Electromagnetic Waves

Class 12 Physics Chapter 8 Important Extra Questions Electromagnetic Waves

Very Short Answer

Question 1.
Name the part of the electromagnetic spectrum which has the longest wavelength and write its one use. (CBSE 2019C)
Answer:

• In the electromagnetic spectrum, long radio waves have the longest wavelength.
• Radio waves are used in communication systems.

Question 2.
The small ozone layer on the top of the stratosphere is crucial for human survival. Why?
Answer:
The ozone layer absorbs the ultraviolet rays, emitted by the sun, which are harmful to the living tissues of human beings.

Question 3.
Name the part of the electromagnetic spectrum which is used in the “greenhouse” to keep plants warm.
Answer:
Infrared rays.

Question 4.
How are radio waves produced? (CBSE AI 2011)
Answer:
They are produced by rapid acceleration and decelerations of electrons in aerials.

Question 5.
How are X-rays produced? (CBSE Al 2011)
Answer:
By the transition of inner-shell electrons.

Question 6.
How are microwaves produced? (CBSE AI 2011)
Answer:
By using a magnetron.

Question 7.
A plane electromagnetic wave travels in a vacuum along the z-direction. What can you say about the direction of electric and magnetic field vectors? (CBSE Delhi 2011)
Answer:
The electric and magnetic field vectors will be along the x and y directions.

Question 8.
What is the frequency of electromagnetic waves produced by the oscillating charge of frequency v? (CBSE Delhi 2011C)
Answer:
The frequency of electromagnetic waves produced by the oscillating charge of frequency v is also v.

Question 9.
What are the directions of electric and magnetic field vectors relative to each other and relative to the direction of propagation of electromagnetic waves? (CBSE AI 2012)
Answer:
The three are mutually perpendicular to one other.

Question 10.
Welders wear special goggles or face masks with glass windows to protect their eyes from electromagnetic radiation. Name the radiations and write the range of their frequency. (CBSE Al 2013)
Answer:
UV radiations, 10¹⁵ to 10¹⁷ Hz

Question 11.
To which part of the electromagnetic spectrum does a wave of frequency 5 × 10¹⁹ Hz belong? (CBSEAI 2014)
Answer:
X – rays

Question 12.
Name the part of the electromagnetic spectrum of wavelength 10^-2 m and mention its one application. (Delhi 2008)
Answer:
Name of the part: Microwave
Applications :

1. It is used in radar communication.
2. It is used in microwave ovens.
3. It is also used in analysis of fine details of molecular and atomic structure.

Question 13.
Write the following radiations in ascending order in respect of their frequencies ;
X-rays, Microwaves, UV rays and radiowaves. (Delhi 2009)
Answer:
Radiowaves, microwaves, UV-rays and X-rays.

Question 14.
Name the electromagnetic radiation to which waves of wavelength in the range of 10^-2 m belong. Give one use of this part of EM spectrum. (Delhi 2009)
Answer:
Name : Microwave, Range 0.1 to 1 mm
Uses : Microwaves are used in aircraft navigation.

Question 15.
Name the part of electromagnetic spectrum which is suitable for

1. radar systems used in aircraft navigation
2. treatment of cancer tumours. (Delhi 2009)

Answer:

1. Micro-waves
2. Gamma-rays.

Question 16.
Name the EM waves used for studying crystal structure of solids. What is its frequency range? (All India 2009)
Answer:
X-rays frequency range : 10¹⁷ Hz to 10²⁰ Hz

Question 17.
Which part of electromagnetic spectrum has largest penetrating power? (Delhi 2010)
Answer:
γ-rays are the electromagnetic waves of frequency range 3 × 10¹⁸ Hz to 5 × 10²² Hz and have the highest penetrating power.

Question 18.
Which part of electromagnetic spectrum is absorbed from sunlight by ozone layer? (Delhi 2010)
Answer:
Ultraviolet rays are absorbed from sunlight by ozone layers.

Question 19.
Which part of electromagnetic spectrum is used in radar systems? (Delhi 2010)
Answer:
Microwave region of electromagnetic spectrum is used in radar systems.

Question 20.
Name the part of electromagnetic spectrum whose wavelength lies in the range of 10^-10 m. Give its one use. (All India 2010)
Answer:
Name : X-rays
Use : In medical diagnosis to look for broken bones; treatment study of crystal structure.

Question 22.
Which of the following has the shortest wavelength :
Microwaves, Ultraviolet rays, X-rays. (All India 2010)
Answer:
X-rays have the shortest wavelength.

Question 23.
Arrange the following in descending order of wavelength :
X-rays, Radio waves, Blue light, Infrared light. (All India 2010)
Answer:
Decreasing order ➝ Radio waves, Infrared light, Blue light, X-rays.

Question 24.
A plane electromagnetic wave travels in vacuum along z-direction. What can you say about the direction of electric and magnetic field vectors? (Delhi 2011)
Answer:
The direction of electric field vector is along X-axis. Magnetic field vector is along Y-axis.

Question 25.
A plane electromagnetic wave travels in vacuum along x-direction. What can you say about the direction of electric and magnetic field vectors? (Delhi 2011)
Answer:
The electric field and magnetic field vectors are in YZ-plane in the Y-direction and Z-direction respectively.

Question 26.
A plane electromagnetic wave travels in vacuum along y-direction. What can you say about the direction of electric and magnetic field vectors? (Delhi 2011)
Answer:
The electric field and magnetic field vector are in ZX-plane in the X-direction and Z-direction respectively.

Question 27.
How are radio waves produced? (All India 2011)
Answer:
Radio waves are produced by the accelerated motion of charges in conducting wires.

Question 28.
How are X-rays produced? (All India 2011)
Answer:
X-rays are produced by sudden deceleration or acceleration of electrons in an X-ray tube.

Question 29.
How are microwaves produced? (All India 2011)
Answer:
Microwaves are produced by Klystron valve or magnetron valve.

Question 30.
Name the physical quantity which remains same for microwaves of wavelength 1 mm and UV radiations of 1600 Å in vacuum. (Delhi 2012)
Answer:
Speed/Velocity of light remains the same.

Question 31.
What are the directions of electric and magnetic field vectors relative to each other and relative to the direction of propagation of electromagnetic waves? (All India 2012)
Answer:
The oscillations of \(\overrightarrow{\mathrm{E}}\) and \(\overrightarrow{\mathrm{B}}\) fields are perpendicular to each other as well as to the direction of propagation of the wave.

Question 32.
The speed of an electromagnetic wave in a material medium is given by \(v=\frac{1}{\sqrt{\mu \varepsilon}}, \mu\) the permeability of the medium and ε its permittivity. How does its frequency change? (All India 2012)
Answer:
Frequency remains unchanged.

Question 33.
A capacitor has been charged by a dc source. What are the magnitudes of conduction and displacement currents, when it is fully charged? (Delhi 2013)
Answer:
On full charging, the source will maintain the potential across the plates. The magnitudes of displacement current and conduction current will be zero.

Question 34.
Welders wear special goggles or face masks with glass windows to protect their eyes from electromagnetic radiations. Name the radiations and write the range of their frequency. (All India 2013)
Answer:
The name of radiations is ultraviolet radiation. Its frequency range is 10¹⁵ to 10¹⁷ Hz.

Question 35.
To which part of the electromagnetic spectrum does a wave of frequency 5 × 10¹⁹ Hz belong? (All India 2013)
Answer:
A wave of frequency 5 × 10¹⁹ Hz belongs to γ-rays region of electromagnetic spectrum.

Question 36.
To which part of the electromagnetic spectrum does a wave of frequency 3 × 10¹³ Hz belong? (All India 2014)
Answer:
Infra-red region of electromagnetic spectrum.

Question 37.
Why are microwaves considered suitable for radar systems used in aircraft navigation? (Delhi 2016)
Answer:
Due to their short wavelengths, microwaves are considered suitable for radar systems in aircraft navigation.

Question 38.
How is the speed of em-waves in vacuum determined by the electric and magnetic fields? (Delhi 2017)
Answer:
Speed of em-waves in vacuum is determined by the ratio of the peak values of electric and magnetic field vectors.

Question 39.
Do electromagnetic waves carry energy and momentum? (All India 2017)
Answer:
Yes, they do, because of change of magnetic flux associated with circular loop.

Question 40.
Write the relation for the speed for electromagnetic waves in terms of the amplitudes of electric and magnetic fields. (All India 2017)
Answer:

Question 41.
In which directions do the electric and magnetic field vectors oscillate in an electromagnetic wave propagating along the x-axis? (All India 2017)
Answer:
Electric field (\(\overrightarrow{\mathrm{E}}\)) oscillates along y-axis and magnetic field ( \(\overrightarrow{\mathrm{B}}\) ) oscillates along z-axis;in an electromagnetic wave propagating along the x-axis.

Question 42.
The available frequency AC source is connected to a capacitor. Will the displacement current change if the frequency of the AC source is decreased? (CBSE Al 2015C)
Answer:
No

Question 42 a.
Why microwaves are considered suitable for radar systems used in aircraft navigation? (CBSE Delhi 2016)
Answer:
They have a small wavelength and travel along a straight line with deflecting.

Question 43.
Do electromagnetic waves carry energy and momentum? (CBSE AI 2017)
Answer:
Yes.

Question 44.
How is the speed of em-waves in vacuum – determined by the electric and magnetic field? (CBSE Delhi 2017)
Answer:
c = \(\frac{E_{0}}{B_{0}}\)

Question 45.
Why is skywave propagation of signals restricted to a frequency of 30 MHz? (CBSE Al 2017 C)
Answer:
The atmosphere is transparent to frequencies higher than 30 MHz.

Question 46.
Name the electromagnetic radiations used for
(a) water purification
Answer:
UV radiation

(b) eye surgery. (CBSEAI 2018, Delhi 2018)
Answer:
Visible light

Question 47.
Write the range of frequencies of electromagnetic waves which propagate through sky wave mode. (CBSE Al 2018 C)
Answer:
A few MHz up to 30 to 40 MHz.

Question 48.
Optical and radio telescopes are built on the ground but X-ray astronomy is possible only from satellites orbiting the earth. Why?
Answer:
This is because of the fact that X-rays are absorbed by the atmosphere, whereas light and radio waves penetrate through it.

Question 49.
A charged particle oscillates about its mean equilibrium position with a frequency of 10⁹ Hz. What is the frequency of the electromagnetic wave produced by the oscillator?
Answer:
Same as that of the oscillating charged particle, i. e. 10⁹ Hz.

Question 50.
Why are infrared radiations referred to as heat waves also? Name the radiations which are next to these radiations in the electromagnetic spectrum having
(a) Shorter wavelength and
(b) Longer wavelength.
Answer:
This is because they produce a heating effect.
(a) Visible light and
(b) Microwaves.

Question 51.
What physical quantity are the same for X-rays of wavelength 10^-10 m, the red light of wavelength 680 nm, and radio waves of wavelength 500 m?
Answer:
Since all of them are electromagnetic waves, their speed in a vacuum will be the same, i.e. 3 × 10⁸ m s^-1.

Question 52.
A charged particle oscillates about its mean equilibrium position with a frequency of 10⁹ Hz. What is the frequency of the electromagnetic waves produced by the oscillator?
Answer:
The frequency of the electromagnetic waves produced by the oscillator is the same as its frequency of vibration, i.e. 10⁹ Hz.

Question 53.
The amplitude of the magnetic field part of a harmonic electromagnetic wave in a vacuum is B₀ = 510 nT. What is the amplitude of the electric field part of the wave?
Answer:
Given B₀ = 510 nT = 510 × 10^-9 T, E₀ = ?

Using the relation E₀ = c × B₀, we have
E₀ = 3 × 108 × 510 × 10^-9 = 153 N C^-1

Question 54.
Why does a microwave oven heat up a food item containing water molecules most efficiently?
Answer:
It is because the frequency of the microwave matches the resonant frequency of water molecules. This makes the molecules vibrate with maximum amplitude thereby producing heat.

Question 55.
Name the most energetic electromagnetic radiation and write its frequency range. (CBSE AI 2019 C)
Answer:
The most energetic radiations are Gamma Rays Frequency range of gamma rays is: 10¹⁸ Hz to 10²³ Hz
Or
Name the electromagnetic radiations used in eye surgery or to kill germs in water purifiers. Write its frequency, range.
Answer:

1. Radiations used for eye surgery or to kill germs are Ultraviolet Rays.
2. The frequency range of ultraviolet rays: 10⁵ Hz to 10¹⁷ Hz.

Short Answer Type

Question 1.
Radio waves and gamma rays both are transverse in nature and electromagnetic in character and have the same speed in a vacuum. In what respect are they different?
Answer:
The radio waves have an atomic origin, while gamma rays have a nuclear origin. Further owing to their very small wavelength, gamma rays are highly penetrating in comparison to radio waves.

Question 2.
Show that the average energy density of the electric field equals the average density of the magnetic field.
Answer:
The average density of the electric field is given by
U_e = \(\frac{1}{2}\)ε₀E² and the average energy density of the magnetic field is given by U_B = \(\frac{B^{2}}{2 \mu_{0}}\).

But B = \(\frac{E}{c}\) and c = \(\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}\) , hence the above equation becomes U_B = \(\frac{B^{2}}{2 \mu_{0}}=\frac{E^{2}}{2 \mu_{0} c^{2}}\)

U_B = \(\frac{E^{2}}{2 \mu_{0} \times \frac{1}{\mu_{0} \varepsilon_{0}}}=\frac{1}{2} \varepsilon_{0} E^{2}\). Hence the result.

Question 3.
State four properties of electromagnetic waves.
Answer:
(a) They do not require any material medium to travel.
(b) They are transverse in nature, i.e. electric and magnetic fields are perpendicular to each other and also to the direction of the propagation of the wave.
(c) The energy of the wave is divided equally amongst the electric and the magnetic field.
(d) They travel, in free space, with a velocity of 3 × 10⁸ m s^-1.

Question 4.
The oscillating magnetic field in a plane electromagnetic wave is given by
By = (8 × 10^-6) sin [2 × 10^-11 t + 300 π x] T
(i) Calculate the wavelength of the electo-magnetic wave.
(ii) Write down the expression for the oscillating electric field. (Delhi 2008)
Answer:
Given: B_y = 8 × 10^-6 sin [2 × 10¹¹ t + 300 π x] T
(i) Standard equation is,

The oscillations of \(\overrightarrow{\mathrm{E}}\) and \(\overrightarrow{\mathrm{B}}\) fields are perpendicular to each other as well as to the direction of propagation of the wave. So we take electric field in z-direction because oscillating magnetic field is in y-di recti on and propagation of the wave is in x-direction.

Question 5.
The oscillating electric field of an electromagnetic wave is given by :
E = 30 sin [2 × 10¹¹ t + 300 π x] Vm^-1
(a) Obtain the value of the wavelength of the electromagnetic wave.
(b) Write down the expression for the oscillating magnetic field. (Delhi 2008)
Answer:
(a) We compare the given expression with

Question 6.
How does a charge q oscillating at certain frequency produce electromagnetic waves? Sketch a schematic diagram depicting electric and magnetic fields for an electromagnetic wave propagating along the Z-direction. (Delhi 2009)
Answer:
As the charge q moves accelerating, the electric field and magnetic field produced will change the space and time E and B varying with time produced the other field B and E respectively and sustain the E.M. pattern.

This is from the interpretation of Maxwell supported by

Question 7.
Arrange the following electromagnetic radiations in ascending order of their frequencies:
(i) Microwave
(ii) Radiowave
(iii) X-rays
(iv) Gamma rays
Write two uses of any one of these. (Delhi 2009)
Answer:
In ascending order of their frequencies :
Radiowave < Microwave < X-rays < Gamma rays.
Two uses of microwaves are :
1. In microwave ovens.
2. In aircraft navigation.

Question 8.
Draw a sketch of a plane electromagnetic wave propagating along the z-direction. Depict clearly the directions of electric and magnetic fields varying sinusoidally with z. (All India 2009)
Answer:
Sketch of a plane electromagnetic wave propagating along the z-direction with oscillating electric field E along the x-direction and the oscillating magnetic field B along the y-direction.

Question 9.
How are infrared waves produced? Why are these referred to as ‘heat waves’? Write their one important use. (Delhi 2009)
Answer:
Infrared rays are produced by hot bodies and molecules. This may involve vibration and bending of molecules. Infrared band lies adjacent to low-frequency or long-wavelength end of the visible spectrum. Infrared waves are sometimes referred to as heat waves.

Use: Infrared rays are used to take photographs in darkness. These are also used to study secret writing. They are also used in physical therapy.

Question 10.
A parallel plate capacitor is being charged by a time varying current. Explain briefly how Ampere’s circuital law is generalized to incorporate the effect due to the displacement current. (All India 2011)
Answer:
Maxwell’s displacement current : According to Ampere’s circuital law, the magnetic field B is related to steady current I as

Maxwell showed that this relation is logically in-consistent. He accounted this inconsistency as follows :
Ampere’s circuital law for loop C₁ gives

which is logically inconsistent. So, Maxwell gave idea of displacement current.

Thus displacement current is that current which comes into play in the region in which the electric field and hence the electric flux is changing with time.

It is now called Ampere-Maxwell law. This is the generalization of Ampere’s circuital law.

Question 11.
When an ideal capacitor is charged by a dc battery, no current flows. However, when an ac source is used, the current flows continuously. How does one explain this, based on the concept of displacement current?
Answer:
A dc battery connected to an ideal capacitor ‘ provides only a momentarily charge, whereas an ac battery allows a continuous flow of current

As charge on capacitor plates changes, electric field associated with that also changes and hence giving rise to a displacement current according to

Question 12.
A capacitor of capacitance ‘C is being charged by connecting it across a dc source along with an ammeter. Will the ammeter show a momentary deflection during the process of charging? If so, how would you explain this momentary deflection and the resulting continuity of current in the circuit? Write the expression for the current inside the capacitor. (All India 2012)
Answer:
Ammeter will definitely show a momentary deflection, which is due to the flow of electron produced in the charging process. As the capacitor plates get charging, the displacement current start flowing in the gap and thus shows a continuity of current.

Question 13.
(a) An em wave is travelling in a medium with a velocity \(\overrightarrow{\mathbf{v}}=\mathbf{v} \hat{i}\). Draw a sketch showing the propagation of the em wave, indicating the direction of the oscillating electric and magnetic fields.
(b) How are the magnitudes of the electric and magnetic fields related to the velocity of the em wave?
Answer:

Question 14.
A capacitor, made of two parallel plates each of plate area A and separation d, is being charged by an external ac source. Show that the displacement current inside the capacitor is the same as the current charging the capacitor. (All India 2012)
Answer:
The displacement current arises due to varying electric field

If q be instantaneous charge, then E is electric field between the plates of capacitor at that time and A is area of plate; then

Question 15.
(a) How are electromagnetic waves produced?
(b) How do you convince yourself that electromagnetic waves carry energy and momentum? (Comptt. Delhi 2012)
Answer:
(a) Electromagnetic Waves : Accelerating electric charge produces electromagnetic waves.

(b) Einstein’s explanation of photoelectric effect led de Broglie to the wave-particle duality, i.e., matter exhibits wave as well as particle properties. Electromagnetic waves are characterised by wave properties, such as periodicity in space-time, wavelength, amplitude, frequency, wave velocity etc. It transports energy but no matter.

The term wave-particle duality refers to the behaviour where both wave-like and particle-like properties are exhibited under different conditions by the same entity. Hence electromagnetic waves show particle properties such as definite position, size, mass, velocity, momentum, energy etc.
For a photon of momentum (p), an associated wavelength is given by \(\lambda=\frac{h}{p}\).

Question 16.
(a) Arrange the following electromagnetic waves in the descending order of their wavelengths :

1. Microwaves
2. Infra-red rays
3. Ultra-violet radiation
4. Gamma rays

(b) Write one use each of any two of them. (Comptt. Delhi 2013)
Answer:
(a) Arrangement:

1. Microwaves
2. Infra-red rays
3. Ultra-violet radiation
4. Gamma rays

(b) Uses :

1. Microwaves are used in radar system.
2. Infra-red rays are used for protecting dehydrated fruits.
3. Ultra-violet rays are used in the study of molecular structure.
4. Gamma rays are used to kill micro-organisms in food industry.

Question 17.
Considering the case of a parallel plate capacitor being charged, show how one is required to generalize Ampere’s circuital law to include the term due to displacement current. (All India 2014)
Answer:

Maxwell’s displacement current : According to Ampere’s circuital law, the magnetic field B is related to steady current I as

Maxwell showed that this relation is logically in-consistent. He accounted this inconsistency as follows :
Ampere’s circuital law for loop C₁ gives

which is logically inconsistent. So, Maxwell gave idea of displacement current.

Thus displacement current is that current which comes into play in the region in which the electric field and hence the electric flux is changing with time.

It is now called Ampere-Maxwell law. This is the generalization of Ampere’s circuital law.

Question 18.
A capacitor is connected in series to an ammeter across a d.c. source. Why does the ammeter show a momentary deflection during the charging of the capacitor? What would be the deflection when it is fully charged? (Comptt. All India 2014)
Answer:
The momentary deflection is due to the transient current flowing through the circuit when the capacitor is getting charged.
The deflection would be zero when the capacitor gets fully charged.

Question 19.
Name the types of e.m. radiations which

1. are used in destroying cancer cells,
2. cause tanning of the skin and
3. maintain the earth’s warmth.

Write briefly a method of producing any one of these waves. (Delhi 2015)
Answer:

1. γ-rays
2. Ultraviolet rays
3. Infrared rays

Mode of production

1. γ-rays are produced by radioactive decay of nucleus.
2. Ultraviolet rays are produced when inner shell electrons in atoms move from one energy level to an other energy level.
3. Infrared rays are produced due to vibration of atoms and molecules.

Question 20.
For a plane electromagnetic wave, propagating along the Z-axis, write the two (possible) pairs of expression for its oscillating electric and magnetic fields. How are the peak values of these (oscillating) fields related to each other? (Comptt. All India 2016)
Answer:
For the e.m. wave, propagating along the z-axis, we have

The two possible forms for electric and magnetic fields are :

The peak values of these two fields are related by

Question 21.
An e.m. wave, Y₁, has a wavelength of 1 cm while another e.m. wave, Y₂, has a frequency of 10¹⁵ Hz. Name these two types of waves and write one useful application for each. (Comptt. All India 2014)
Answer:
(i) Y₁ ➝ Microwaves
Applications : Microwaves are used in Microwave ovens, Aircraft Navigators etc.

(ii) Y₂ ➝ Ultraviolet waves
Applications : Ultraviolet rays are used in sterilizing surgical instruments, food preservation etc.

Question 22.
How does Ampere-Maxwell law explain the flow of current through a capacitor when it is being charged by a battery? Write the expression for the displacement current in terms of the rate of change of electric flux. (Delhi 2017)
Answer:
During charging, the electric flux between the plates of a capacitor keeps on changing; this results in the production of a displacement current between the plates.

Question 23.
Identify the electromagnetic waves whose wavelengths vary as
(a) 10^-12 < λ < 10^-8 m
(b) 10^-3 m < X < 10^-1 m
Write one use for each. (All India 2017)
Answer:
(a) X-rays—Used in medical science for the purpose of detection of fractures, stones in gall bladder, stones in kidney etc.

(b) Microwaves—Used in radar systems for aircraft navigation.

Question 24.
Identify the electromagnetic waves whose wavelengths lie in the range
(a) 10^-11 m < λ < 10^-8 m
(b) 10^-4 m < λ < 10^-6 m Write one use of each. (All India 2017)
Answer:
(a) Uses of X-Rays and Gamma rays :
X-rays are used as a diagnostic tool in medicine and as a treatment for certain forms of cancer. Gamma rays are used in medicine to destroy cancer cells.

(b) Uses of Infrared, visible and microwaves :

• Infrared waves are widely used in remote switches of household electronic systems such as remotes for TVs, video recorders etc.
• Visible rays provide us information about the world.
• Microwaves are used in the radar systems in aircraft navigation.

Question 25.
How is electromagnetic wave produced? Draw a sketch of a plane e.m. wave propagating along X-axis depicting the directions of the oscillating electric and magnetic fields. (Comptt. Delhi 2017)
Answer:
Electromagnetic waves are produced due to oscillating/accelerating charged particles.
Sketch of e.m. wave :

Question 26.
Electromagnetic radiations with wavelength
(a) λ₁ are used to kill germs in water purifiers.
(b) λ₂ are used in TV communication systems.
(c) λ₃ plays an important role in maintaining the earth’s warmth.
Name the part of the electromagnetic spectrum to which these radiations belong. Arrange these wavelengths in decreasing order of their magnitude.
Answer:
(a) λ₁ – Ultraviolet radiations.
(b) λ₂ – Microwaves
(c) λ₃ – Infrared rays
Their order is λ₁ < λ₃ < λ₂.

Question 27.
Name the constituent radiation of the electromagnetic spectrum which
(a) is used in satellite communication.
Answer:
Microwaves.

(b) is used for studying crystal structure.
Answer:
X-rays

(c) is similar to the radiations emitted during the decay of a radioactive nucleus.
Answer:
Gamma rays

(d) is absorbed from sunlight by the ozone layer.
Answer:
UV rays

(e) produces an intense heating effect.
Answer:
Infrared rays

(f) has its wavelength range between 390 nm and 770 nm.
Answer:
Visible light.

Question 28.
Name the radiations of the electromagnetic spectrum which are used in
(a) warfare to look through the haze.
Answer:
Infrared rays

(b) radar and geostationary satellites
Answer:
Microwaves.

(c) studying the structure and properties of atoms and molecules.
Answer:
Gamma rays.

Question 29.
Why are microwaves used in RADAR?
Answer:
Microwaves are electromagnetic waves of very short wavelength. Such waves are used in RADAR due to the reason that they can travel in a particular direction in the form of a beam without being deflected.

Question 30.
Electromagnetic waves with wavelength
(a) λ₁ are used to treat muscular strain.
(b) λ₂ are used by an FM radio station for broadcasting.
(c) λ₃ are used to detect fractures in bones.
(d) λ₄ are absorbed by the ozone layer of the atmosphere.
Identify and name the part of the electromagnetic spectrum to which these radiations belong. Arrange
these wavelengths in decreasing order of magnitude.
Answer:
(a) Infrared radiations are used to treat muscular strain.
(b) Radio and microwave radiations are used for FM transmission.
(c) X-rays are used to detect fractures in bones.
(d) Ultraviolet radiation is absorbed by the ozone layer of the atmosphere.
The decreasing order of their wavelength is
λ₂ > λ₁ > λ₄ > λ₃.

Question 31.
(a) Draw a graph of a linearly polarised em wave propagating in the Z-direction showing the directions of the oscillating electric and magnetic fields.
Answer:
Graph of linearly polarised em wave propagating in the Z-axis.

(b) Write the relations (i) between the speed of light and the amplitudes of electric and magnetic fields, (ii) for the speed of em wave in terms of a permittivity e0, and magnetic permeability p0, of the medium. (CBSE 2019C)
Answer:
(i) Relation between speed of light and amplitudes of electric and magnetic field c = \(\frac{E_{0}}{B_{0}}\)

(ii) Speed of light in terms of ε₀ and μ0,
c = \(\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}\)

Question 32.
Arrange the following electromagnetic waves in the order of their increasing wavelength:
(a) Gamma rays
(b) Microwaves
(c) X-rays
(d) Radio waves
How are infrared waves produced? What role does infrared radiation play in
(a) maintaining the Earth’s warmth and
(b) physical therapy? (CBSE Al 2015)
Answer:
Gamma(γ) rays, X-rays, Microwaves, Radio waves:
Infrared rays are produced by hot bodies/ vibration of atoms and molecules Infrared rays: (a) Maintain the earth’s warmth through the greenhouse effect, (b) produce heat

Question 33.
Name the parts of the electromagnetic spectrum which is
(a) suitable for radar systems used in aircraft navigation.
Answer:
Microwave: They are produced by oscillating circuits.

(b) used to treat muscular strain.
Answer:
Infrared rays: They are produced by the vibration of atoms and molecules.

(c) used as a diagnostic tool in medicine. Write in brief, how these waves can be produced. (CBSE Delhi 2015)
Answer:
X-rays: They are produced by bombarding high atomic number targets with electrons.

Question 34.
An e.m wave Y₁ has a wavelength of 1 cm while another e.m wave, Y₂ has a frequency of 10¹⁵ Hz. Name these two types of waves and write one useful application for each. (CBSE AI 2016 C)
Answer:
Y₁ – Microwaves and
Y₂ – Ultraviolet waves.

• Microwaves: used for communication.
• Ultraviolet waves: used for sterilization.

Question 35.
Identify the electromagnetic waves whose wavelengths vary as
(a) 10^-12 m < λ < 10^-8 m
Answer:
X – rays: a study of crystal structure

(b) 10^-3 m < λ < 10^-1 m. Write one of their uses. (CBSE Al 2017)
Answer:
Microwaves: radar and communication

Question 36.
Name the type of e.m waves having a wavelength range of 0.1 m to 1 mm. How are these waves generated? Write their two uses. (CBSE Al 2017 C)
Answer:

• Microwaves: These are generated with the help of special vacuum tubes (called klystrons, magnetrons, and Gunn diodes).
• Uses: Cooking, radar, and communication

Question 37.
Identify the following electromagnetic radiations as per the wavelengths given below. Write one application of each. (All India 2008)
(a) 10^-3 nm
(b) 10^-3 m
(c) 1 nm
Answer:
(a) 10^-3 nm : γ-rays
Application :

1. γ-rays are used in the treatment of cancer and tumour.
2. γ-rays are used in radiation therapy. (any one)

(b) 10^-3m : Microwave
Application : Microwaves are used in Radar systems for aircraft navigation.

(c) 1 nm : X-rays Application :

1. Infra-red waves are used for taking photographs during the conditions of fog, smoke etc.
2. These are also used as a diagonostic tool for the detection of fractures, (any one)

Question 38.
Identify the following electromagnetic radiations as per the wavelengths given below. Write one application of each.
(a) 1 mm
(b) 10^-12 m
(c) 10^-8 m (All India 2008)
Answer:
(a) 1 mm : Microwaves
Application : In aircraft navigation for the radar system. Also used in microwave ovens.

(b) 10^-12 m : Gamma rays
Application : Gamma rays are used as medicine to destroy cancer cells

(c) 10^-8 m : Ultraviolet rays
Application : Ultraviolet rays are used in LASIK eye surgery.

Question 39.
(a) How does an oscillating charge produce electromagnetic wave? Explain.
(b) Draw a sketch showing the propagation of a plane em wave along the Z-direction, clearly depicting the directions of oscillating electric and magnetic field vectors. (Comptt. Delhi 2012)
Answer:
(a) Consider a charge oscillating with same frequency. This produces an oscillating electric field in space, which produces an oscillating magnetic field which in turn is a source of oscillating electric field and so on. The oscillating electric and magnetic fields thus regenerate each other, as the waves propagate through the space. The frequency of the electromagnetic wave naturally equals the frequency of the oscillation of the charge.

(b)
Sketch of a plane electromagnetic wave propagating along the z-direction with oscillating electric field E along the x-direction and the oscillating magnetic field B along the y-direction.

Question 40.
When an ac source is connected across a capacitor, current starts flowing through the circuit. Show how Ampere’s circuital law is generalized to explain the flow of current through the capacitor. Hence obtain the expression for the displacement current inside the capacitor. (Comptt. All India 2012)
Answer:
When an ‘ac’ source is connected across a capacitor, the charge on the capacitor also becomes time dependent. It gives rise to a time dependent electric field between the plates of capacitor. As a result the electric flux changes.

It was suggested that we need to regard this changing electric flux, between the plates of capacitor, as equivalent to a current which is called the displacement current.

which is generalised form of an Ampere’s circuital law. .

Question 41.
(a) When the oscillating electric and magnetic fields are along the x- and indirection respectively

1. point out the direction of propagation . of electromagnetic wave.
2. express the velocity of propagation in terms of the amplitudes of the oscillating electric and magnetic fields.

(b) How do you show that the em wave carries energy and momentum?(Comptt. All India)
Answer:
(a)

1. Along z-direction.
2. Velocity of propogation will be, \(\mathbf{C}=\frac{\mathbf{E}_{0}}{\mathbf{B}_{0}}\)

(b) Photoelectric effect shows the particle nature of electromagnetic waves. As such the photons carry energy and momentum. The energy is given by

Question 42.
Answer the following :
(a) Name the em waves which are suitable for radar systems used in aircraft navigation. Write the range of frequency of these waves.
(b) If the. earth did not have atmosphere, would its average surface temperature be higher or lower than what it is now? Explain.
(c) An em wave exerts pressure on the surface on which it is incident. Justify. (Delhi 2014)
Answer:
(a) Microwaves are used in radar systems. Its frequency range : 10¹⁰ to 10¹² Hz

(b) In the absence of earth’s atmosphere, there would have no ozone layer to prevent ultraviolet radiations reaching the earth, the temperature on earth’s surface would have been lower due to green house effect, making it difficult for human survival.

(c) Since em wave carries both energy and momentum, hence exerts pressure on the surface on which it is incident.

An em wave exerts negligibly very small pressure on the surface on which it is incident.

It is due to the fact that momentum of the photon is extremely small, which can be
calculated by de-Broglie relation \(\left(\lambda=\frac{h}{p}\right)\)

Question 43.
Answer the following :
(a) Name the em waves which are used for the treatment of certain forms of cancer. Write their frequency range.
(b) Thin ozone layer on top of stratosphere is crucial for human survival. Why?
(c) Why is the amount of the momentum transferred by the em waves incident on the surfrace so small? (Delhi 2014)
Answer:
(a) Gamma (γ) rays are used for the treatment of certain forms of cancer. Their frequency range is 10¹⁸ Hz to 10²² Hz.

(b) The thin ozone layer on top of stratosphere absorbs most of the harmful ultraviolet rays coming from the Sun towards the Earth. They include UVA, UVB and UVC radiations, which can destroy the life system on the Earth.
Hence, this layer is crucial for human survival.

(c) Thus, the amount of the momentum transferred by the em waves incident on the surface is very small, because of small value of planks constant. For example, an electromagnetic wave of wavelength 1.00 nm will provide momentum (p) according to de-Broglie’s relation,

It is extremely small value of the momentum.

Question 44.
Answer the following questions :
(a) Name the em waves which are produced during radioactive decay of a nucleus. Write their frequency range.
(b) Welders wear special glass goggles while working. Why? Explain.
(c) Why are infrared waves often called as heat waves? Give their one application. (Delhi 2014)
Answer:
(a) γ-rays; Frequency range : 10¹⁸ Hz to 10²² Hz

(b) Because to protect eyes from intense ultra-violet radiations produced during welding; and also to protect from glare and flying sparks.

(c) Because infrared waves are em waves of higher wavelength (less frequency) and are produced by highly vibrating molecules of hot bodies.
Applications :

1. used in the remote switches of household electronic systems.
2. used for protecting dehydrated fruits.
3. used in solar water heaters and cookers. (Any one)

Question 45.
Answer the following questions:
(i) Show, by giving a simple example, how em waves carry energy and momentum.
(i) 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?
(iii) Write two important uses of infrared waves. (Comptt. Delhi 2014)
Answer:
(i) 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 em wave, incident on this plane. This illustrates that em waves carry energy and momentum.

(ii) Microwaves are produced by special vacuum tubes like the Klystron/Magnetron/Gunn diode.
In microwave ovens, the frequency of microwaves is selected to match the resonant frequency of water molecules, so that energy is transferred efficiently to the kinetic energy of the molecules.

(iii) Important uses of infra-red waves :
1. These are associated with the green house effect.
2. These are used in remote switches of household electrical appliances.

Question 46.
(a) A capacitor is connected in series to an ammeter across a d.c. source. Why does the ammeter show a momentary deflection during the charging of the capacitor? What would be the deflection when it is fully charged?
(b) How is the generalized form of Ampere’s circuital law obtained to include the term due to displacement current? (Comptt. All India 2014)
Answer:
(a) The momentary deflection is due to the transient current flowing through the circuit when the capacitor is getting charged.
The deflection would be zero when the capacitor gets fully charged.

(b)
Maxwell’s displacement current : According to Ampere’s circuital law, the magnetic field B is related to steady current I as

Maxwell showed that this relation is logically in-consistent. He accounted this inconsistency as follows :
Ampere’s circuital law for loop C₁ gives

which is logically inconsistent. So, Maxwell gave idea of displacement current.

Thus displacement current is that current which comes into play in the region in which the electric field and hence the electric flux is changing with time.

It is now called Ampere-Maxwell law. This is the generalization of Ampere’s circuital law

Question 47.
Name the parts of the electromagnetic spectrum which is
(a) suitable for radar systems used in aircraft navigation.
(b) used to treat muscular strain.
(c) used as a diagnostic tool in medicine.
Write in brief, how these waves can be produced. (Delhi 2014)
Answer:
(a) Microwaves
Production : Klystron/magnetron

(b) Infrared Radiations
Production ; Hot bodies/vibrations of atoms and molecules.

(c) X-Rays
Production : Bombarding high energy electrons on a metal target.

Question 48.
Write the expression for the generalized form of Ampere’s circuital law. Discuss its significance and describe briefly how the concept of displacement current is explained through charging/discharging of a capacitor in an electric circuit. (All India 2014)
Answer:
Maxwell’s displacement current : According to Ampere’s circuital law, the magnetic field B is related to steady current I as

Maxwell showed that this relation is logically inconsistent. He accounted this inconsistency as follows :
Ampere’s circuital law for loop C₁ gives

which is logically inconsistent. So, Maxwell gave idea of displacement current.
Thus displacement current is that current which comes into play in the region in which the electric field and hence the electric flux is changing with time.

It is now called Ampere-Maxwell law. This is the generalization of Ampere’s Circuital law.

Question 49.
How are em waves produced by oscillating charges?
Draw a sketch of linearly polarized em waves propagating in the Z-direction. Indicate the directions of the oscillating electric and magnetic fields. (Delhi 2016)
Answer:
em waves by oscillating charges.

(a) Consider a charge oscillating with same frequency. This produces an oscillating electric field in space, which produces an oscillating magnetic field which in turn is a source of oscillating electric field and so on. The oscillating electric and magnetic fields thus regenerate each other, as the waves propagate through the space. The frequency of the electromagnetic wave naturally equals the frequency of the oscillation of the charge.

(b)
Sketch of a plane electromagnetic wave propagating along the z-direction with oscillating electric field E along the x-direction and the oscillating magnetic field B along the y-direction.

Sketch of em waves.
Sketch of a plane electromagnetic wave propagating along the z-direction with oscillating electric field E along the x-direction and the oscillating magnetic field B along the y-direction.

Question 50.
Write Maxwell’s generalization of Ampere’s Circuital Law. Show that in the process of charging a capacitor, the current produced within the plates of the capacitor is

where ϕ E is electric flux produced during charging of the capacitor plates. (Delhi 2016)
Answer:

Maxwell’s displacement current : According to Ampere’s circuital law, the magnetic field B is related to steady current I as

Maxwell showed that this relation is logically in-consistent. He accounted this inconsistency as follows :
Ampere’s circuital law for loop C₁ gives

which is logically inconsistent. So, Maxwell gave idea of displacement current.

Thus displacement current is that current which comes into play in the region in which the electric field and hence the electric flux is changing with time.

It is now called Ampere-Maxwell law. This is the generalization of Ampere’s circuital law.

Question 51.
(i) Identify the part of the electromagnetic spectrum which is :
(a) suitable for radar system used in aircraft navigation,
(b) produced by bombarding a metal target by high speed electrons.
(ii) Why does a galvanometer show a momentary deflection at the time of charging or discharging a capacitor? Write the necessary expression to explain this observation. (All India 2016)
Answer:
(i)
(a) Microwaves
(b) X-rays

(ii) The total current
(i) is the sum of conduction current
(i_c) and displacement current (i_d), so we have

This means that outside the capacitor plates in connecting wires, we have only conduction current i_c = i and no displacement current (i_d = 0). On the other hand, inside the capacitor, there is no conduction current (i_c = 0) and there is only displacement current hence i = i_d.
It is why there is momentary deflection in the galvanometer at the time of charging or discharging a capacitor.

Question 52.
Name the e.m. waves in the wavelength range 10 nm to 10^-3 nm. How are these waves generated? Write their two uses.
Answer:

• e.m. waves in the wavelength range 10 nm to 10^-3 nm are X-rays.
• X-rays are generated by bombarding a metal target with high energy electrons.

• Uses :

1. Diagnosis of bone fractures.
2. Treatment of some forms of cancer.

Question 53.
Name the type of e.m. waves having a wavelength range of 0.1 m to 1 mm. How are these waves generated? Write their two uses. (Comptt. All India 2017)
Answer:

1. e.m. waves having a wavelength range 0.1 m to 1 mm are MICROWAVES.
2. Microwaves are generated by special vacuum tubes such as klystron, magnetron and gunn diodes.
3. Microwaves are used in :
   • Radar system in aircraft navigation
   • Ovens for heating and cooking.

Question 54.
Name the type of e.m. waves having a wavelength range 10^-7 m to 10^-9 m. How are these waves generated? Write their two uses. (Comptt. All India 2017)
Answer:

1. e.m. waves having a wavelength range 10^-7 m to 10^-9 m are ultra violet rays.
2. Sun is an important source of UV rays. Some special lamps and very hot bodies also produce UV rays.

• Uses :

• UV rays are used in lasik eye surgery.
• UV lamps are being used to kill germs in water purifiers.

Question 55.
(a) Give one use of electromagnetic radiations obtained in nuclear disintegrations.
Answer:
Treating cancer.

(b) Give one example each to illustrate the situation where there is
(i) displacement current but no conduction current and
Answer:
Between the plates of a capacitor

(ii) only conduction current but no displacement current.(CBSE Al 2018 C)
Answer:
Outside the plates of a capacitor

Question 56.
Scientists predict that a global nuclear war on the earth will be followed by a severe nuclear winter, with devastating effects on the earth. What is the basis of this prediction?
Answer:
The explosions will produce so much dust, which will cover the whole atmosphere, thereby blocking the sun’s rays from reaching the earth. This will cause the setting in of a long winter, which is called nuclear winter.

Question 57.
If the earth did not have an atmosphere, would its average surface temperature be higher or lower than what it is now?
Answer:
Due to the Greenhouse effect, the temperature of the earth’s surface is raised in the presence of the atmosphere. In the absence of the atmosphere, the heat received by the earth during the day is completely lost during the night. Hence the average surface temperature will be lower than the preset temperature.

Question 58.
A capacitor of capacitance ‘C is being charged by connecting it across a dc source along with an ammeter. Will the ammeter show a momentary deflection during the process of charging? If so, how would you explain this momentary deflection and the resulting continuity of current in the circuit? Write the expression for the current inside the capacitor. (CBSE AI 2012)
Answer:
Yes, this is due to the rate of change of electric flux inside the capacitor due to the production of displacement current. The expression for the current inside the capacitor is l_D = ε_o \(\frac{d \phi_{E}}{d t}\)

Question 59.
Define displacement current. What role does it play while charging a capacitor by dc source? Is the value of displacement current the same as that of the conduction current? Explain. (CBSE AI 2019)
Answer:

• Displacement current is the current due to the change of electric flux.
• It provides continuity of current in circuits containing capacitors.
• Yes, the value of displacement current is equal to the conduction current.
• l_d = ε_o \(\frac{d \phi_{e}}{d t}\)

Question 60.
Why is the orientation of the portable radio with respect to the broadcasting station important? (NCERT Exemplar)
Answer:
This is because the electromagnetic waves are plane polarised; hence the receiving antenna should be parallel to the electric/magnetic part of the wave.

