The magnetic field in a plane EM wave traveling in the positive x-direction is given by 

$B=\left(100\mu T\right)\sin \left[\right(2\times {10}^{15}{s}^{-1}\left)\right(t-x/c\left)\right]\hat{j}$

The equation for electric field is :

 

(1) E=100sin [(2$\times {10}^{15}{s}^{-1})$(t-x/c)]$\left(-\hat{k}\right)$

(2) E=3$\times {10}^{10}$sin [(2$\times {10}^{15}{s}^{-1})$(t-x/c)]$\left(-\hat{k}\right)$

(3) E=3$\times {10}^{10}$sin [(2$\times {10}^{15}{s}^{-1})$(t-x/c)] $\hat{k}$

(4) E=100sin [(2$\times {10}^{15}{s}^{-1})$(t-x/c)] $\hat{k}$

The electric field part of an electromagnetic wave in a medium is represented by :

${\mathrm{E}}_{\mathrm{x}}=0;$
${\mathrm{E}}_{\mathrm{y}}=2.5\frac{\mathrm{N}}{\mathrm{C}}\cos \left[\left(2\mathrm{\pi }\times {10}^6\frac{\mathrm{rad}}{s}\right)\mathrm{t} -\left(\mathrm{\pi }\times {10}^{-2}\frac{\mathrm{rad}}{m}\right)\mathrm{x}\right]$
${\mathrm{E}}_{\mathrm{z}}=0.$
$\mathrm{The} \mathrm{wave} \mathrm{is}-$

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

2. moving along +x-direction with frequency ${10}^6 \mathrm{Hz}$ and wavelength 100 m

3. moving along +x-direction with frequency ${10}^6 \mathrm{Hz}$ and wavelength 200 m

4. moving along - x-direction with frequency ${10}^6 \mathrm{Hz}$ and wavelength 200 nm

Statement-I: Gamma rays are more energetic than X-rays.

Statement-II: Gamma rays are of nuclear origin but X-rays are produced due to sudden deceleration of high energy electrons while falling on a metal of high atomic number.

(1) If both statement-I and Statement-II are true, and Statement-II is the correct explanation of Statement-I.

(2) If both Statement-I and Statement-II are true but Statement-II is not the correct explanation of Statement-I.

(3) If Statement-I is true but Statement-II is false.

(4) If Statement-I is false but Statement-II is true.

Which of the following have zero average value in a plane electromagnetic wave?

(1) electric field

(2) magnetic field

(3) magnetic & electric field both

(4) none of these

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