The energy of an electromagnetic wave contained in a small volume oscillates with

What physical quantity is the same for $X-$rays of wavelength $10^{-10} \;m ,$ $red$ light of wavelength $6800\; \mathring A$ and radiowaves of wavelength $500 \;m ?$

There exists a uniform magnetic and electric field of magnitude $1\, T$ and $1\, V/m$ respectively along positive $y-$ axis. A charged particle of mass $1\,kg$ and of charge $1\, C$ is having velocity $1\, m/sec$ along $x-$ axis and is at origin at $t = 0.$ Then the co-ordinates of particle at time $\pi$ seconds will be :-

The electric field of an electromagnetic wave in free space is represented as $\vec{E}=E_0 \cos (\omega t-k z) \hat{i}$.The corresponding magnetic induction vector will be :

The electric field part of an electromagnetic wave in a medium is represented by $E_x = 0\,;$

${E_y} = 2.5\,\frac{N}{C}\,\,\cos \,\left[ {\left( {2\pi \, \times \,{{10}^6}\,\frac{{rad}}{m}} \right)t - \left( {\pi  \times {{10}^{ - 2}}\frac{{rad}}{s}} \right)x} \right];$

$E_z = 0$. The wave is

The optical properties of a medium are governed by the relative permitivity $({ \in _r})$ and relative permeability $(\mu _r)$. The refractive index is defined as $n = \sqrt {{ \in _r}{\mu _r}} $. For ordinary material ${ \in _r} > 0$ and $\mu _r> 0$ and the positive sign is taken for the square root. In $1964$, a Russian scientist V. Veselago postulated the existence of material with $\in _r < 0$ and $u_r < 0$. Since then such 'metamaterials' have been produced in the laboratories and their optical properties studied. For such materials $n =  - \sqrt {{ \in _r}{\mu _r}} $. As light enters a medium of such refractive index the phases travel away from the direction of propagation.

$(i) $ According to the description above show that if rays of light enter such a medium from air (refractive index $=1)$  at an angle $\theta $ in $2^{nd}$ quadrant, then the refracted beam is in the $3^{rd}$ quadrant.

$(ii)$ Prove that Snell's law holds for such a medium.