The ratio of the magnitudes of the electric field and $10^8$ times the magnetic field of a plane electromagnetic wave is

In an $EM$ wave,the amplitude of the magnetic field $H_0$ and the amplitude of the electric field $E_0$ at any place are related as:

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 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:

$A$ laser beam has intensity $2.1 \times 10^{15} \ W/m^2$. The amplitude of the magnetic field in the beam is approximately: (in $T$)

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: