Suppose that the intensity of a laser is $\left(\frac{315}{\pi}\right) \ W/m^2$. The $rms$ electric field,in units of $V/m$,associated with this source is close to the nearest integer. Given: $\epsilon_0 = 8.86 \times 10^{-12} \ C^2 N^{-1} m^{-2}$ and $c = 3 \times 10^8 \ m/s$.

The vectors $\vec{E}$ and $\vec{B}$ of an electromagnetic wave in vacuum are

In vacuum,the speed of light depends upon

$A$ 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 electric field $(E)$ and magnetic field $(B)$ of an electromagnetic wave passing through vacuum are given by
$E = E_0 \sin (kx - \omega t)$
$B = B_0 \sin (kx - \omega t)$
Then the correct statement among the following is

An electromagnetic wave travels in a medium with a speed of $2 \times 10^8 \ m/s$. The relative permeability of the medium is $1$. Then the relative permittivity is: