Electromagnetic Waves - Mind Map based Questions

In an electromagnetic wave in free space the root mean square value of the electric field is $E_{r m s} = 6$ 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. $4.23 \times 10^{- 8}$ $T$

The energy of the EM wave is of the order of $15$ KeV. To which part of the spectrum does it belong?
1. X-rays
2. Infrared rays
3. Ultraviolet rays
4. Y-rays

The condition under which a microwave oven heats up a food item containing water molecules most efficiently in

1. the frequency of the microwave must match the resonant frequency of the water molecules
2. the frequency of the microwave has no relation with the natural frequency of water molecules
3. microwave are heatwaves, so always produce heating
4. infrared waves produce heating in a microwave oven

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

The decreasing order of the wavelength of infrared, microwave, ultraviolet and gamma rays is
(1) gamma rays, ultraviolet, infrared, microwaves
(2) microwaves, gamma rays, infrared, ultraviolet
(3) infrared, microwave, ultraviolet, gamma rays
(4) microwave, infrared, ultraviolet, gamma rays

6. 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)

The electric field part of an electromagnetic wave in a medium is represented by :
$E_{x} = 0;$
$E_{y} = 2.5 \frac{N}{C} \cos [(2 π \times 10^{6} \frac{rad}{s}) t - (π \times 10^{- 2} \frac{rad}{m}) x]$
$E_{z} = 0 .$
$The wave is -$
1. moving along y-direction with frequency $2 π \times 10^{6} Hz$ and wavelength 200 m.
2. moving along +x-direction with frequency $10^{6} Hz$ and wavelength 100 m
3. moving along +x-direction with frequency $10^{6} Hz$ and wavelength 200 m
4. moving along - x-direction with frequency $10^{6} Hz$ and wavelength 200 nm

Which of the following rays are not electromagnetic waves?
1. $γ$ -rays
2. $β$ -rays
3. Heat rays
4. X-rays

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.

10.

The S.I. unit of displacement current is:
1. Henry
2. Coulomb
3. Ampere
4. Farad

11.

An electromagnetic wave going through Vaccum is described by
$E = E_{0} \sin (k x - ω t)$
$B = B_{0} \sin (k x - ω t)$
(1) $E_{0} B_{0} = ω k$
(2) $E_{0} ω = B_{0} k$
(3) $E_{0} k = B_{0} ω$
(4) none of these

12. 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

13.

A plane E M wave of frequency 25 MHz travels in free space in the x-direction. At a particular point in space and time $E = 6.3 \hat{j} V / m$ then B at the point is
(1) $2.1 \times 10^{- 8} - \hat{k}$
(2) $2.1 \times 10^{- 8} \hat{k}$
(3) 2.1 $\hat{k}$
(4) $2.1 \times 10^{- 8} \hat{i}$

14.

In an electromagnetic wave, the amplitude of the electric field is $1~\text{V/m}.$ The frequency of a wave is $5\times 10^{14}~\text{Hz}.$ The wave is propagating along the $z\text-$axis. The average energy density of the electric field in $\text{J/m}^3,$ will be:
1. $2.2\times 10^{-12}$
2. $4.4\times 10^{-12}$
3. $6.6\times 10^{-12}$
4. $8.8\times 10^{-12}$

15.

The infra-red spectrum lies between :
(1) radio wave and microwave region
(2) the micro-wave and visible region
(3) the visible and ultraviolet region
(4) the ultraviolet and the X-ray region

16. 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.	$1.873 \times 10^{10}~\text{V/s}$

17.

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

18.

A parallel plate capacitor consists of two circular plates each of radius 2 cm, separated by a distance of 0.1 mm. If the voltage across the plates is varying at the rate of $5 \times 10^{13}$ V/s, then the value of displacement current is :
(1) 5.50 A
(2) $5.56 \times 10^{2} A$
(3) 5.56 $\times 10^{3}$ A
(4) $2.28 \times 10^{4} A$

19.

In an electromagnetic wave
(1) Power is transmitted along the magnetic field
(2) Power is transmitted along the electric field
(3) Power is equally transferred along with the electric and magnetic fields
(4) power is transmitted in a direction perpendicular to both the fields

20.

For any E.M. wave if E = 100 V/m and the magnetising field is equal to 0.265 A/m. Then the rate of maximum energy flow per unit area is:
(1) $3.33 \times 10^{- 5} J / m^{2}$
(2) 26.5 W/ $m^{2}$
(3) $3 \times 10^{8} J / m^{2}$
(4) None of these

21.

A variable frequency AC source is connected to a capacitor. Then on increasing the frequency:

1.	Both conduction current and displacement current will increase
2.	Both conduction current and displacement current will decrease
3.	Conduction current will increase and displacement current will decrease
4.	Conduction current will decrease and displacement current will increase

22.

Instantaneous displacement current of $2.0~\text A$ is set up in the space between two parallel plates of $1~\mu \text{F}$ capacitor. The rate of change in potential difference across the capacitor is:
1. $3\times 10^{6}~\text{V/s}$
2. $4\times 10^{6}~\text{V/s}$
3. $2\times 10^{6}~\text{V/s}$
4. None of these

23.

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

24.

In a plane electromagnetic wave propagating in space has an electric field of amplitude $9 \times 10^{3}$ V/m, then the amplitude of the magnetic field is
(1) $2.7 \times 10^{12} T$
(2) $9.0 \times 10^{- 3} T$
(3) $3.0 \times 10^{- 4} T$
(4) $3.0 \times 10^{- 5} T$

25.

A radiowave has a maximum magnetic field induction of $10^{- 4}$ T on arrival at a receiving antenna. The maximum electric field intensity of such a wave is
(1) zero
(2) $3 \times 10^{4} V / m$
(3) $5.8 \times 10^{- 9} V / m$
(4) $3.3 \times 10^{13} V / m$

26. 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. $9~\text A$

27.

X-rays and $γ$ -rays are both electromagnetic waves, which one of the following statements is true?
(1) in general, X-rays have a larger wavelength than that of $γ$ -rays
(2) X-rays have a smaller wavelength than that of $γ$ -rays
(3) $γ$ -rays have smaller frequency than that of X-rays
(4) wavelength and frequency of X-rays are both larger than those of $γ$ -rays.

28.

The frequencies of X-rays, $γ$ -rays and ultraviolet rays are respectively a, b and c. Then :
(1) a < b, b < c
(2) a > b, b > c
(3) a > b, b > a
(4) a < b, b > c

29.

A plane electromagnetic wave of frequency 40 MHz travels in free space in the x-direction. At some point and at some instant, the electric field $\vec{E}$ has its maximum value of 750 N/C in y-direction. The wavelength of the wave is
(1) 3.5 m
(2) 5.5 m
(3) 7.5 m
(4) 9.5 m

30.

The waves used in telecommunication are
(1) infrared
(2) visible light
(3) microwaves
(4) ultraviolet rays

31.

The frequency 1057 MHz of radiation arising from two close energy levels in hydrogen belongs to
(1) radio waves
(2) infrared waves
(3) micro waves
(4) $γ$ -rays

32.

The shortest wavelength of X-rays emitted from an X-ray tube depends upon
(1) nature of the gas in the tube
(2) the voltage applied to the tube
(3) current in the tube
(4) nature of the target of the tube

33.

X-rays are not used for radar purposes, because they are not
(1) reflected by target
(2) partly absorbed by the target
(3) electromagnetic waves
(4) completely absorbed by the target

34.

The energy of the X-rays photon is 3.3 $\times 10^{- 16}$ J. Its frequency is :
(1) $2 \times 10^{19} H z$
(2) $5 \times 10^{18} H z$
(3) $5 \times 10^{17} H z$
(4) $5 \times 10^{16} H z$

35.

In X-ray tube, the accelerating potential applied at the anode is V volt. The minimum wavelength of the emitted X-ray will be :
(1) eV/h
(2) h/eV
(3) eV/ch
(4) hc/eV

36.

A plane electromagnetic wave $E_{z} = 100 \cos (6 \times 10^{8} t + 4 x) V / m$ propagates in a medium of dielectric constant
(1) 1.5
(2) 2.0
(3) 2.4
(4) 4.0

37.

The magnetic field between the plates of radius 12 cm separated by a distance of 4 mm of a parallel plate capacitor of capacitance 100 pF along the axis of plates having conduction current of 0.15 A is
(1) zero
(2) 1.5 T
(3) 15 T
(4) 0.15 T

38.

A larger parallel plate capacitor, whose plates have an area of 1 $m^{2}$ are separated from each other by 1 mm, is being charged at a rate of 25.8 V/s. If the plates has dielectric constant 10, then the displacement current at this instant is
(1) 25 $μ A$
(2) 11 $μ A$
(3) 2.2 $μ A$
(4) 1.1 $μ A$

39.

A parallel plate capacitor with plate area A and separation between the plates d, is charged by a constant current i. Consider a plane surface of area A/2 parallel to the plates and drawn symmetrically between the plates. The displacement current through this area is
(1) i
(2) i/2
(3) i/4
(4) i/8

40.

The sun delivers $10^{3} W / m^{2}$ of electromagnetic flux to the earth's surface. The total power that is incident on a roof of dimensions 8 m $\times$ 20 m will be
(1) $2.56 \times 10^{4} W$
(2) $6.4 \times 10^{5} W$
(3) $4.0 \times 10^{5} W$
(4) 1.6 $\times 10^{5} W$

41.

The transmitting antenna of a radio station is mounted vertically. At a point 10 km due north of the transmitter, the peak electric field is $10^{- 3}$ V/m. The amplitude of the radiated magnetic field is
(1) $3.33 \times 10^{- 10} T$
(2) $3.33 \times 10^{- 12} T$
(3) $10^{- 3} T$
(4) $3 \times 10^{5} T$

42.

In a region of free space, the electric field at some instant of time is $\vec{E} = (80 \hat{i} + 32 \hat{j} - 64 \hat{k})$ V/m and the magnetic field is $\vec{B} = (0.2 \vec{i} + 0.08 \hat{j} + 0.29 \hat{k}) μ T$ . The Poynting vector for these fields is-
(1) $- 11.52 \hat{i} + 28.8 \hat{j}$
(2) $- 28.8 \hat{i} + 11.52 \hat{i}$
(3) $28.8 \hat{i} - 11.52 \hat{j}$
(4) $11.52 \hat{i} - 28.8 \hat{j}$

43.

A plane electromagnetic wave propagating in the x-direction has wavelength of 60 mm. The electric field is in the y-direction and its maximum magnitude is 33 V/ $m^{- 1}$ . The equation for the electric field as function of x and t is
(1) 11 sin $π$ (t - x/c)
(2) 33 sin $π \times 10^{10}$ (t - x/c)
(3) 33 sin $π$ (t - x/c)
(4) 11 sin $π \times 10^{11}$ (t - x/c)

44.

In an electromagnetic wave, the electric field oscillates sinusoidally with amplitude 48 V $m^{- 1}$ , the RMS value of the oscillating magnetic field will be :
(1) $1.6 \times 10^{- 8} T$
(2) $1.6 \times 10^{- 9} T$
(3) $144 \times 10^{- 8} T$
(4) $11.3 \times 10^{- 8} T$

45. 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.	$E_y=60 \sin \left(0.5 \times 10^3 x-1.5 \times 10^{11} t\right)~\text{V/m}$

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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

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

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.	\(1.873 \times 10^{10}~\text{V/s}\)

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

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