If the magnetic field in a plane progressive wave is represented by the equation $B_{y} = 2 \times 10^{-7} \sin(0.5 \times 10^3 x + 1.5 \pi \times 10^{11} t) \ T$,then the frequency of the wave is (In the equation,time $t$ is in seconds).

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by, $E_y = 20 \sin(3 \times 10^6 x - 4.5 \times 10^{14} t) \text{ V/m}$ (where $x, t$ and other values are in $S$.$I$. units). The dielectric constant of the medium is . . . . . . . (Speed of light in free space is $c = 3 \times 10^8 \text{ m/s}$)

For a plane electromagnetic wave,the electric field is given by $\vec{E} = 10 \cos(10^7t + kx) \hat{j} \text{ V/m}$. Where $t$ is in seconds and $x$ is in meters,then: $(i)$ The wavelength of this wave is $188.4 \text{ m}$. $(ii)$ The wave vector of this wave is $0.33 \text{ rad/m}$. $(iii)$ The amplitude of the electric field of this wave is $10 \text{ V/m}$. $(iv)$ This wave is propagating in the positive $X$-direction.

Select the incorrect statement regarding electromagnetic waves.

If $E$ and $B$ denote electric and magnetic fields respectively,which of the following is dimensionless?

$A$ plane polarized monochromatic $EM$ wave is travelling in a vacuum along the $z$-direction such that at $t = t_1$,it is found that the electric field is zero at a spatial point $z_1$. The next zero that occurs in its neighborhood is at $z_2$. The frequency of the electromagnetic wave is: