In a plane electromagnetic wave,the magnetic field is given by $\vec{B} = 3 \times 10^{-7} \sin (100 \pi x + 10^{12} t) \ T$. The wavelength of the wave is (where $x$ is in meters and $t$ is in seconds). (in $m$)

$A$ monochromatic beam of light has a frequency $v = \frac{3}{2\pi} \times 10^{12} \, Hz$ and is propagating along the direction $\vec{n} = \frac{\hat{i} + \hat{j}}{\sqrt{2}}$. It is polarized along the $\hat{k}$ direction. The acceptable form for the magnetic field $\vec{B}$ is:

The electric field of an electromagnetic wave in free space is given by $\vec E = 10 \cos (10^7 t + kx) \hat j \, V/m$,where $t$ and $x$ are in seconds and metres respectively. It can be inferred that:
$(1)$ The wavelength $\lambda$ is $188.4 \, m$.
$(2)$ The wave number $k$ is $0.33 \, rad/m$.
$(3)$ The wave amplitude is $10 \, V/m$.
$(4)$ The wave is propagating along $+x$ direction.
Which one of the following pairs of statements is correct?

When an electromagnetic wave enters the ionized layer of the ionosphere,the relative permittivity of the ionized layer is found to be:

$A$ plane electromagnetic wave travels in free space along the $z$-axis. At a particular point in space, the electric field along the $x$-axis is $8.7 \ V \ m^{-1}$. The magnetic field along the $y$-axis is:

An electromagnetic $(EM)$ wave is propagating in a medium with a velocity $\vec{v} = v\hat{i}$. The instantaneous oscillating electric field of this $EM$ wave is along the $+y$ axis. Then the direction of the oscillating magnetic field of the $EM$ wave will be along: