$A$ 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 $Wm^{-2}$)

Three observers $A, B$ and $C$ measure the speed of light coming from a source. Observer $A$ moves towards the source,observer $C$ moves away from the source with the same speed,and observer $B$ remains stationary. The surrounding space is a vacuum everywhere. Which of the following is true regarding the measured speeds ${v_A}, {v_B}$ and ${v_C}$?

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by, $E_y = 20 \sin(3 \times 10^6 x - 4.5 \times 10^{14} t) \text{ V/m}$ (where $x, t$ and other values are in $S$.$I$. units). The dielectric constant of the medium is . . . . . . . (Speed of light in free space is $c = 3 \times 10^8 \text{ m/s}$)

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

The unit of $\sqrt{\frac{2 I}{\varepsilon_0 c}}$ is
($I$: intensity of an electromagnetic wave,$c$: speed of light)

The electric field and magnetic field associated with an electromagnetic $(e.m.)$ wave,propagating along the $-z$ axis,can be represented by: