Assignments Class 12 Physics Electromagnetic Waves

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Electromagnetic Waves Assignments Class 12 Physics

Question: The photon energy in units of eV for electromagnetic waves of wavelength 2 cm is
(a) 2.5 × 10^–19
(b) 5.2 × 10¹⁶
(c) 3.2 × 10^–16
(d) 6.2 × 10^–5 

Question: Which of the following electromagnetic wave play an important role in maintaining the earth’s warmth or average temperature through the greenhouse effect?
(a) Visible rays
(b) Infrared waves
(c) Gamma rays
(d) Ultraviolet rays 

Question: Which of the following statement is false for the properties of electromagnetic waves? 
(a) Both electric and magnetic field vectors attain the maxima and minima at the same place and same time.
(b) The energy in electromagnetic wave is divided equally between electric and magnetic field vectors.
(c) Both electric and magnetic field vectors are parallel to each other and perpendicular to the direction of propagation of wave 
(d) These waves do not require any material medium for propagation. 

Question: The amplitude of an electromagnetic wave in vacuum is doubled with no other changes made to the wave. As a result of this doubling of the amplitude, which of the following statement is correct?
(a) The speed of wave propagation changes only
(b) The frequency of the wave changes only
(c) The wavelength of the wave changes only
(d) None of these. 

Question: A microwave and an ultrasonic sound wave have the same wavelength. Their frequencies are in the ratio (approximately)
(a) 10²
(b) 10⁴
(c) 10⁶
(d) 10₈

Question: Frequency of radiations arising from two close energy levels in hydrogen, known as lamb shift is 1057 MHz. This frequency falls in which range of electromagnetic wave?
(a) Infrared rays
(b) X-rays
(c) g-rays
(d) Radio waves   

Question: The electric field part of an electromagnetic wave in vacuum is E =3.1N C^-1 COS[(1.8rad m^-1)Y+(5.4X10⁸ rads^-1)t] ^{^}j The wavelength of this part of electromagnetic wave is
(a) 1.5 m
(b) 2 m
(c) 2.5 m
(d) 3.5 m 

Question: The frequency of electromagnetic wave which is best suitable to observe a particle of radius 3 × 10^–4 cm is of the order of
(a) 10¹⁵ Hz
(b) 10¹¹ Hz
(c) 10¹³ Hz
(d) 10¹² Hz 

Question: The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to 
(a) the speed of light in vacuum
(b) reciprocal of speed of light in vacuum
(c) the ratio of magnetic permeability to the electric susceptibility of vacuum
(d) unity 

Question: X-rays, gamma rays and microwaves travelling in vacuum have
(a) same wavelength but different velocities
(b) same frequency but different velocities
(c) same velocity but different wavelengths
(d) same velocity and same frequency

Question: The electric field part of an electromagnetic wave in a medium is represented by E_x = 0,

(a) moving along x direction with frequency 10⁶ Hz and wavelength 100 m
(b) moving along x direction with frequency 10⁶ Hz and wavelength 200 m
(c) moving along –x direction with frequency 10⁶ Hz and wavelength 200 m
(d) moving along y direction with frequency 2π × 10⁶ Hz and wavelength 200 m   

Question: Which one of the following is the property of a monochromatic, plane electromagnetic wave in free space?
(a) Electric and magnetic fields have a phase difference of π/2.
(b) The energy contribution of both electric and magnetic fields are equal.
(c) The direction of propagation is in the direction of ^→B x ^→E.
(d) The pressure exerted by the wave is the product of its speed and energy density. 

Question: An electromagnetic wave is propagating along x-axis. At x = 1 m and t = 10 s, its electric vector |^→Ε|=6 V/m then the magnitude of its magnetic vector is
(a) 2 × 10^–8 T
(b) 3 × 10^–7 T
(c) 6 × 10^–8 T
(d) 5 × 10^–7 T   

Question:An electromagnetic wave propagating along north has its electric field vector upwards. Its magnetic field vector point towards
(a) north
(b) east
(c) west
(d) downwards   

Question: The magnetic field of a beam emerging from a filter facing a flood light as given by B = 12 × 10^–8 sin (1.20 × 10⁷ z – 3.60 × 10¹⁵ t) T.
The average intensity of the beam is
(a) 1.71 W m^–2
(b) 2.1 W m^–2
(c) 3.2 W m^–2
(d) 2.9 W m^–2 

Question: A plane electromagnetic wave of frequency 25 MHz travels in free Space along the x-direction. At a particular point in space and time,^→E = 6.3 j^{^}V m⁻¹ . At this point ^→B is equal to
(a) 8.33 X 10 -8 ^{^} − k T
(b) 18.9 X 10 -8 ^{^} − k T
(c) 2.1 X10- 8 ^{^}  − k T
(d) 2.1 X10- 8 ^{^}− k T   

Question: Assume a bulb of efficiency 2.5% as a point source. The peak values of electric and magnetic fields produced by the radiation coming from a 100 W bulb at a distance of 3 m is respectively
(a) 2.5 V m^–1, 3.6 × 10^–8 T
(b) 4.2 V m^–1, 2.8 × 10^–8 T
(c) 4.08 V m^–1, 1.36 × 10^–8 T
(d) 3.6 V m^–1, 4.2 × 10^–8 T 

Question: The waves used by artificial satellites for communication is
(a) microwaves
(b) infrared waves
(c) radio waves
(d) X-rays   

Question: The electric field of a plane electromagnetic wave varies with time of amplitude 2 Vm^–1 propagating along z-axis. The average energy density of the magnetic field is (in J m^–3)
(a) 13.29 × 10^–12
(b) 8.85 ×  10^–12
(c) 17.72 ×  10^–12
(d) 4.43 ×  10^–12  

Question: An electromagnetic radiation has an energy of 13.2 keV. Then the radiation belongs to the region of
(a) visible light
(b) ultraviolet
(c) infrared
(d) X-ray 

Question: Radio waves diffract around buildings, although light waves do not. The reason is that radio waves
(a) travel with speed larger than c
(b) have much larger wavelength than light
(c) are not electromagnetic waves
(d) none of these    

Assertion & Reasoning Based MCQs
two statements are given-one labelled Assertion (A) and the other labelled Reason (R).
Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

Question: Assertion (A) : X-rays in vacuum travel faster than light waves in vacuum.
Reason (R) : The energy of X-rays photon is less than that of light photon.

Question: Assertion (A) : The microwaves are better carriers of signals than radio waves.
Reason (R) : The electromagnetic waves do not required any material medium for propagation 

Question: Assertion (A) : Infrared waves sometimes referred as heat waves.
Reason (R) : Infrared waves heat up the earth surface.

Question: Assertion (A) : Electromagnetic waves exert pressure called radiation pressure.
Reason (R) : Electromagnetic waves carries energy. 

Question: Assertion (A) : X-ray astronomy is possible only from satellites orbiting the earth.
Reason (R) : Efficiency of X-rays telescope is large as compared to any other telescope. 

Very Short Answer Type Questions

Question: The small ozone layer on top of the stratosphere is crucial for human survival. Why ?
Answer: The small ozone layer on the top of the atmosphere is crucial for human survival because it absorbs harmful ultraviolet radiations present in sunlight and prevents it from reaching the earth’s surface. These radiations can penetrate our skin and can cause harmful diseases like skin cancer etc.

Question: In which directions do the electric and magnetic field vectors oscillate in an electromagnetic wave propagating along the x-axis ?
Answer: When an electromagnetic wave is propagating along the x-axis then, electric field vector oscillates in y-axis and magnetic field vector oscillates in z-axis.

Question: An e.m. wave exerts pressure on the surface on which it is incident. Justify.
Answer: An e.m. wave carries momentum with itself and given by P= Energy of wave (U ) /Speed of the wave (C )When it is incident upon a surface it exerts pressure on it.

Question: Do electromagnetic waves carry energy and momentum?
Answer: Yes, electromagnetic waves carry energy and momentum.

Question: If the Earth did not have atmosphere, would its average surface temperature be higher or lower than what it is now? Explain.
Answer: If the Earth did not have atmosphere, then there would be absence of green house effect of the atmosphere. Due to this reason, the temperature of the earth would be lower than what it is now.

Question: How is the speed of em-waves in vacuum determined by the electric and magnetic fields?
Answer: The speed of em-waves in vacuum determined by the electric (E0) and magnetic fields (B₀) is, c= E₀/B₀. 

Short Answer Type Questions  

Question: A plane electromagnetic wave travels in vacuum along z-direction. What can you say about the direction of electric and magnetic field vectors?
Answer: The electric and magnetic field vectors  ^→E and ^→B are perpendicular to each other and also perpendicular to the direction of propagation of the electromagnetic wave. If a plane electromagnetic wave is propagating along the z-direction, then the electric field is along x-axis, and magnetic
field is along y-axis.

Question: An e.m. wave is travelling in a medium with a velocity ^→v = v i^{^}. Draw a sketch showing the propagation of the e.m. wave, indicating the direction of the oscillating electric and magnetic fields.
Answer: In figure the velocity of propagation of e.m. wave is along
X-axis ^→v = vi^∧ and electric field E along Y-axis and magnetic field ^→B along Z-axis.

Question: Name the physical quantity which remains same for microwaves of wavelength 1 mm and UV radiations of 1600 Å in vacuum.
Answer: The speed in vacuum (i.e., c = 3 × 10⁸ m s^–1) remains same for both the given wavelengths. It is because both microwaves and UV rays are electromagnetic waves.

Question: Illustrate by giving suitable examples, how you can show that electromagnetic waves carry both energy and momentum.
Answer: Electromagnetic waves like other waves carry energy and momentum as they travel through empty space. If light didn’t carry energy and momentum, it wouldn’t be able to heat stuff up or generate photocurrent in photocells.

Question: The electric field intensity produced by the radiations coming from 100 W bulb at a 3 m distance is E. Find the electric field intensity produced by the radiations coming from 50 W bulb at the same distance.
Answer: Electric field intensity on a surface due to the incident radiation is

Question: One requires 11 eV of energy to dissociate a carbon monoxide molecule into carbon and oxygen atoms. The minimum frequency of the
appropriate electromagnetic radiation to achieve the dissociation lies in which region?
Answer:

Question: The electric field in an electromagnetic wave is given by E = (50 N C–¹)sin w(t – x/c). Find the energy contained in a cylinder of cross-section 10 cm2 and length 50 cm along the x-axis.
Answer:

Question: How are infrared waves produced? Why are these referred as heat waves? Write their one important use?
Answer: Infra red waves are produced by hot bodies and molecules.
They are produced due to the de-excitation of atoms.
Infrared waves incident on a substance increase the internal energy and hence the temperature of the substance. That is why they are called heat waves.
Infra red radiations play an important role in maintaining the earth’s warmth or average temperature through the greenhouse effect.

Question: Explain briefly how electromagnetic waves are produced by an oscillating charge. How is the frequency of the e.m. waves produced related to that of the oscillating charge?
Answer: An oscillating or accelerated charge is supposed to be source of an electromagnetic wave. An oscillating charge produces an oscillating electric field in space which further produces an oscillating magnetic field which in turn is a source of electric field. These oscillating electric and magnetic field hence, keep on regenerating each other and an electromagnetic wave is produced.

Question: Identify the electromagnetic waves whose wavelengths vary as
(a) 10–¹¹ m < λ< 10^–14 m
(b) 10^–4 m < λ < 10^–6 m
Write one use of each.

Answer: (a) Gamma rays lie between 10^–11 m to 10^–14 m.
These rays are used in radiotherapy to treat certain cancers and tumors.
(b) Infrared waves lie between 10^–4 m to 10^–6 m. These waves are used in taking photographs during conditions of fog, smoke etc., as these waves are scattered less than visible rays.

