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

Electric field in a plane electromagnetic wave is given by ${E}=50 \sin \left(500 {x}-10 \times 10^{10} {t}\right) \,{V} / {m}$ The velocity of electromagnetic wave in this medium is :

(Given ${C}=$ speed of light in vacuum)

The electric field of a plane electromagnetic wave is given by $\vec E = {E_0}\hat i\,\cos \,\left( {kz} \right)\,\cos \,\left( {\omega t} \right)$ The corresponding magnetic field $\vec B$ is then given by

This question has Statement $-1$ and Statement $-2$ . Of the four choices given after the statements, choose the one that best describes the two statements

Statement $-1$ : Sky wave signals are used for long distance radio communication. These signals are in general, less stable than ground wave signals

Statement $-2$ : The state of ionosphere varies from hour to hour, day to day and season to season

There exists a uniform magnetic and electric field of magnitude $1\, T$ and $1\, V/m$ respectively along positive $y-$ axis. A charged particle of mass $1\,kg$ and of charge $1\, C$ is having velocity $1\, m/sec$ along $x-$ axis and is at origin at $t = 0.$ Then the co-ordinates of particle at time $\pi$ seconds will be :-

The velocity of electromagnetic radiation in a medium of permittivity ${\varepsilon _0}$  and permeability ${\mu _0}$ is given by