Question 61.
(a) Give one use of electromagnetic radiations obtained in nuclear disintegrations.
Answer:
used to destroy cancer cells

(b) Give one example each to illustrate the situation where there is
(i) displacement current but no conduction current and
Answer:
The region, between the plates of a capacitor, connected to a time-varying voltage source, has a displacement current but no conduction current.

(ii) only conduction current but no displacement current. (CBSE Delhi 2018C)
Answer:
The wires, connected to the plates of a capacitor, joined to a time-varying or steady voltage source, carry a conduction current but no displacement current. (Alternatively, A circuit, having no capacitor in it, and carrying a current has conduction current but no displacement current.)

Long Answer Type

Question 1.
Answer the following:
(a) Name the em waves which are used for the treatment of certain forms of cancer. Write their frequency range.
Answer:
Gamma rays.
Frequency range > 3 × 10²⁰ Hz

(b) Thin ozone layer on top of the stratosphere is crucial for human survival. Why?
Answer:
The thin ozone layer on top of the stratosphere is crucial for human survival because it absorbs most of the ultraviolet rays coming from the sun. If the ozone layer had not been there, then ultraviolet rays would have entered the earth and caused danger to the survival of the human race.

(c) An em wave exerts pressure on the surface on which it is incident. Justify. (CBSE Delhi 2014)
Answer:
An em wave carries a linear momentum with it. The linear momentum carried by a portion of a wave having energy U is given by p = U/c.

Thus, if the wave incident on a material surface is completely absorbed, it delivers energy U and momentum p = U/c to the surface. If the wave is totally reflected, the momentum delivered is p = 2U/c because the momentum of the wave changes from p to – p. Therefore, it follows that an em wave incident on a surface exerts a force and hence a pressure on the surface.

Question 2.
Answer the following questions:
(a) Why is the thin ozone layer at the top of the stratosphere crucial for human survival? Identify to which part of the electromagnetic spectrum does this radiation belongs and write one important application of the radiation.
Answer:
The thin ozone layer on top of the stratosphere is crucial for human survival because it absorbs most of the ultraviolet rays coming from the sun. If the ozone layer had not been there, then ultraviolet rays would have entered the earth and caused danger to the survival of the human race. This radiation is UV radiation. It is used in sterilization.

(b) Why are infrared waves referred to as heat rays? How are they produced? What role do they play in maintaining the earth’s warmth through the greenhouse effect? (CBSE Delhi 2015C)
Answer:
Infrared radiations heat up the material on which they fall, hence they are also called heat rays. They are produced by the vibration of atoms and molecules. After falling on the earth, they are reflected back into the earth’s atmosphere. The earth’s atmosphere does not allow these radiations to pass through as such they heat up the earth’s atmosphere.

Question 3.
How are electromagnetic waves produced? What is the source of energy of these waves? Write mathematical expressions for electric and magnetic fields of an electromagnetic wave propagating along the z-axis. Write any two important properties of electromagnetic waves. (CBSE AI 2016)
Answer:
Electromagnetic waves are produced by accelerated charges which produce an oscillating electric field and magnetic field (which regenerate each other).

• Source of the Energy: Energy of the accelerated charge or the source that accelerates the charges.
• Expression: E_x = E_o sin (kz – ωt) and B_y = B_o sin (kz – ωt)
  (a) They are transverse in nature.
  (b) They don’t require a medium to propagate.

Question 4.
How are em waves produced by oscillating charges?
Draw a sketch of linearly polarised em waves propagating in the Z-direction. Indicate the directions of the oscillating electric and magnetic fields. (CBSE Delhi 2016)
Answer:
(a) An oscillating charge produces an oscillating electric field in space, which produces an oscillating magnetic field. The oscillating electric and magnetic fields regenerate each other, and this results in the production of em waves in space.
(b) See Figure.

Question 5.
Write Maxwell’s generalization of Ampere’s Circuital Law. Show that in the process of charging a capacitor, the current produced within the plates of the capacitor is i = ε_o\(\frac{d \phi_{E}}{d t}\) where ΦE is the electric flux produced during charging of the capacitor plates. (CBSE Delhi 2016)
Answer:
The generalized form of Maxwell ampere law is
\(\oint \vec{B} \cdot \overrightarrow{d l}\)= μ_o(l + l_D) where l_D = ε_o\(\frac{d \phi_{E}}{d t}=\frac{d q}{d t}\)

The electric flux Φ between the plates of the parallel plate capacitor through which a time-dependent current flow is given by:
Φ_E = E A, but E = σ/ε_o
Therefore we have

Question 6.
(a) Why are Infrared waves often called heatwaves? Explain.
Answer:
Infrared waves have frequencies lower than those of visibLe Light; they have the ability to vibrate not only the electrons but the entire atoms or molecules of a body. This vibration increases the internal energy and temperature of the body. That is why infrared waves are often called heat waves.

(b) What do you understand by the statement, “Electromagnetic waves transport momentum”? (CBSE AI, Delhi 2018)
Answer:
If we consider a plane perpendicular to the direction of propagation of the electromagnetic wave, then electric charges present on the plane will be set and sustained in motion by the electric and magnetic fields of the electromagnetic wave. The charges present on the surface thus acquire energy and momentum from the waves. This just illustrates the fact that an electromagnetic wave (like other waves) transfers energy and momentum.

Question 7.
(a) When the oscillating electric and magnetic fields are along the x- and y-direction respectively
(i) point out the direction of propagation of the electromagnetic wave,
Answer:
Z-axis

(ii) express the velocity of propagation in terms of the amplitudes of the oscillating electric and magnetic fields.
Answer:
c = E_o / B_o

(b) How do you show that the em wave carries energy and momentum? (CBSE A! 2013C)
Answer:
Consider a plane perpendicular to the direction of propagation of the electromagnetic wave. If there are, on this plane, electric charges, they will be set and sustained in motion by the electric and magnetic fields of the electromagnetic wave. The charges thus acquire energy and momentum from the waves. This illustrates the fact that an electromagnetic wave carries energy and momentum.

Question 8.
Answer the following questions:
(a) Show, by giving a simple example, how em waves carry energy and momentum.
Answer:
Consider a plane perpendicular to the direction of propagation of the electromagnetic wave. If there are, on this plane, electric charges, they will be set and sustained in motion by the electric and magnetic fields of the electromagnetic wave. The charges thus acquire energy and momentum from the waves. This just illustrates the fact that an electromagnetic wave (like other waves) carries energy and momentum.

(b) How are microwaves produced? Why is it necessary in microwave ovens to select the frequency of microwaves to match the resonance frequency of water molecules?
Answer:
Microwaves (short-wavelength radio waves), with frequencies in the gigahertz (GHz) range, are produced by special vacuum tubes (called klystrons, magnetrons, and Gunn diodes). In such ovens, the frequency of the microwaves is selected to match the resonant frequency of water molecules so that energy from the waves is transferred efficiently to the kinetic energy of the molecules. This raises the temperature of any food containing water.

