The wavelength of an electromagnetic wave radiated by a charge oscillating with a frequency of $1 \, \text{kHz}$ is ..... $km$.

In an apparatus, the electric field was found to oscillate with an amplitude of $18 \text{ V/m}$. The magnitude of the oscillating magnetic field will be:

In the given electromagnetic wave $E_y = 600 \sin (\omega t - kx) \ Vm^{-1}$,the intensity of the associated light beam is (in $W/m^2$); (Given $\epsilon_0 = 9 \times 10^{-12} \ C^2 N^{-1} m^{-2}$ and $c = 3 \times 10^8 \ m/s$)

To radiate $EM$ signal of wavelength $\lambda$ with high efficiency,the antennas should have a minimum size equal to

$X$-rays,gamma rays and microwaves travelling in vacuum have

$A$ 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 $I_{av} = \frac{1}{2} c \epsilon_0 E_0^2$.