Question: Gamma rays and radio waves travel with the same velocity in free space. Distinguish between them in terms of their origin and the main application.
Answer: Gamma rays : These rays are of nuclear origin and are produced in the disintegration of radioactive atomic nuclei and in the decay of certain subatomic particles. They are used in the treatment of cancer and tumours.
Radio waves : These waves are produced by the accelerated motion of charges in conducting wires or oscillating electric circuits having inductor and capacitor. These are used in satellite, radio and television communication

Long Answer Type Questions 

Question: Answer the following questions:
(a) Show, by giving a simple example, how e.m. waves carry energy and momentum.
(b) How are microwaves produced? Why is it necessary in microwave ovens to select the frequency of microwaves to match the resonant frequency of water molecules?
(c) Write two important uses of infrared waves.
Answer: (a) Consider a plane perpendicular to the direction of propagation of the wave. An electric charge, on the plane will be set in motion by the electric and magnetic fields of e.m. wave, incident on this plane. This illustrates that e.m. waves carry energy and momentum.
(b) Microwaves are produced by special vacuum tube like the klystron, magnetron and Gunn diode.
The frequency of microwaves is selected to match the resonant frequency of water molecules, so that energy is transformed efficiently to the kinetic energy of the molecules.
(c) Uses of infra-red waves :
(i) They are used in night vision devices during warfare.
This is because they can pass through haze, fog and mist.
(ii) Infra-red waves are used in remote switches of household electrical appliances.

Question: A plane EM wave travelling along z-direction is described by
^→E = E₀ sin(z − ωt) ^∧i
and B = B₀ sin(kz − ωt) ^∧j . Show that
(a) The average energy density of the wave is  given by  u_av=1/4εOE₀²+1/4B²0/μ₀.
(b) The time averaged intensity of the wave is given by I_av = 1/2Cε₀E₀²
Answer:

Case Based MCQs
Momentum and Pressure of an Electromagnetic Wave An electromagnetic wave transports linear momentum as it travels through space. If an electromagnetic wave transfers a total energy U to a surface in time t, then total linear momentum delivered to the surface is p = U/c.
When an electromagnetic wave falls on a surface, it exerts pressure on the surface. In 1903, the American scientists Nichols and Hull succeeded in measuring radiation pressures of visible light where other had failed, by making a detailed empirical analysis of the ubiquitous gas heating
and ballistic effects. 

Question: Light with an energy flux of 18 W/cm2 falls on a non-reflecting surface at normal incidence.
The pressure exerted on the surface is
(a) 2 N/m²
(b) 2 × 10^–4 N/m²
(c) 6 N/m²
(d) 6 × 10^–4 N/m²   

Question: A point source of electromagnetic radiation has an average power output of 1500 W. The maximum value of electric field at a distance of 3 m from this source (in V m^–1) is
(a) 500
(b) 100
(c) 500/3 
(d) 250/3 

Question: The pressure exerted by an electromagnetic wave of intensity I(W m^–2) on a non-reflecting surface is (c is the velocity of light)
(a) Ic
(b) Ic²
(c) I/c
(d) I/c² 

Oscillating Charge

A stationary charge produces only an electrostatic field while a charge in uniform motion produces a magnetic field, that does not change with time.
An oscillating charge is an example of accelerating charge. It produces an oscillating magnetic field, which in turn produces an oscillating electric fields and so on. The oscillating electric and magnetic fields regenerate each other as a wave which propagates through space. 

Question: Magnetic field in a plane electromagnetic wave is given by

Question: A plane em wave of frequency 25 MHz travels in a free space along x-direction. At a particular point in space and time, E = (6.3 j^ ) V/m.
What is magnetic field at that time?
(a) 0.095 μT
(b) 0.124 μT
(c) 0.089 μT
(d) 0.021 μT 

Question: The electric field component of a monochromatic radiation is given by