Physics · Textbook solutions
Electromagnetic Waves
Every solved example, exercise, and miscellaneous question, in the order the textbook teaches them. Plus every board question asked from this chapter. · 19 questions
Worked Examples
2 q
Solved Examples
Worked · 2
- Eg 8.1A plane electromagnetic wave of frequency travels in free space along the -direction. At a particular point in space and time, . What is at this point?
- Eg 8.2The magnetic field in a plane electromagnetic wave is given by . (a) What is the wavelength and frequency of the wave? (b) Write an expression for the electric field.
Exercises
17 q
- Ex 8.1(a)Figure 8.5 shows a capacitor made of two circular plates each of radius , and separated by . The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to . (a) Calculate the capacitance and the rate of change of potential difference between the plates.
- Ex 8.1(b)Figure 8.5 shows a capacitor made of two circular plates each of radius , and separated by . The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to . (b) Obtain the displacement current across the plates.
- Ex 8.1(c)Figure 8.5 shows a capacitor made of two circular plates each of radius , and separated by . The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to . (c) Is Kirchhoff's first rule (junction rule) valid at each plate of the capacitor? Explain.
- Ex 8.2(a)A parallel plate capacitor (Fig. 8.6) made of circular plates each of radius has a capacitance . The capacitor is connected to a ac supply with a (angular) frequency of . (a) What is the rms value of the conduction current?
- Ex 8.2(b)A parallel plate capacitor (Fig. 8.6) made of circular plates each of radius has a capacitance . The capacitor is connected to a ac supply with a (angular) frequency of . (b) Is the conduction current equal to the displacement current?
- Ex 8.2(c)A parallel plate capacitor (Fig. 8.6) made of circular plates each of radius has a capacitance . The capacitor is connected to a ac supply with a (angular) frequency of . (c) Determine the amplitude of at a point from the axis between the plates.
- Ex 8.3What physical quantity is the same for X-rays of wavelength , red light of wavelength and radiowaves of wavelength ?
- Ex 8.4A plane electromagnetic wave travels in vacuum along -direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is , what is its wavelength?
- Ex 8.5A radio can tune in to any station in the to band. What is the corresponding wavelength band?
- Ex 8.6A charged particle oscillates about its mean equilibrium position with a frequency of . What is the frequency of the electromagnetic waves produced by the oscillator?
- Ex 8.7The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is . What is the amplitude of the electric field part of the wave?
- Ex 8.8(a)Suppose that the electric field amplitude of an electromagnetic wave is and that its frequency is . (a) Determine , , , and .
- Ex 8.8(b)Suppose that the electric field amplitude of an electromagnetic wave is and that its frequency is . (b) Find expressions for and .
- Ex 8.9The terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula (for energy of a quantum of radiation: photon) and obtain the photon energy in units of eV for different parts of the electromagnetic spectrum. In what way are the different scales of photon energies that you obtain related to the sources of electromagnetic radiation?
- Ex 8.10(a)In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of and amplitude . [Take .] (a) What is the wavelength of the wave?
- Ex 8.10(b)In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of and amplitude . [Take .] (b) What is the amplitude of the oscillating magnetic field?
- Ex 8.10(c)In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of and amplitude . [Take .] (c) Show that the average energy density of the field equals the average energy density of the field.
What the board has asked from this chapter
Questions per paper · 26 papers · 2022 to 2026
Bars average the full papers of each year. 37 further questions come from set variants and are listed below.
2022: 1.2 questions per paper. 2023: 2.4 questions per paper. 2024: 2 questions per paper. 2025: 2 questions per paper. 2026: 2 questions per paper
2026
20 q
- 3A plane electromagnetic wave travels through a medium and the magnetic field associated with it is given by T where x is in metres and t is in seconds. The velocity of the wave is :
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 5An electromagnetic wave passes from vacuum into a dielectric medium with relative electrical permittivity (3/2) and relative magnetic permeability (8/3). Then, its
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 6The magnetic field in a plane electromagnetic wave travelling in glass (n = ) is given by where x is in metres and t is in seconds. The value of is :
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 7The electric field and the magnetic field components of an electromagnetic wave travelling in vacuum are represented as where m, n, and are constants characterising the wave. Then
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 7The ratio of amplitude of electric field to the amplitude of the magnetic field associated with an electromagnetic wave propagating in glass is :
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 7Electromagnetic waves used for purification of water are
Tap an option to check your answer.
Electromagnetic Spectrum - 7The expression of magnetic fields associated with four electromagnetic waves are given below : I. II. III. IV. Which wave is travelling in free space ?
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 7Electromagnetic waves used in a diagnostic tool in medicine have a wavelength range
Tap an option to check your answer.
Electromagnetic Spectrum - 9Welders wear special glass goggles or face masks with glass windows to protect their eyes from
Tap an option to check your answer.
Electromagnetic Spectrum - 11An electromagnetic wave is propagating along x-axis. At any instant, the phase difference (in radian) between the electric field and the magnetic field associated with the wave is
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 22What is meant by displacement current ? A capacitor is being charged by a battery. Show that Ampere-Maxwell law justifies continuity and constancy of the current flowing in the circuit.Displacement Current
- 24Name the electromagnetic waves which are used for (i) detection of fractures in bones (ii) physiotherapy (iii) radar systems Also write their wavelength range.Electromagnetic Spectrum
- 25What is displacement current ? Considering the case of charging of a capacitor, show that . What is the value of for a conductor across which a constant voltage is applied ?Displacement Current
- 24Name the electromagnetic waves which are used (i) as a diagnostic tool in medicine (ii) in remote switches for TV sets (iii) in water purifiers Also write their wavelength range.Electromagnetic Spectrum
- 25What are infrared waves ? Why are these waves referred to as 'heat waves' ? Give any two uses of these waves.Electromagnetic Spectrum
- 25What are X-rays ? How are they produced ? Give two uses of X-rays.Electromagnetic Spectrum
- 25(a) Depict the variation of electric field and magnetic field with respect to the direction of propagation of an electromagnetic wave. Write their two important characteristics. (b) Show that gives the velocity of an electromagnetic wave in free space.Electromagnetic Waves and their Properties
- 26What are microwaves ? How are they produced ? Give any two uses of microwaves.Electromagnetic Spectrum
- 27Name the electromagnetic waves which are (i) also known as 'heat waves', (ii) used in LASIK eye surgery, (iii) used to destroy cancer cells. Also write their wavelength range.Electromagnetic Spectrum
- 27Differentiate between conduction current and displacement current. A capacitor is connected across a source providing time-dependent current. Explain how the total current at an instant is the sum of conduction current and displacement current in the circuit at that instant.Displacement Current
2025
20 q
- 7The amplitude of electric field in an electromagnetic wave in free space is 1000 . The amplitude of the magnetic field in this electromagnetic wave is :
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 7Which of the following rays coming from the Sun plays an important role in maintaining the Earth's warmth ?
Tap an option to check your answer.
Electromagnetic Spectrum - 7In an electromagnetic wave travelling in free space, the amplitude of magnetic field is T. The amplitude of its electric field is :
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 7X-rays are more harmful to human beings than ultraviolet radiations because X-rays -
Tap an option to check your answer.
Electromagnetic Spectrum - 7The electric field in space between the plates of a parallel plate capacitor (each of area ) is changing at the rate of . The displacement current between the plates of the capacitor is :
Tap an option to check your answer.
Displacement Current - 7Which one of the following correctly represents the change in wave characteristics (all in vacuum) from microwaves to X-rays in electromagnetic spectrum ?
Tap an option to check your answer.
Electromagnetic Spectrum - 7The given diagram exhibits the relationship between the wavelength of the electromagnetic waves and the energy of photon associated with them. The three points P, Q and R marked on the diagram may correspond respectively to :
Tap an option to check your answer.
Electromagnetic Spectrum - 8The dimensions of , where is permittivity and is permeability of a medium, are :
Tap an option to check your answer.
Electromagnetic Waves and their Properties - Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.15Assertion (A) : X-rays are produced when slow moving electrons are stopped by a metal target of high atomic number. Reason (R) : X-rays consist of low-energy photons.
Tap an option to check your answer.
Electromagnetic Spectrum - Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.15Assertion (A) : EM waves do not require a medium for their propagation. Reason (R) : EM waves are transverse waves.
