In an electromagnetic wave,$E = 50 \sin(\omega t - kx)$. If $\mu = 4\mu_0$ and $\varepsilon = \varepsilon_0$,then the average power per unit area is $-$ (in $W/m^2$)

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

The electric field in a plane electromagnetic wave is given by $E = 50 \sin(500x - 10 \times 10^{10}t) \, V/m$. The velocity of the electromagnetic wave in this medium is: (Given $C = \text{speed of light in vacuum}$)

The electric field in a plane electromagnetic wave is given by $\overrightarrow{E} = 200 \cos \left[ (0.5 \times 10^{3} \text{ m}^{-1}) x - (1.5 \times 10^{11} \text{ rad/s}) t \right] \hat{j} \text{ V/m}$. If this wave falls normally on a perfectly reflecting surface having an area of $100 \text{ cm}^{2}$,and the radiation pressure exerted by the electromagnetic wave on the surface is $\frac{x}{10^{9}} \text{ N/m}^{2}$,find the value of $x$.

If $c$ is the speed of electromagnetic waves in vacuum,its speed in a medium of dielectric constant $K$ and relative permeability $\mu_r$ is:

In an electromagnetic wave,the amplitude of the electric field is $1 \ V/m$ and the frequency of the wave is $5 \times 10^{14} \ Hz$. The wave propagates in the positive $Z$-direction. The average energy density of the electric field in this wave is ........ $J \ m^{-3}$.