$A$ sky wave with a frequency of $55 \text{ MHz}$ is incident on the $D$-region of the ionosphere at an angle of $45^\circ$. What is the angle of refraction? (The electron density in the $D$-region is $400 \text{ electrons/cm}^3$).

An electromagnetic wave travels in free space along the $x$-direction. At a particular point in space and time, $\vec{B} = 2 \times 10^{-7} \hat{j} \text{ T}$ is associated with this wave. The value of corresponding electric field $\vec{E}$ at this point is . . . . . . $V$/m. (in $\hat{k}$)

If $c$ is the speed of electromagnetic waves in vacuum,its speed in a medium of dielectric constant $K$ and relative permeability $\mu_r$ is

$A$ carbon dioxide laser emits a sinusoidal electromagnetic wave that travels in a vacuum in the negative $x-$ direction. The wavelength is $10.6\,\mu m$ and the $\vec E$ field is parallel to the $z-$ axis,with $E_{max} = 1.5 \times 10^6\, V/m$. Then the vector equations for $\vec E$ and $\vec B$ as a function of time and position are:

In a plane electromagnetic wave,the electric field oscillates sinusoidally at a frequency of $2.0 \times 10^{10} \; Hz$ and amplitude $48 \; V m^{-1}$.
$(a)$ What is the wavelength of the wave?
$(b)$ What is the amplitude of the oscillating magnetic field?
$(c)$ Show that the average energy density of the $E$ field equals the average energy density of the $B$ field. $[c = 3 \times 10^{8} \; m s^{-1}]$.

If the rms value of the electric field of electromagnetic waves at a distance of $3 \ m$ from a point source is $3 \ N C^{-1}$,then the power of the source is (in $W$)