Tap an option to check your answer.
Electromagnetic Waves and their Properties - For Questions 13 to 16, two statements are given – one labelled Assertion (A) and other labelled Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below :15Assertion (A) : Out of Infrared and radio waves, the radio waves show more diffraction effect. Reason (R) : Radio waves have greater frequency than infrared waves.
Tap an option to check your answer.
Electromagnetic Spectrum - 25(a) The amplitude of a light wave becomes n times. This results in intensity of the wave becoming m times. What is the relation between n and m ? (b) White light is incident on three identical surfaces – a black surface, a yellow surface and a white surface, one by one. For which surface, the pressure exerted on the surface by the incident light will be (i) maximum (ii) minimum ? Justify your answer.Electromagnetic Waves and their Properties
- 25(a) How is an electromagnetic wave produced ? (b) An electromagnetic wave is travelling in vertically upward direction. At an instant, its electric field vector points in west direction. In which direction does the magnetic field vector point at that instant ? (c) Estimate the ratio of shortest wave length of radio waves to the longest wave length of gamma waves.Electromagnetic Waves and their Properties
- 25(a) The electric field of an electromagnetic wave propagating in north direction is oscillating in up and down direction. Describe the direction of magnetic field of the wave. (b) Are the wave length of radio waves and microwaves longer or shorter than those detectable by human eyes ? (c) Write main use of each of the following in human life : (i) Infrared waves (ii) Gamma raysElectromagnetic Spectrum
- 25(a) State any three characteristics of electromagnetic waves. (b) Briefly explain how and where the displacement current exists during the charging of a capacitor.Electromagnetic Waves and their Properties
- 25(a) Differentiate between 'conduction current' and 'displacement current', giving one similarity and one dissimilarity between them. (b) Explain the existence of electromagnetic waves in free space, using the concept of displacement current.Displacement Current
- 25Name the electromagnetic wave used (i) in radar, (ii) in eye surgery and (iii) as diagnostic tool in medicine. Write their wavelength range also.Electromagnetic Spectrum
- 25(a) A parallel plate capacitor is charged by an ac source. Show that the sum of conduction current and the displacement current has the same value at all points of the circuit. (b) In case (a) above, is Kirchhoff's first rule (junction rule) valid at each plate of the capacitor ? Explain.Displacement Current
- 25(a) How are electromagnetic waves produced ? (b) Write the wavelength range and one use of : (i) Microwaves, and (ii) Ultraviolet waves.Electromagnetic Spectrum
- 26Name the electromagnetic radiations and write their frequency range : (a) Used to take the photograph of the bones (b) Produced by hot bodies (c) Used in television communication systemsElectromagnetic Spectrum
2024
19 q
- 6The electromagnetic waves used to purify water are
Tap an option to check your answer.
Electromagnetic Spectrum - 7Welders wear special glass goggles or face masks with glass windows to protect their eyes from radiations produced by welding arcs. These radiations are :
Tap an option to check your answer.
Electromagnetic Spectrum - 7In four regions I, II, III and IV, the magnetic field is given by : I. II. III. IV. The electromagnetic wave will exist in the region :
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 7Electromagnetic waves with wavelength 10 nm are called :
Tap an option to check your answer.
Electromagnetic Spectrum - 8Electromagnetic waves with frequency Hz are known as :
Tap an option to check your answer.
Electromagnetic Spectrum - 8Which one of the following has the highest frequency ?
Tap an option to check your answer.
Electromagnetic Spectrum - 8The electric and magnetic fields of electromagnetic waves are :
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 8A plane electromagnetic wave is travelling in air in + x direction. At a particular moment, its electric field is along + y direction. At that moment, the magnetic field is along :
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 8The first scientist who produced and observed electromagnetic waves of wavelengths in the range 25 mm – 5 mm was :
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 8In the four regions, I, II, III and IV, the electric fields are described as : Region I : Region II : Region III : Region IV : The displacement current will exist in the region :
Tap an option to check your answer.
Displacement Current - 10The phase difference between electric field and magnetic field in an electromagnetic wave propagating along z-axis is -
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 23(a) On what factors does the speed of an electromagnetic wave in a medium depend ? (b) How is an electromagnetic wave produced ? (c) Sketch a schematic diagram depicting the electric and magnetic fields for an electromagnetic wave propagating along z-axis.Electromagnetic Waves and their Properties
- 25The electric field in an electromagnetic wave in vacuum is given by : (a) Find the wavelength and frequency of the wave. (b) What is the amplitude of the magnetic field of the wave ? (c) Write an expression for the magnetic field of this wave.Electromagnetic Waves and their Properties
- 25Name the part of the electromagnetic spectrum which are (i) stopped by face mask worn by welders. (ii) used in detectors in Earth satellites. (iii) used in 'short-wave band' in communication. Also write the order of wavelengths, in each case.Electromagnetic Spectrum
- 26What is meant by displacement current ? How is this current different from the conduction current ? A capacitor is being charged by a source of emf. Justify the continuity of current in the circuit.Displacement Current
- 26(a) “The wavelength of the electromagnetic wave is often correlated with the characteristic size of the system that radiates.” Give two examples to justify this statement. (b) (i) Long distance radio broadcasts use short-wave bands. Why ? (ii) Optical and radio telescopes are built on the ground, but X-ray astronomy is possible only from satellites orbiting the Earth. Why ?Electromagnetic Spectrum
- 27Name the electromagnetic waves with their wavelength range which are used for (i) FM radio broadcast (ii) detection of fracture in bones (iii) treatment of muscular strainElectromagnetic Spectrum
- 26(a) Name the parts of the electromagnetic spectrum which are (i) also known as 'heat waves' and (ii) absorbed by ozone layer in the atmosphere. (b) Write briefly one method each, of the production and detection of these radiations.Electromagnetic Spectrum
- 27Explain the following giving reasons : (i) 'Electromagnetic waves differ considerably in their mode of interaction with matter'. (ii) 'Food items to be heated in microwave oven must contain water'. (iii) 'Welders wear face mask with glasses during welding'.Electromagnetic Spectrum
2023
22 q
- 1The ratio of the magnitudes of the electric field and magnetic field of a plane electromagnetic wave is
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 3An electromagnetic wave is produced by a charge
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 5Which one of the following electromagnetic radiation has the least wavelength ?
Tap an option to check your answer.
Electromagnetic Spectrum - 5The electromagnetic waves used in radar systems are :
Tap an option to check your answer.
Electromagnetic Spectrum - 5Choose the correct option related to wavelengths () of different parts of electromagnetic spectrum.
Tap an option to check your answer.
Electromagnetic Spectrum - 5A capacitor is charged by a battery. Between the plates, during process of charging :
Tap an option to check your answer.
Displacement Current - 7The electromagnetic radiations used to kill germs in water purifiers are called :
Tap an option to check your answer.
Electromagnetic Spectrum - 7and represent the electric and the magnetic field of an electromagnetic wave respectively. The direction of propagation of the wave is along
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 8Name the electromagnetic waves also known as 'heat waves'.
Tap an option to check your answer.
Electromagnetic Spectrum - 8In the process of charging of a capacitor, the current produced between the plates of the capacitor is : (where symbols have their usual meanings.)
Tap an option to check your answer.
Displacement Current - 12Electromagnetic waves of wavelength of the order of a few meters were first produced and detected in the laboratory by :
Tap an option to check your answer.
