The energy density of an electromagnetic wave in a vacuum is given by the relation:

For a plane electromagnetic wave, the electric field is given by $\overrightarrow{E} = 90 \sin (0.5 \times 10^{3} x + 1.5 \times 10^{11} t) \hat{k} \text{ V/m}$. The corresponding magnetic field $\vec{B}$ will be

The following travelling electromagnetic wave $E_x=0$,$E_y=E_0 \sin (kx + \omega t)$,$E_z=-2E_0 \sin (kx - \omega t)$ is:

An $EM$ wave from air enters a medium. The electric fields are $\overrightarrow {{E_1}} = {E_{01}}\hat x\cos[2\pi v(\frac{z}{c} - t)]$ in air and $\overrightarrow {{E_2}} = {E_{02}}\hat x\cos[k(2z - ct)]$ in medium,where the wave number $k$ and frequency $v$ refer to their values in air. The medium is nonmagnetic. If $\varepsilon_{r_1}$ and $\varepsilon_{r_2}$ refer to relative permittivities of air and medium respectively,which of the following options is correct?

An electromagnetic wave of frequency $3.0 \ MHz$ passes from vacuum into a non-magnetic medium with permittivity $\epsilon = 16 \epsilon_0$,where $\epsilon_0$ is the free space permittivity. The change in wavelength is

The dielectric constant of a medium is $8$ and its relative permeability is $200$. If an electromagnetic wave of frequency $100 \text{ MHz}$ travels in this medium,then its wavelength is