For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric $\left( U _{ e }\right)$ and magnetic $\left( U _{ m }\right)$ fields is

An electromagnetic wave is represented by the electric field $\vec E = {E_0}\hat n\,\sin \,\left[ {\omega t + \left( {6y - 8z} \right)} \right]$. Taking unit vectors in $x, y$ and $z$ directions to be $\hat i,\hat j,\hat k$ ,the direction of propogation $\hat s$, is

The electric field of a plane electromagnetic wave is given by

$\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}} \cos (\mathrm{kz}+\omega \mathrm{t})$ At $\mathrm{t}=0,$ a positively charged particle is at the point $(\mathrm{x}, \mathrm{y}, \mathrm{z})=\left(0,0, \frac{\pi}{\mathrm{k}}\right) .$ If its instantaneous velocity at $(t=0)$ is $v_{0} \hat{\mathrm{k}},$ the force acting on it due to the wave is

The magnetic field of a plane electromagnetic wave is given by $\overrightarrow{ B }=3 \times 10^{-8} \cos \left(1.6 \times 10^3 x +48 \times 10^{10} t \right) \hat{ j }$, then the associated electric field will be :

In an electromagnetic wave, the electric and magnetising fields are $100\,V\,{m^{ - 1}}$ and $0.265\,A\,{m^{ - 1}}$. The maximum energy flow is.......$W/{m^2}$

The magnetic field in a plane electromagnetic wave is given by, $B_{y}=2 \times 10^{-7} \sin \left(\pi \times 10^{3} x+3 \pi \times 10^{11} t\right) \;T$ Calculate the wavelength.