If ${\mathrm{\lambda }}_{\mathrm{v}},<mspace\; width="1em"></mspace>{\mathrm{\lambda }}_{\mathrm{x}}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{\lambda }}_{\mathrm{m}}$ represent the wavelength of visible light, X-rays, and microwaves respectively, then

1.  ${\mathrm{\lambda }}_{\mathrm{m}}<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\mathrm{\lambda }}_{\mathrm{x}}<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\mathrm{\lambda }}_{\mathrm{v}}$

2.  ${\mathrm{\lambda }}_{\mathrm{v}}<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\mathrm{\lambda }}_{\mathrm{m}}<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\mathrm{\lambda }}_{\mathrm{x}}$

3.  ${\mathrm{\lambda }}_{\mathrm{v}}<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\mathrm{\lambda }}_{\mathrm{x}}<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\mathrm{\lambda }}_{\mathrm{m}}$

4.  ${\mathrm{\lambda }}_{\mathrm{m}}<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\mathrm{\lambda }}_v<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\mathrm{\lambda }}_{\mathrm{x}}$

The electric and magnetic field of electromagnetic waves are

1.  in the opposite phase and perpendicular to each other.

2.  in the opposite phase and parallel to each other.

3.  in phase and perpendicular to each other.

4.  in phase and parallel to each other.

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

1.  $\sqrt{\frac{{\mu }_0}{{\epsilon }_0}}$

2.  $\sqrt{\frac{{\epsilon }_0}{{\mu }_0}}$

3.  $\sqrt{{\mu }_0{\epsilon }_0}$

4.  $\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$

The electric field part of an electromagnetic wave in a medium is represented by $E_x<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>0;$

$E_y<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>2.5\frac{N}{C}\cos \left[\left(2\pi <mspace\; width="1em"></mspace>\times <mspace\; width="1em"></mspace>{10}^6\frac{rad}{s}\right)t<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>\left(\mathrm{\pi }<mspace\; width="1em"></mspace>\times <mspace\; width="1em"></mspace>{10}^{-2}\frac{\mathrm{rad}}{\mathrm{m}}\right)x\right];<mspace\; width="1em"></mspace>E_z<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>0$

The wave is

1.  moving along x-direction with frequency ${10}^6$ Hz and wavelength 100 m.
2.  moving along x-direction with frequency ${10}^6$ Hz and wavelength 200 m.
3.  moving along —x-direction with frequency ${10}^6$ Hz and wavelength 200 m.
4.  moving along y-direction with frequency 2$\mathrm{\pi }$ x ${10}^6$ Hz and wavelength 200 m.

Which of the following statement is false for the properties of electromagnetic waves?

1.  These waves do not require any material medium for propagation.

2.  Both electric and magnetic field vectors attain the maxima and minima at the same place and same time.

3.  The energy in the electromagnetic waves is divided equally between electric and magnetic vectors.

4.  Both electric and magnetic fields are parallel to each other and perpendicular to the direction of propagation of the wave.

The electric field of an electromagnetic wave in free space is given by:

$\overrightarrow{E}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>10<mspace\; width="1em"></mspace>\cos ({10}^{7}t<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>kx)\hat{j}<mspace\; width="1em"></mspace>V{m}^{-1}$, where, t and x are in seconds and meters respectively. It can be inferred that

a. The wavelength $\lambda$ is 188.4 m.

b. The wavenumber k is 0.33 rad ${\mathrm{m}}^{-1}$.

c. The wave amplitude is 10 V ${\mathrm{m}}^{-1}$.

d. The wave is propagating along + x direction.

Which of the following pairs of statements is correct?

1.  a, and b

2.  b, and c

3.  a, and c

4.  c, and d

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

1.  $\left[\overrightarrow{\mathrm{E}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{E}}_0\hat{\mathrm{j}},<mspace\; width="1em"></mspace>\overrightarrow{\mathrm{B}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{B}}_0\hat{\mathrm{k}}\right]$

2.  $\left[\overrightarrow{\mathrm{E}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{E}}_0\hat{i},<mspace\; width="1em"></mspace>\overrightarrow{\mathrm{B}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{B}}_0\hat{\mathrm{j}}\right]$

3.  $\left[\overrightarrow{\mathrm{E}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{E}}_0\hat{\mathrm{k}},<mspace\; width="1em"></mspace>\overrightarrow{\mathrm{B}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{B}}_0\hat{\mathrm{i}}\right]$

4.  $\left[\overrightarrow{\mathrm{E}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{E}}_0\hat{\mathrm{j}},<mspace\; width="1em"></mspace>\overrightarrow{\mathrm{B}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{B}}_0\hat{\mathrm{i}}\right]$

The decreasing order of wavelength Of infrared. microwave, ultraviolet and gamma rays is

1.  infrared, microwave, ultraviolet, gamma rays.

2.  microwave, infrared, ultraviolet, gamma rays.

3.  gamma rays, ultraviolet, infrared, microwaves.

4.  microwaves, gamma rays, infrared, ultraviolet.

the electric field associated with an E.M. wave in vacuum is given by $\overrightarrow{\mathrm{E}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\hat{i}<mspace\; width="1em"></mspace>40<mspace\; width="1em"></mspace>\cos <mspace\; width="1em"></mspace>(kz<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>6<mspace\; width="1em"></mspace>\times <mspace\; width="1em"></mspace>{10}^{8}t)$, where e, z, and t are in $\mathrm{V}<mspace\; width="1em"></mspace>{\mathrm{m}}^{-1}$, m and s respectively. The value of wave vector k is

1.  2 ${\mathrm{m}}^{-1}$

2.  0.5 ${\mathrm{m}}^{-1}$

3.  6 ${\mathrm{m}}^{-1}$

4.  3 ${\mathrm{m}}^{-1}$

The ratio of the amplitude of the magnetic field to the amplitude of the electric field for an electromagnetic wave propagating in a vacuum is equal to

1.  The ratio of magnetic permeability to the electric susceptibility of vacuum.

2.  Unity.

3.  The speed of light in vacuum.

4.  Reciprocal of the speed of light in vacuum.