$A$ linearly polarized electromagnetic wave in vacuum is given by $E = 3.1 \cos \left[(1.8)z - (5.4 \times 10^6)t\right] \hat{i} \text{ N/C}$. It is incident normally on a perfectly reflecting wall at $z = a$. Choose the correct option.

$A$ 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 $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$.

For a given electromagnetic wave,the magnitude of the electric field is $6.6 \,V \,m^{-1}$ at a point in space. The magnitude of the magnetic field at this point is . . . . . . $T$.

The magnetic field of a plane electromagnetic wave is given by $\vec B = B_0 \hat i \cos(kz - \omega t) + B_1 \hat j \cos(kz - \omega t)$,where $B_0 = 3 \times 10^{-5} \, T$ and $B_1 = 2 \times 10^{-6} \, T$. The rms value of the force experienced by a stationary charge $Q = 10^{-4} \, C$ at $z = 0$ is closest to:

$A$ plane electromagnetic wave of wavelength $3.0 \ m$ travels in vacuum along the positive $X$-axis. The electric field of amplitude $300 \ Vm^{-1}$ oscillates parallel to the $Y$-axis. Then the intensity of the wave is $(\mu_0 = 4\pi \times 10^{-7} \ Hm^{-1}, c = 3 \times 10^8 \ ms^{-1})$ (in $Wm^{-2}$)

The magnetic field in a travelling electromagnetic wave has a peak value of $20 \ nT$. The peak value of electric field strength is ...... $Vm^{-1}$.