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

1.	\(\left[\mathrm{E}=\mathrm{E}_0 \widehat{\mathrm{k}}, \mathrm{B}=\mathrm{B}_0 \hat{\mathrm{i}}\right]\)
2.	\(\left[\mathrm{E}=\mathrm{E}_0 \widehat{\mathrm{j}}, ~\mathrm{B}={\mathrm{B}_0} \hat{\mathrm{j}}\right]\)
3.	\(\left[\mathrm{E}=\mathrm{E}_0 \widehat{\mathrm{j}}, ~\mathrm{B}={\mathrm{B}_0} \hat{\mathrm{k}}\right]\)
4.	\(\left[\mathrm{E}=\mathrm{E}_0 \widehat{\mathrm{i}}, ~\mathrm{B}={\mathrm{B}_0} \hat{\mathrm{j}}\right]\)

The electric field of an electromagnetic wave in free space is given by \(\overrightarrow E = 10\cos(10^7t+kx)\hat j ~\text{V/m}, \) where \(t\) and \(x\) are in seconds and meters respectively. It can be inferred that:

Which one of the following pairs of statements is correct?
1.  (3) and (4)
2.  (1) and (2)
3.  (2) and (3)
4.  (1) and (3)  

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 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 $m^{-1}$             

The energy of the EM wave is of the order of 15 KeV. To which part of the spectrum does it belong?
1. X-rays
2. Infrared rays
3. Ultraviolet rays
4. $\gamma$-rays

Maxwell's equation describes the fundamental laws of:

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

In an electromagnetic wave in free space, the root mean square value of the electric field is \(E_{\text{rms}} = 6~\text{V/m}\). The peak value of the magnetic field is:
1. \(2.83\times 10^{-8}~\text{T}\)
2. \(0.70\times 10^{-8}~\text{T}\)
3. \(4.23\times 10^{-8}~\text{T}\)
4. \(1.41\times 10^{-8}~\text{T}\)

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

The electric and magnetic fields of an electromagnetic wave are: