The electric field in a plane electromagnetic wave is given by $E = 50 \sin(500x - 10 \times 10^{10}t) \, V/m$. The velocity of the electromagnetic wave in this medium is: (Given $C = \text{speed of light in vacuum}$)

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.

Dimension of $\frac{1}{\mu_0 \varepsilon_0}$ should be equal to

The oscillating electric and magnetic vectors of an electromagnetic wave are oriented along

$A$ plane electromagnetic wave of wavelength $\lambda$ has an intensity $I$. It is propagating along the positive $Y$-direction. The allowed expressions for the electric and magnetic fields are given by:

The ratio of the magnitude of the magnetic field $(B_0)$ and electric field intensity $(E_0)$ of a plane electromagnetic wave in free space with permeability $\mu_0$ and permittivity $\varepsilon_0$ is (Given that $c$ is the velocity of light in free space):