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

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

The energy density of the electromagnetic wave in vacuum is given by the relation:
1. $\frac{1}{2}.\frac{E^2}{{\epsilon }_0}+\frac{B^2}{2{\mu }_0}$ 
2. $\frac{1}{2}{\epsilon }_0{E}^2+\frac{1}{2}{\mu }_0{B}^2$
3. $\frac{E^2+B^2}{C}$
4. $\frac{1}{2}{\epsilon }_0{E}^2+\frac{B^2}{2{\mu }_0}$

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

On an EM wave, the amplitude of electric and magnetic fields are 100 v/m and 0.265 A/m.  The maximum energy flow is
(1) 26.5 $W/m^2$           (2) 46.7 $W/m^2$
(3) 66.5 $W/m^2$            (4) 86.5 $W/m^2$

Which of the following statements about electromagnetic waves is/are correct:

1. A and B 
2. B and C
3. A, B and C
4. B only

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.

If an electromagnetic wave going through a medium is given by; 
\(E=E_{0}sin\left ( kx-\omega t \right )\) and \(B=B_{0}sin\left ( kx-\omega t \right ),\) then:

A parallel plate capacitor consists of two circular plates each of radius 12 cm and separated by 5.0 mm. The capacitor is being charged by an external source. The charging current is constant and is equal to 0.15 A. The rate of change of the potential difference between the plates will be:

A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be:
1. 1.34 V/m
2. 2.68 V/m
3. 4.02 V/m
4. 5.36 V/m

Which statement is incorrect?

A capacitor is having a capacity of 2 pF. The electric potential across the capacitor is changing with a value of \(10^{12}~\mathrm{V/s}\). The displacement current is:

The magnetic field in a plane electromagnetic wave is given by
${\mathrm{B}}_{\mathrm{z}}=2\times {10}^{-7}$ $\sin$ $(0.5\times {10}^3\mathrm{x}-1.5\times {10}^{11}\mathrm{t}) T\mathrm{esla}$
The expression for the electric field will be:

Which of the following is not an electromagnetic wave?
1. Radio wave
2. Micro wave
3. Cosmic rays
4. $\mathrm{\gamma }$-rays