$A$ plane electromagnetic wave of frequency $25 \text{ MHz}$ travels in free space along the $X$-direction. At a particular point in space and time, the electric field is $\vec{E} = 6.3 \hat{j} \text{ V m}^{-1}$. What is the magnetic field $\vec{B}$ at that point?

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 relation between the permittivity of free space $(\epsilon_0)$, the permeability of free space $(\mu_0)$, and the speed of light $(c)$ is:

The velocity of an electromagnetic wave is in the direction of

The electron density of $E, F_1,$ and $F_2$ layers of the ionosphere is $4 \times 10^{11} \, m^{-3}, 9 \times 10^{11} \, m^{-3},$ and $16 \times 10^{11} \, m^{-3}$ respectively. What is the ratio of the critical frequencies for the reflection of radio waves?

An electric bulb is rated as $200 \, W$. What will be the peak magnetic field $(\times 10^{-8} \, T)$ at $4 \, m$ distance produced by the radiations coming from this bulb? Consider this bulb as a point source with $3.5 \%$ efficiency.