Magnetic field in a plane electromagnetic wave is given by 

$\vec B = {B_0}\,\sin \,\left( {kx + \omega t} \right)\hat jT$

 Expression for corresponding electric field will be Where $c$ is speed of light

A mathematical representation of electromagnetic wave is given by the two equations $E = E_{max}\,\, cos (kx -\omega\,t)$ and $B = B_{max} cos\, (kx -\omega\,t),$ where $E_{max}$ is the amplitude of the electric field and $B_{max}$ is the amplitude of the magnetic field. What is the intensity in terms of $E_{max}$ and universal constants $μ_0, \in_0.$

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.\overrightarrow {dl} } $ over the rectangular loop $1234$ shown in figure.

$(ii)$ Evaluate $\int {\vec B} .\overrightarrow {ds} $ over the surface bounded by loop $1234$.

$(iii)$ $\int {\vec E.\overrightarrow {dl}  =  - \frac{{d{\phi _E}}}{{dt}}} $ to prove $\frac{{{E_0}}}{{{B_0}}} = c$

$(iv)$ By using similar process and the equation $\int {\vec B} .\overrightarrow {dl}  = {\mu _0}I + { \in _0}\frac{{d{\phi _E}}}{{dt}}$ , prove that  $c = \frac{1}{{\sqrt {{\mu _0}{ \in _0}} }}$ 

For a transparent medium relative permeablity and permittlivity, $\mu_{\mathrm{r}}$ and $\epsilon_{\mathrm{r}}$ are $1.0$ and $1.44$ respectively. The velocity of light in this medium would be,

A point source of $100\,W$ emits light with $5 \%$ efficiency. At a distance of $5\,m$ from the source, the intensity produced by the electric field component is :

The ratio of the magnitude of the magnetic field and electric field intensity of a plane electromagnetic wave in free space of permeability $\mu_0$ and permittivity $\varepsilon_0$ is (Given that $c$ - velocity of light in free space)