An electromagnetic wave has its electric and magnetic fields given by $\vec{E}(t) = \vec{E}_m \sin(kx - \omega t)$ and $\vec{B}(t) = \vec{B}_m \sin(kx - \omega t)$. If the directions of $\vec{E}_m$ and $\vec{B}_m$ are in the direction of $\hat{i} + \hat{j}$ and $\hat{i} - \hat{j}$ respectively,the unit vector that gives the direction of propagation of the wave is:

Suppose that the electric field part of an electromagnetic wave in vacuum is $E = \{(3.1 \; N/C) \cos [(1.8 \; rad/m) y + (5.4 \times 10^{6} \; rad/s) t] \} \hat{i}$.
$(a)$ What is the direction of propagation?
$(b)$ What is the wavelength $\lambda$?
$(c)$ What is the frequency $\nu$?
$(d)$ What is the amplitude of the magnetic field part of the wave?
$(e)$ Write an expression for the magnetic field part of the wave.

An electromagnetic wave of intensity $50 \ W m^{-2}$ enters a medium of refractive index $n$ without any loss. The ratio of the magnitudes of electric fields and the ratio of the magnitudes of magnetic fields of the wave before and after entering the medium are respectively given by:

In an electromagnetic wave,the amplitude of the electric field is $1 \ V/m$. The frequency of the wave is $5 \times 10^{14} \ Hz$. The wave is propagating along the $z$-axis. The average energy density of the electric field,in $J/m^3$,will be:

The electric field of a plane electromagnetic wave in a medium is given by $\vec{E}(x, y, z, t) = E_0 \hat{n} e^{i k_0[(x+y+z)-ct]}$, where $c$ is the speed of light in free space. The $\vec{E}$ field is polarized in the $x-z$ plane. If the speed of the wave in the medium is $v$, then:

The velocity of electromagnetic radiation in a medium of permittivity $\varepsilon_0$ and permeability $\mu_0$ is given by: