$ are respectively, the electric permittivity and the magnetic permeability of free space. $\varepsilon $ and $\mu $ the corresponding quantities in a medium, the refractive index of the medium is

Electromagnetic wave consists of periodically oscillating electric and magnetic vectors

The electric field in an electromagnetic wave is given by ${E}=\left(50\, {NC}^{-1}\right) \sin \omega({t}-{x} / {c})$

The energy contained in a cylinder of volume ${V}$ is $5.5 \times 10^{-12} \, {J}$. The value of ${V}$ is $......{cm}^{3}$ $\left(\right.$ given $\left.\in_{0}=8.8 \times 10^{-12} \,{C}^{2} {N}^{-1} {m}^{-2}\right)$

The magnetic field in a plane electromagnetic wave is given by

${B_y} = \left( {2 \times {{10}^{ - 7}}} \right)\sin \left( {0.5 \times {{10}^3}x + 1.5 \times {{10}^{11}}t} \right)T$

$(a)$ What is the wavelength and frequency of the wave?

$(b)$ Write an expression for the electric field.

An $EM$ wave propagating in $x$-direction has a wavelength of $8\,mm$. The electric field vibrating $y$ direction has maximum magnitude of $60\,Vm ^{-1}$. Choose the correct equations for electric and magnetic fields if the $EM$ wave is propagating in vacuum