The velocity of electromagnetic radiation in a medium of permittivity ${\epsilon }_0$ and permeability ${\mu }_0$ is given by:

1. $\sqrt{\frac{{\epsilon }_o}{{\mu }_o}}$

2. $\sqrt{{\mu }_o{\epsilon }_o}$

3. $\frac{1}{\sqrt{{\mu }_o{\epsilon }_o}}$

4. $\sqrt{\frac{{\mu }_o}{{\epsilon }_o}}$

The electric and the magnetic field, associated with an electromagnetic wave, propagating along the +z-axis, can be represented by:

The electric field associated with an electromagnetic wave in vacuum is given by \(\mathrm{E}=40 \cos \left(k z-6 \times 10^8 t\right)\), where E, z, and t are in volt/m, meter, and second respectively. The value of the wave vector k would be:

1. $2$ $m^{-1}$                               
2. $0.5$ $m^{-1}$
3. $6$ $m^{-1}$                               
4. 3 $m^{-1}$             

An EM wave is propagating in a medium with a velocity \(\overrightarrow{{v}}={v} \hat{i}\). The instantaneous oscillating electric field of this EM wave is along the \(+y\) axis. The direction of the oscillating magnetic field of the EM wave will be along:
1. \(-z \text-\)direction
2. \(+z \text-\) direction
3. \(-y \text-\) direction
4.  \(+y \text-\) direction

Out of the following options which one can be used to produce a propagating electromagnetic wave?

The velocity of electromagnetic wave is parallel to:

1. $\overrightarrow{\mathrm{B}}\times \overrightarrow{\mathrm{E}}$

2. $\overrightarrow{E}\times \overrightarrow{B}$

3. $\overrightarrow{\mathrm{E}}$

4. $\overrightarrow{\mathrm{B}}$

An electromagnetic radiation has an energy \(14.4~\text{keV}\). To which region of the electromagnetic spectrum does it belong?

The charge of a parallel plate capacitor is varying as $q=q_0\sin \omega t$. Find the magnitude of displacement current through the capacitor. 
(Plate Area = A, separation of plates = d)

1. $q_0\cos \left(\omega t\right)$

2. $q_0\omega \sin \omega t$

3. $q_0\omega \cos \omega t$

4. $\frac{q_{0}A\omega }{d}\cos \omega t$

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

1. $\frac{1}{2}.\frac{E^2}{{\epsilon }_0}+\frac{B^2}{2{\mu }_0}$ 

2. $\frac{1}{2}{\epsilon }_0{E}^2+\frac{1}{2}{\mu }_0{B}^2$

3. $\frac{E^2+B^2}{C}$

4. $\frac{1}{2}{\epsilon }_0{E}^2+\frac{B^2}{2{\mu }_0}$

The S.I. unit of displacement current is:
1. Henry
2. Coulomb
3. Ampere
4. Farad