Electromagnetic Wave

01

PYQ 2024

medium

physics ID: up-board

What do you mean by the current sensitivity of a moving coil galvanometer? Resistance of a galvanometer is and for full-scale deflection, the current is . What would be the required length of a wire to convert it into an ammeter of 5 A range? (Area of cross-section of wire =, specific resistance of the wire material =)

02

PYQ 2024

medium

physics ID: up-board

The amplitude of the magnetic field of an electromagnetic wave in vacuum is . What is the amplitude of the electric field of the wave?

03

PYQ 2025

easy

physics ID: up-board

Equation of electric field of a plane electromagnetic wave is given as: Write the equation for the magnetic field of the wave.

04

PYQ 2025

easy

physics ID: up-board

What are the electromagnetic waves? Write down its characteristics.

05

PYQ 2025

medium

physics ID: up-board

What are electromagnetic waves? Give a brief description of the main properties of electromagnetic waves. The equation for oscillation of the magnetic field of an electromagnetic wave is . Find the wavelength and equation for the oscillating electric field. Mention the direction of propagation of the wave also.}

Official Solution

Correct Option: (1)

$Electromagnetic waves are a combination of electric and magnetic fields that oscillate perpendicular to each other and to the direction of propagation. They travel at the speed of light,, and do not require a medium for propagation. The general equation for a magnetic field in an electromagnetic wave is given by: Where: - is the magnetic field, - is the maximum magnetic field (amplitude), - is the wave number, - is the angular frequency, - is the position along the x-axis, and - is time. From the given equation, we can compare the terms with the standard wave equation. Here: -, - The angular frequency, - The wave number . Now, the wavelength is related to the wave number by the equation: Substitute : Next, the electric field oscillates in the same direction as the magnetic field but is perpendicular to it. The magnitude of the electric field is related to the magnetic field by the equation: Substitute and : Thus, the equation for the oscillating electric field is: Where . The direction of propagation is along the -axis, which is determined by the cross-product of the electric field and magnetic field vectors. Thus, the wave is traveling in the positive -direction.$

06

PYQ 2025

medium

physics ID: up-board

$A free electron is placed in the path of a plane electromagnetic waves. The electron will start moving$

1

$along the direction of electric field.$

2

$along the direction of magnetic field.$

3

$along the direction of propagation of wave.$

4

$in a plane containing the magnetic field and direction of propagation.$

Official Solution

Correct Option: (1)

$Step 1: Understanding the Concept: An electromagnetic (EM) wave consists of oscillating electric () and magnetic () fields. These fields are perpendicular to each aother and to the direction of wave propagation. A charge placed in the path of an EM wave will experience forces from both these fields, as described by the Lorentz force equation. Step 2: Key Formula or Approach: The total force (Lorentz force) on a charge in the presence of electric field and magnetic field is: Here, for an electron. The electron is initially free, so we can assume its initial velocity is zero. Step 3: Detailed Explanation: When the free electron is initially placed in the path of the EM wave, its velocity is zero. Let's analyze the Lorentz force at this initial moment (): The magnetic force component is initially zero because the electron is at rest. The only force acting on the electron at the moment it is placed in the wave is the electric force, . This force will cause the electron to accelerate. The direction of this initial acceleration (and hence the initial motion) is opposite to the direction of the electric field (due to the negative charge). However, since the electric field of an EM wave is oscillating, the force will also be oscillating. The motion of the electron will be along the line of the electric field vector. Comparing the magnitudes of the forces: The force due to the electric field is . Once the electron starts moving, it will also experience a magnetic force . For an EM wave, the magnitudes of the fields are related by, where is the speed of light. Thus, . Since the velocity of the electron will be much smaller than the speed of light (), the magnetic force is significantly weaker than the electric force . The dominant force that governs the motion of the electron is the electric force. Step 4: Final Answer: The electron will primarily be driven by the electric field and will start moving along the direction of the electric field.$

07

PYQ 2025

medium

physics ID: up-board

$What is meant by displacement current? The amplitude of electric field of an electromagnetic wave is and frequency is . Find out: i) Amplitude of the magnetic field ii) Wavelength of the electromagnetic wave.$

Official Solution

Correct Option: (1)

