The electric field associated with an electromagnetic wave in a vacuum is given by;  \(\vec{E}=40\cos\left ( kz-6\times 10^{8}t \right )\hat{i}, \) where \(E,z\) and \(t \) are in volt/m, meter, and second respectively. The value of the wave vector \(k\) is: 
1. \(2~\text{m}^{-1}\)
2. \(0.5~\text{m}^{-1}\)
3. \(6~\text{m}^{-1}\)
4. \(3~\text{m}^{-1}\)

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

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

1.  $\sqrt{\frac{{\mathrm{\epsilon }}_{\mathrm{o}}}{{\mathrm{\mu }}_{\mathrm{o}}}}$

2.  $\sqrt{{\mathrm{\mu }}_{\mathrm{o}}{\mathrm{\epsilon }}_{\mathrm{o}}}$

3.  $\frac{1}{\sqrt{{\mathrm{\mu }}_{\mathrm{o}}{\mathrm{\epsilon }}_{\mathrm{o}}}}$

4.  $\sqrt{\frac{{\mathrm{\mu }}_{\mathrm{o}}}{{\mathrm{\epsilon }}_{\mathrm{o}}}}$

The electric and magnetic fields of an electromagnetic wave are:

For an electromagnetic wave the elctric and magnetic field vectors are along +y and +z directions respectively. Then the propogation of the EM wave should be along:-

1. +y direction

2. -y direction

3. +x direction

4. +z direction

The electric field of an electromagnetic wave
in free space is given by :
$\overrightarrow{\mathrm{E}}=10 \cos \left({10}^7\mathrm{t}+\mathrm{kx}\right)\hat{\mathrm{j}} \mathrm{V}/\mathrm{m}$, where t and x
are in seconds and metres respectively. It can
be inferred that :-
(a) The wavelength $\mathrm{\lambda }$ is 188.4 m
(b) The wave number k is 0.33 rad/m
(c) The wave amplitude is 10 V/m
(d) The wave is propagating along +x direction
Which one of the following pairs of statements
is correct :-

1. (a) and (b) 

2. (b) and (c)

3. (a) and (c) 

4. (c) and (d)

In an electric circuit, there is a capacitor of reactance \(100~\Omega\) connected across the source of \(220~\text{V}\). The rms value of displacement current will be:
1. \(2.2~\text{A}\)
2. \(0.22~\text{A}\)
3. \(4.2~\text{A}\)
4. \(2.4~\text{A}\)

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

What is the magnitude of momentum that is contained in a unit volume for an electromagnetic wave:

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

2.  ${\mathrm{\epsilon }}_0 \left(\overrightarrow{\mathrm{E}}\times \overrightarrow{\mathrm{B}}\right)$

3.  ${\mathrm{\mu }}_0 \left(\overrightarrow{\mathrm{E}}\times \overrightarrow{\mathrm{B}}\right)$

4.  $\sqrt{{\mathrm{\mu }}_0{\mathrm{\epsilon }}_0} \left(\overrightarrow{\mathrm{E}}\times \overrightarrow{\mathrm{B}}\right)$