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1. The electric and the magnetic field, associated with an electromagnetic wave, propagating along the \(+z\text-\)axis, can be represented by:

1.	\(\left[{E}={E}_0 \hat{k}, {B}={B}_0 \hat{i}\right]\)
2.	\(\left[E={E}_0 \hat{j}, ~{B}={{B}_0} \hat{j}\right]\)
3.	\(\left[{E}={E}_0 \hat{j}, ~{B}={B}_0 \hat{k}\right]\)
4.	\(\left[{E}={E}_0 \hat{i}, ~{B}={{B}_0} \hat{j}\right]\)

2. 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:

1.	The wavelength \(\lambda\) is \(188.4~\text{m}\).
2.	The wave number \(k\) is \(0.33~\text{rad/m}.\)
3.	The wave amplitude is \(10~\text{V/m}\).
4.	The wave is propagating along \(+x\) direction

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)

3.

The charge of a parallel plate capacitor is varying as; \(q = q_{0} \sin\omega t\). The magnitude of displacement current through the capacitor is:
(the 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. \(\frac{q_{0} A \omega}{d} \cos \omega t\)

4.

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. $\frac{1}{2}{\epsilon }_0{E}^2+\frac{B^2}{2{\mu }_0}$

5.

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. \(E_{0} = \frac{P_{0}}{2 \pi\varepsilon_{0} cr^{2}}\)
2. \(E_{0} = \sqrt{\frac{P_{0}}{2 \pi\varepsilon_{0} cr^{2}}}\)
3. \(E_{0} = \sqrt{\frac{P_{0}}{4 \pi\varepsilon_{0} cr^{2}}}\)
4. \(E_{0} = \sqrt{\frac{P_{0}}{8 \pi\varepsilon_{0} cr^{2}}}\)

6.

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 $W/m^2$

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

A.	\(X\text-\)rays in a vacuum travel faster than light waves in a vacuum.
B.	The energy of a \(X\text-\)ray photon is greater than that of a light photon.
C.	Light can be polarised but \(X\text-\)rays cannot.

Choose the correct option from the given ones:

1. \(A\) and \(B\) only
2. B and \(C\) only
3. \(A,B,\) and \(C\) only
4. \(B\) only

8.

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.

9. 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:

1.	\(E_0k = B_0 \omega\)
2.	If the electric field is in the \(z\text-\)direction then the magnetic field should be in the \(-y\text-\)direction
3.	Both 1 and 2 are correct
4.	Only 1 is correct

10. 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:

1.	\(1.873 \times 10^7~\text{V/s} \)
2.	\(1.873 \times 10^8~\text{V/s}\)
3.	\(1.873 \times 10^9~\text{V/s}\)
4.	\(1.873 \times 10^{10}~\text{V/s}\)

11.

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

12.

Which statement is incorrect?

1.	Speed of light in free space \(=\frac{1}{\sqrt{\mu_0 \epsilon_0}}\)
2.	Speed of light in the medium \(=\frac{1}{\sqrt{\mu \epsilon}}\)
3.	\(\frac{E_0}{B_0}=c\)
4.	\(\frac{B_0}{E_0}=c\)

13. A capacitor is having a capacity of \(2~\text{pF}\). The electric potential across the capacitor is changing with a value of \(10^{12}~\text{V/s}\). The displacement current is:
1. \(2~\text A\)
2. \(3~\text A\)
3. \(6~\text A\)
4. \(9~\text A\)

14. The magnetic field in a plane electromagnetic wave is given by 
\(B_{z} = 2 \times10^{- 7}\sin\left(0 . 5 \times10^{3} x - 1 . 5 \times10^{11} t \right)~\text{T} \).
The expression for the electric field will be:

1.	\(E_z=30 \sqrt{2} \sin \left(0.5 \times 10^3 x-1.5 \times 10^{11} t\right)~\text{V/m}\)
2.	\(E_z=60 \sin \left(0.5 \times 10^3 x-1.5 \times 10^{11} t\right)~\text{V/m}\)
3.	\(E_y=30 \sqrt{2} \sin \left(0.5 \times 10^{11} x-1.5 \times 10^3 t\right)~\text{V/m}\)
4.	\(E_y=60 \sin \left(0.5 \times 10^3 x-1.5 \times 10^{11} t\right)~\text{V/m}\)

15.

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