A plane electromagnetic wave, has frequency of $2.0 \times 10^{10}\, Hz$ and its energy density is $1.02 \times 10^{-8}\, J / m ^{3}$ in vacuum. The amplitude of the magnetic field of the wave is close to$....nT$

$\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{\circ} \frac{ Nm ^{2}}{ C ^{2}}\right.$ and speed of $1 ight$ $\left.=3 \times 10^{8}\, ms ^{-1}\right)$

A plane $EM$ wave travelling along $z-$ direction is described$\vec E = {E_0}\,\sin \,(kz - \omega t)\hat i$ and $\vec B = {B_0}\,\sin \,(kz - \omega t)\hat j$. Show that

$(i)$ The average energy density of the wave is given by $U_{av} = \frac{1}{4}{ \in _0}E_0^2 + \frac{1}{4}.\frac{{B_0^2}}{{{\mu _0}}}$

$(ii)$ The time averaged intensity of the wave is given by  $ I_{av}= \frac{1}{2}c{ \in _0}E_0^2$ વડે આપવામાં આવે છે.

A charged particle oscillates about its mean equilibrium position with a frequency of $10^9 \;Hz$. What is the frequency of the electromagnetic waves produced by the oscillator?

The electric field in an electromagnetic wave is given by $\overrightarrow{\mathrm{E}}=\hat{\mathrm{i}} 40 \cos \omega\left(\mathrm{t}-\frac{\mathrm{z}}{\mathrm{c}}\right) N \mathrm{NC}^{-1}$. The magnetic field induction of this wave is (in SI unit):

A red $LED$ emits light at $0.1$ watt uniformly around it. The amplitude of the electric field of the light at a distance of $1\ m$ from the diode is....$ Vm^{-1}$

Wavelength of light of frequency $100\;Hz$