A plane electromagnetic wave with frequency of $30 {MHz}$ travels in free space. At particular point in space and time, electric field is $6 {V} / {m}$. The magnetic field at this point will be ${x} \times 10^{-8} {T}$. The value of ${x}$ is ….. .

Electromagnetic waves travel in a medium which has relative permeability $1.3$ and relative permittivity $2.14$. Then the speed of the electromagnetic wave in the medium will be

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 :-

Pointing vectors $\vec S$ is defined as a vector whose magnitude is equal to the wave intensity and whose direction is along the direction of wave propagation. Mathematically, it is given by  $\vec S = \frac{1}{{{\mu _0}}}(\vec E \times \vec B)$. Show the nature of $\vec S$  vs $t$ graph.

An electromagnetic wave in vacuum has the electric and magnetic field $\vec E$ and $\vec B$ , which are always perpendicular to each other. The direction of polarization is given by $\vec X$ and that of wave propagation by $\vec k$ . Then