Electromagnetic Waves and their Properties - 20What is meant by the term ‘displacement current’ ? Briefly explain how this current is different from a conduction current.Displacement Current
- 20Consider an induced magnetic field due to changing electric field and an induced electric field due to changing magnetic field. Which one is more easily observed ? Justify your answer.Displacement Current
- 20 (a)How are infrared waves produced ? Why are these waves referred to as heat waves ? Give any two uses of infrared waves.Electromagnetic Spectrum
- 20 (b)How are X-rays produced ? Give any two uses of these.Electromagnetic Spectrum
- 22 (a)What is a displacement current ? How is it different from a conduction current ?Displacement Current
- 21Identify the electromagnetic wave whose wavelengths range is from about (a) m to about m. (b) m to about m. Write one use of each.Electromagnetic Spectrum
- 21Identify the electromagnetic radiation and write its wavelength range, which is used to kill germs in water purifier. Name the two sources of these radiations.Electromagnetic Spectrum
- 21How are electromagnetic waves produced ? Write their two characteristics.Electromagnetic Waves and their Properties
- 22 (b)Write any two characteristics of an electromagnetic wave. Why are microwaves used in radar systems ?Electromagnetic Waves and their Properties
- 22A plane electromagnetic wave propagates in vacuum along x-axis. (a) Give the direction of electric field and magnetic field vectors. (b) and are the magnitudes of electric and magnetic fields respectively in a plane electromagnetic wave. Find the ratio of energy densities of electric field and magnetic field.Electromagnetic Waves and their Properties
- 24Identify the part of electromagnetic spectrum which is : (a) next to the lowest frequency end of the visible part of electromagnetic spectrum, and (b) produced by bombarding a metal target by high energy electrons. Give one use of each of them.Electromagnetic Spectrum
2022
6 q
- 4 (a)(i) Depict a plane electromagnetic wave propagating along the x-axis. Write the expressions for its oscillating electric and magnetic fields. (ii) Write three characteristics of electromagnetic waves.Electromagnetic Waves and their Properties
- 4 (b)Name the electromagnetic waves which are produced by the following : (i) Radioactive decays of nucleus (ii) Welding arcs (iii) Hot bodies Write one use each of these waves.Electromagnetic Spectrum
- 11 (a)Electromagnetic waves of wavelengths , and are used in radar systems, in water purifiers and in remote switches of TV, respectively. (i) Identify the electromagnetic waves, and (ii) Write one source of each of them.Electromagnetic Spectrum
- 11 (a)(i) Arrange the following electromagnetic radiation in the ascending order of their frequencies : X-rays, microwaves, gamma rays, radio waves (ii) Write two uses of any two of these radiation.Electromagnetic Spectrum
- 11 (a)Identify electromagnetic waves which : (i) are used in radar system. (ii) affect a photographic plate. (iii) are used in surgery. Write their frequency range.Electromagnetic Spectrum
- 11 (a)(i) Monochromatic light is incident on a surface separating two media. The frequency of the light after refraction remains unaffected but its wavelength changes. Why ? (ii) The frequency of an electromagnetic radiation is Hz. Identify the radiation and mention its two uses.Electromagnetic Spectrum
The 10 board questions to practise first
The questions the board asked again come first, most asked first. Each one says how often and when.
Question 1
Asked 3 times: 2023, 2024, 2026
7Electromagnetic waves used for purification of water areTap an option to check your answer.
Question 2
Asked 2 times: 2024, 2026
9Welders wear special glass goggles or face masks with glass windows to protect their eyes fromTap an option to check your answer.
Question 3
Asked 2 times: 2023, 2026
25What are infrared waves ? Why are these waves referred to as 'heat waves' ? Give any two uses of these waves.Question 4
Asked 2 times: 2023, 2026
25What are X-rays ? How are they produced ? Give two uses of X-rays.Question 5
Asked 2 times: 2024, 2026
11An electromagnetic wave is propagating along x-axis. At any instant, the phase difference (in radian) between the electric field and the magnetic field associated with the wave isTap an option to check your answer.
Question 6
Asked 2 times: 2024, 2026
22What is meant by displacement current ? A capacitor is being charged by a battery. Show that Ampere-Maxwell law justifies continuity and constancy of the current flowing in the circuit.Question 7
This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026
24Name the electromagnetic waves which are used for (i) detection of fractures in bones (ii) physiotherapy (iii) radar systems Also write their wavelength range.Question 8
This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2025
25(a) Differentiate between 'conduction current' and 'displacement current', giving one similarity and one dissimilarity between them. (b) Explain the existence of electromagnetic waves in free space, using the concept of displacement current.Question 9
This type asked 4 times: 2022, 2023, 2024, 2025. This one: 2025
7Which one of the following correctly represents the change in wave characteristics (all in vacuum) from microwaves to X-rays in electromagnetic spectrum ?Tap an option to check your answer.
Question 10
This type asked 3 times: 2023, 2025, 2026. This one: 2026
25What is displacement current ? Considering the case of charging of a capacitor, show that . What is the value of for a conductor across which a constant voltage is applied ?