A plane electromagnetic wave propagating along y-direction can have the following pair of electric field $(\vec{E} )$ and magnetic field $(\overrightarrow{ B })$ components.

The intensity of light from a source is $\left( {\frac{{500}}{\pi }} \right)W/{m^2}$ . Find the amplitude of electric field in this wave

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  $c = \frac{1}{{\sqrt {{\mu _0}{ \in _0}} }}$ 

Show that average value of radiant flux density $'S'$ over a single period $'T'$ is given by $S = \frac{1}{{2c{\mu _0}}}E_0^2$.

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 closet to