In electromagnetic wave the phase difference between electric and magnetic field vectors $\overrightarrow{E} and \overrightarrow{B}$ is :

(1) 0         (2) $\mathrm{\pi }/2$            (3) $\mathrm{\pi }$             (4) $\mathrm{\pi }/4$

Select the correct option based on statements below:

In an electromagnetic wave in free space the root mean square value of the electric field is $E_{rms}=6$ V/m. The peak value of the magnetic field is:

1. 1.41$\times {10}^{-8}T$

2. $2.83\times {10}^{-8}T$

3. $0.70\times {10}^{-8}T$

4. $4.23\times {10}^{-8} T$

If ${\in }_0 and {\mu }_0$ represent the permittivity and permeability of vacuum and $\in and \mu$ represent the permittivity and permeability of the medium, then refractive index of the medium is given by :

(1) $\sqrt{\frac{{\in }_0{\mu }_0}{\in \mu }}$                 (2) $\sqrt{\frac{\in \mu }{{\in }_0{\mu }_0}}$

(3) $\sqrt{\frac{\in }{{\mu }_0{\in }_0}}$                  (4) $\sqrt{\frac{{\mu }_0{\in }_0}{\in }}$

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

1. $2 m^{-1}$                               2. $0.5 m^{-1}$

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

A lamp radiates power $P_0$ uniformly in all directions, the amplitude of electric field strength $E_0$ at a distance r from it is:

(1) $E_0=\frac{P_0}{2{\mathrm{\pi \epsilon }}_0{\mathrm{cr}}^2}$                    (2) $E_0=\sqrt{\left\{\frac{P_0}{2{\mathrm{\pi \epsilon }}_{0}c{r}^2}\right\}}$

(3) $E_0=\sqrt{\left\{\frac{P_0}{4{\mathrm{\pi \epsilon }}_0{\mathrm{cr}}^2}\right\}}$             (4) $E_0=\sqrt{\left\{\frac{P_0}{8{\mathrm{\pi \epsilon }}_0{\mathrm{cr}}^{}}\right\}}$

Which of the following statements is false regarding the properties of electromagnetic waves?

An electromagnetic wave is propagating along Y-axis. Then:

(1) The oscillating electric field is along X-axis and the oscillating magnetic field is along Y-axis.

(2) The oscillating electric field is along Z-axis and the oscillating magnetic field is along X-axis.

(3) Both oscillating electric and magnetic fields are along Y-axis, but the phase difference between them is ${90}^{°}$

(4) Both oscillating electric and magnetic fields are mutually perpendicular in arbitrary directions.

In a plane E.M. wave, the electric field oscillates sinusoidally at a frequency of 2.5 $\times {10}^{10}$ Hz and amplitude 480 V/m.  The amplitude of the oscillating magnetic field will be:

(1) $1.52\times {10}^{-8} Wb/m^2$

(2) $1.52\times {10}^{-7} Wb/m^2$

(3) $1.6\times {10}^{-6} Wb/m^2$

(4) $1.6\times {10}^{-7} Wb/m^2$

The charge of a parallel plate capacitor is varying as $q=q_0 \sin \omega t$.  Then 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) $\frac{q_{0}A\omega }{d}\cos \omega t$