$A$ plane electromagnetic wave has a 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 $....nT$. (Given: $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \ Nm^2/C^2$ and speed of light $c = 3 \times 10^8 \ m/s$)

$A$ plane electromagnetic wave of frequency $50\, MHz$ travels in free space along the positive $x-$ direction. At a particular point in space and time, $\vec E = 6.3\,\hat j\,V/m$. The corresponding magnetic field $\vec B$ at that point will be:

$A$ plane electromagnetic wave propagating in $x$-direction is described by $E_{y} = (200 \ Vm^{-1}) \sin [1.5 \times 10^7 t - 0.05 \ x]$. The intensity of the wave is: (Use $\epsilon_0 = 8.85 \times 10^{-12} \ C^2 \ N^{-1} \ m^{-2}$) (in $Wm^{-2}$)

$A$ plane $EM$ wave travelling in vacuum along $z$-direction is given by $\vec E = E_0 \sin(kz - \omega t) \hat i$ and $\vec B = B_0 \sin(kz - \omega t) \hat j$.
$(i)$ Evaluate $\int \vec E \cdot d\vec l$ over the rectangular loop $1234$ shown in the figure.
$(ii)$ Evaluate $\int \vec B \cdot d\vec s$ over the surface bounded by loop $1234$.
$(iii)$ Use $\int \vec E \cdot d\vec l = -\frac{d\phi_E}{dt}$ to prove $\frac{E_0}{B_0} = c$.
$(iv)$ By using a similar process and the equation $\int \vec B \cdot d\vec l = \mu_0 I + \mu_0 \epsilon_0 \frac{d\phi_E}{dt}$,prove that $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$.

In a plane $EM$ wave,the electric field oscillates sinusoidally at a frequency of $5 \times 10^{10} \,Hz$ and an amplitude of $50 \,Vm^{-1}$. The total average energy density of the electromagnetic field of the wave is :
[Use $\varepsilon_0 = 8.85 \times 10^{-12} \,C^2 / Nm^2$ ]

$A$ radiation is emitted by a $1000 \, W$ bulb and it generates an electric field and magnetic field at point $P$, placed at a distance of $2 \, m$. The efficiency of the bulb is $1.25 \%$. The value of the peak electric field at $P$ is $x \times 10^{-1} \, V/m$. The value of $x$ is (rounded off to the nearest integer).
[Take $\varepsilon_{0} = 8.85 \times 10^{-12} \, C^2 N^{-1} m^{-2}, c = 3 \times 10^8 \, m/s$]