(c) Write two important uses of infrared waves. (CBSE Delhi 2014C)
Answer:
Remote control of electronic devices, heating

Question 9.
A parallel plate capacitor is being charged by a time-varying current. Explain briefly how Ampere’s circuital law is generalized to incorporate the effect due to the displacement current. (CBSE AI 2011)
Answer:
Consider the curve C bounding two surfaces S₁ and S₂. For the bound surface S1; the current passes through it, as such, we can write Ampere’s circuital law as
\(\oint_{s_{1}} \vec{\phi} \cdot \vec{d}\) = μ_ol …(1)

If however, we choose the bound surface S2 that passes through the plates of the capacitor and is not pierced by a current-carrying conductor, then Ampere’s circuital law is written as
\(\oint_{s_{2}} \vec{\phi} \cdot \vec{d}\) = 0 ….(2)

The above two equations contradict each other. To resolve this contradiction, Maxwell showed that this inconsistency is due to the assumed discontinuity of the current. According to Maxwell a current called displacement current “flows” between the plates of the capacitor, where there is no conduction current.

Therefore Ampere’s circuital law takes the generalised expression \(\oint \vec{B} \cdot d \vec{l}\) = μ_o (l + l_D),

here l is the conduction current and lD is the displacement current given by
l_D = ε_o \(\frac{d \phi_{E}}{d t}=\frac{d q}{d t}\).

Outside the plates of the capacitor, conduction current flows and displacement current is zero, whereas inside the plates of the capacitor, displacement current exists and there is no conduction current.

Question 10.
(a) Identify the part of the electromagnetic spectrum used in (i) radar and (ii) eye surgery. Write their frequency range.
Answer:
Microwaves:
Frequency range (10¹⁰ to 10¹² Hz) Ultraviolet rays:
Frequency range (10¹⁵ to 10¹⁷ Hz)

(b) Prove that the average energy density of the oscillating electric field is equal to that of the oscillating magnetic field. (CBSE Delhi 2019)
Answer:
The average density of the electric field is
u_E = \(\frac{1}{2}\)εo E²

Question 11.
Answer the following questions:
(a) Long-distance radio broadcasts use short-wave bands. Why?
Answer:
The long-distance radio broadcast is not possible using long or medium wave bands because these waves, traveling as ground waves, can cover a maximum distance of 200 km. When used as sky waves, the short waves pass through the lower portion of the atmosphere but are reflected back from the ionosphere. In this way, short waves can travel very large distances and can even travel around the earth.

(b) It is necessary to use satellites for long-distance TV transmission. Why?
Answer:
TV waves have a frequency range of 47 MHz to 940 MHz. These frequencies are not reflected by the ionosphere. As space waves, they can cover a distance of 50-60 km only. Therefore, for long-distance TV transmission, we make use of satellites that reflect the TV signal wave back towards the earth.

(c) Optical and radio telescopes are built on the ground but X-ray astronomy is possible only from satellites orbiting the earth. Why?
Answer:
In optical and radio-telescopes we use visible light and radio waves, respectively, which can pass through the atmosphere. Hence, such telescopes are built on the ground. However, X-rays have extremely small wavelengths and are absorbed by the atmosphere. Hence, X-ray astronomy is not possible from ground stations. X-ray astronomy is possible only from satellites orbiting the earth at a height of 500 km or more.

(d) The small ozone layer on top of the stratosphere is crucial for human survival. Why?
Answer:
The thin ozone layer on top of the stratosphere is crucial for human survival because it absorbs most of the ultraviolet rays coming from the sun. If the ozone layer had not been there, then ultraviolet rays would have entered the earth and caused danger to the survival of the human race.

(e) If the earth did not have an atmosphere, would its average surface temperature be higher or lower than what it is now?
Answer:
If the earth did not have an atmosphere, then its average surface temperature would be lesser than what it is now because in that case greenhouse effect will be absent.

(f) Some scientists have predicted that a global nuclear war on the earth would be followed by a severe nuclear winter’ with a devastating effect on life on the earth. What might be the basis of this prediction?
Answer:
The prediction is based on the assumption that the large dust clouds produced by global nuclear war would perhaps cover a substantial part of the sky and solar radiations will not be able to reach the earth. It may cause a severe winter on the earth with a devastating effect on life on the earth.

Numerical Problems

Question 1.
The frequency values v₁ and v₂, for two spectral lines of the e.m. spectrum are found to be 5 × 10²⁰ Hz and 2.5 × 10¹¹ Hz respectively. Find the ratio, λ₁/λ₂ of their wavelengths.
Answer:

Question 2.
In a plane electromagnetic wave, the electric field oscillates with a frequency of 2 × 10¹⁰ Hz and an amplitude of 40 VM.
(i) What is the wavelength of the wave and
(ii) what is the energy density due to the field?
Answer:

Question 3.
A plane electromagnetic wave of frequency 25 MHz travels In free space along the x-direction. At a particular point In space and time, the electric vector is \(\vec{E}\) = 6.3 Vm^-1 ĵ. Calculate \(\vec{B}\) at this point. (NCERT)
Answer:
The magnitude of B and E are related as c = \(\frac{E}{B}\), therefore B = \(\frac{E}{c}=\frac{6.3}{3 \times 10^{8}}\) = 2.1 × 10^-8. This field is along the z-axis, i.e. perpendicular to both the propagation of the wave and the electric field.

Question 4.
The magnetic field in a plane electromagnetic wave Is given by B = 2 × sin (0.5 × 10^-3 x + 1.5 × 10¹¹ t) T
(a) What are the wavelength and frequency of the wave?
Answer:
(a) Comparing the given equation with the equation

(b) Write an expression for the electric field. (NCERT)
Answer:
E_o = cB_o = 2 × 10⁷ × 3 × 10⁸ = 60 Vm^-1

The electric field component is perpendicular to the direction of propagation and the direction of the magnetic field. Therefore, the electric field component aLong the z-axis is obtained as
E_z = 60 sin(0.5 × 10^{3 ×} + 1.5 × 10¹¹ t)Vm^-1

Question 5.
A radio can tune In to any station in the 7.5 MHz to 12 MHz bands. What is the corresponding wavelength band? (NCERT)
Answer:

Thus the wavelength band is 40 m to 25m.

Question 6.
Suppose that the electric field amplitude of an electromagnetic wave E₀ = 120 N C^-1 and that Its frequency is v = 50.0 MHz. (a) Determine, B0, ω k, and λ. (b) Find expressions for E and B. (NCERT)
Answer:


Question 7.
In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 × 10¹⁰ Hz and amplitude 48 V m^-1.
(a) What is the wavelength of the wave?
(b) What is the amplitude of the oscillating magnetic field?
(c) Show that the average energy density of the E field equals the average energy density of the 8 fields. [c = 3 × 10⁸ms^-1.] (NCERT)
Answer:

(c) The average density of electric field is
given by U_e = \(\frac{1}{2}\)ε₀E² and the average energy density of the magnetic field is given by U_B = \(\frac{B^{2}}{2 \mu_{0}}\). But B = \(\frac{E}{c}\) and C = \(\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}\) , hence the above equation becomes UB = \(\frac{B^{2}}{2 \mu_{0}}=\frac{E^{2}}{2 \mu_{0} c^{2}}\),

Question 8.
Suppose that the electric field part of an electromagnetic wave in a vacuum is
E = {(3.1 NC^-1>)cos(1.8 rad m^-1)y + (5.4 × 106 rad s^-1)t}î
(a) What is the direction of propagation?
(b) What is the wavelength?
(c) What is the frequency v?
(d) What is the amplitude of the magnetic field part of the wave?
(e) Write an expression for the magnetic field part of the wave. (NCERT)
Answer:
The electric field is of the form

(e) Expression for magnetic field part of the wave
\(\vec{B}\) = B_o cos (ky + ωt) k̂
or
\(\vec{E}\) = {(10.3 n T)cos[(1.8 rad m^-1)y + (5.4 × 10⁶ rad s^-1)t} î