If an optical medium possesses a relative permeability of $\frac{10}{\pi}$ and relative permittivity of $\frac{1}{0.0885}$,then the velocity of light is greater in vacuum than that in this medium by . . . . . . times. $\left(\mu_0=4 \pi \times 10^{-7} \ H/m, \varepsilon_0=8.85 \times 10^{-12} \ F/m, c=3 \times 10^8 \ m/s\right)$

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

In an electromagnetic wave,the amplitude of the electric field is $1 \ V/m$. The frequency of the wave is $5 \times 10^{14} \ Hz$. The wave is propagating along the $z$-axis. The average energy density of the electric field,in $J/m^3$,will be:

In free space,an electromagnetic wave of $3 \; GHz$ frequency strikes an object of size $\frac{\lambda}{100}$,where $\lambda$ is the wavelength of the wave in free space. The phenomenon that occurs is .....

$A$ plane $EM$ wave travelling along $z-$ direction is described by $\vec E = E_0 \sin(kz - \omega t)\hat i$ and $\vec B = B_0 \sin(kz - \omega t)\hat j$. Show that:
$(i)$ The average energy density of the wave is given by $U_{av} = \frac{1}{4} \epsilon_0 E_0^2 + \frac{1}{4} \frac{B_0^2}{\mu_0}$.
$(ii)$ The time-averaged intensity of the wave is given by $I_{av} = \frac{1}{2} c \epsilon_0 E_0^2$.

The frequency of radio waves corresponding to a wavelength of $10 \, m$ is