The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to

A particle of charge $q$ and mass $m$ is moving along the $x-$ axis with a velocity $v,$ and enters a region of electric field $E$ and magnetic field $B$ as shown in figures below. For which figure the net force on the charge may be zero :-

If a source is transmitting electromagnetic wave of frequency $8.2 \times {10^6}Hz$, then wavelength of the electromagnetic waves transmitted from the source will be.....$m$

An electromagnetic wave with frequency $\omega $ and wavelength $\lambda $ travels in the $+ y$ direction . Its magnetic field is along $+\, x-$ axis. The vector equation for the associated electric field ( of amplitude $E_0$) is

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

Consider an electromagnetic wave propagating in vacuum . Choose the correct statement