For an electromagnetic wave travelling in free space,the relation between average energy densities due to electric $(U_{e})$ and magnetic $(U_{m})$ fields is

What is the dimension of $\frac{1}{\mu_0 \varepsilon_0}$? ($\mu_0 =$ magnetic permeability and $\varepsilon_0 =$ permittivity of free space)

In vacuum,the speed of light depends upon

$A$ mathematical representation of an electromagnetic wave is given by the two equations $E = E_{max} \cos(kx - \omega t)$ and $B = B_{max} \cos(kx - \omega t)$,where $E_{max}$ is the amplitude of the electric field and $B_{max}$ is the amplitude of the magnetic field. What is the intensity $I$ in terms of $E_{max}$ and universal constants $\mu_0, \epsilon_0$?

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.

The speed of an electromagnetic wave in a medium (whose dielectric constant is $2.25$ and relative permeability is $4$) is equal to .......... $\times 10^8 \, m/s$.