The magnetic field vector of an electromagnetic wave is given by ${B}={B}_{o} \frac{\hat{{i}}+\hat{{j}}}{\sqrt{2}} \cos ({kz}-\omega {t})$; where $\hat{i}, \hat{j}$ represents unit vector along ${x}$ and ${y}$-axis respectively. At $t=0\, {s}$, two electric charges $q_{1}$ of $4\, \pi$ coulomb and ${q}_{2}$ of $2 \,\pi$ coulomb located at $\left(0,0, \frac{\pi}{{k}}\right)$ and $\left(0,0, \frac{3 \pi}{{k}}\right)$, respectively, have the same velocity of $0.5 \,{c} \hat{{i}}$, (where ${c}$ is the velocity of light). The ratio of the force acting on charge ${q}_{1}$ to ${q}_{2}$ is :-

The oscillating electric and magnetic vectors of an electromagnetic wave are oriented along

An electromagnetic wave of frequency $5\, GHz ,$ is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are $2 .$ Its velocity in this medium is $\times 10^{7}\, m / s$

The ratio of contributions made by the electric field and magnetic fleld components to the intensity of an electromagnetic wave is :

$(c=$ speed of electromagnetic waves)

The electric field in an electromagnetic wave is given by $E =56.5 \sin \omega( t - x / c ) \;NC ^{-1}$. Find the intensity of the wave if it is propagating along $x-$axis in the free space. (Given $\left.\varepsilon_{0}=8.85 \times 10^{-12} \;C ^{2} N ^{-1} m ^{-2}\right)$

A plane electromagnetic wave of frequency $100\, MHz$ is travelling in vacuum along the $x -$ direction. At a particular point in space and time, $\overrightarrow{ B }=2.0 \times 10^{-8} \hat{ k } T$. (where, $\hat{ k }$ is unit vector along $z-$direction) What is $\overrightarrow{ E }$ at this point ?