$Displacement Current: Displacement current is a term introduced by James Clerk Maxwell to extend Ampère's law to situations involving time-varying electric fields. The displacement current density is given by: where: - is the displacement current density, - is the permittivity of free space, - is the rate of change of the electric field with respect to time. The displacement current plays a crucial role in explaining how electric fields can generate magnetic fields in a vacuum or in materials with varying electric fields, forming the foundation of electromagnetic wave propagation. i) Amplitude of the Magnetic Field : The electric field and the magnetic field in an electromagnetic wave are related by the speed of light . The relationship between the electric and magnetic field amplitudes in an electromagnetic wave is: where: - is the speed of light in vacuum (), - is the amplitude of the magnetic field. Rearranging the formula to solve for : Substituting the given values and : So, the amplitude of the magnetic field is . ii) Wavelength of the Electromagnetic Wave: The wavelength of an electromagnetic wave is related to its frequency by the equation: where: - is the speed of light in vacuum (), - is the frequency of the wave. Substituting the given value of frequency : So, the wavelength of the electromagnetic wave is .$

08

PYQ 2025

medium

physics ID: up-board

$Write down any two uses of microwaves.$

Official Solution

Correct Option: (1)

$Microwaves are a form of electromagnetic radiation with wavelengths ranging from 1 mm to 1 m, which places them between radio waves and infrared light in the electromagnetic spectrum. Their unique properties make them ideal for various applications. Two important uses of microwaves are: 1. Communication: Microwaves are widely used for communication, especially in satellite communication and mobile phone networks. In satellite communication, microwaves are transmitted through the atmosphere to relay signals between satellites and the Earth. These waves are capable of traveling long distances and can pass through clouds, rain, and fog, making them ideal for long-distance communication. Additionally, microwaves are used in radar systems to detect objects and measure distances, speeds, and velocities. 2. Cooking: Microwaves are commonly used in microwave ovens to heat and cook food. The microwaves are absorbed by water molecules in the food, causing them to vibrate and produce heat. This results in the cooking or heating of food, with the process being much faster than traditional heating methods. Microwaves penetrate the food and excite water molecules, which helps in evenly heating the food from within.$

09

PYQ 2025

medium

physics ID: up-board

$What is the effect on the capacitance of a parallel plate capacitor when (i) distance between the plates is doubled. (ii) area of the plates is halved. (iii) a dielectric medium is filled between the plates.$

Official Solution

Correct Option: (1)

$Step 1: Key Formula: The capacitance (C) of a parallel plate capacitor with plate area A, distance between plates d, and vacuum (or air) between the plates is given by the formula: where is the permittivity of free space. We will use this formula as the baseline for all three cases. Step 2: Analysis of each case: (i) Distance between the plates is doubled. The initial capacitance is . The new distance is . The new capacitance,, will be: Effect: The capacitance is halved. (ii) Area of the plates is halved. The initial capacitance is . The new area is . The new capacitance,, will be: Effect: The capacitance is halved. (iii) A dielectric medium is filled between the plates. When a dielectric medium of dielectric constant K is completely filled between the plates, the capacitance formula becomes: Since the original capacitance was, we can write: For any dielectric medium, the dielectric constant K is always greater than 1 (). Effect: The capacitance increases by a factor of K.$

10

PYQ 2025

medium

physics ID: up-board

$What are electromagnetic waves ? By drawing its propagation diagram, show the electric field and magnetic field in it.$

Official Solution

Correct Option: (1)

$Step 1: Definition of Electromagnetic Waves: Electromagnetic (EM) waves are disturbances consisting of time-varying, sinusoidal electric and magnetic fields that oscillate perpendicular to each other and also perpendicular to the direction of wave propagation. Key properties include: They are transverse in nature. They are produced by accelerating electric charges. They do not require a material medium for their propagation and can travel through a vacuum. In a vacuum, they travel at a constant speed, the speed of light, m/s. The electric field ( ) and magnetic field ( ) are always in the same phase. Step 2: Propagation Diagram: The diagram below shows the orientation of the electric field, magnetic field, and the direction of propagation for a plane-polarized electromagnetic wave. \begin{center} \begin{tikzpicture}[scale=1.5, transform shape] % Axes \draw[→, thick] (0,0,0) -- (4,0,0) node[below] {X (Propagation)}; \draw[→, thick] (0,0,0) -- (0,1.5,0) node[left] {Y (E-field)}; \draw[→, thick] (0,0,0) -- (0,0,1.5) node[below right] {Z (B-field)}; % E-field wave (in XY plane) \draw[red, thick] plot[domain=0:3.5, samples=100] (\x, {sin(\x*180/pi r)}, 0); % Arrows for E-field \foreach \x in {0.5, 2.5} { \draw[→, red, thick] (\x*pi/2, 0, 0) -- (\x*pi/2, {sin(\x*pi/2*180/pi r)}, 0) node[left] { }; } % B-field wave (in XZ plane) \draw[blue, thick] plot[domain=0:3.5, samples=100] (\x, 0, {sin(\x*180/pi r)}); % Arrows for B-field \foreach \x in {0.5, 2.5} { \draw[→, blue, thick] (\x*pi/2, 0, 0) -- (\x*pi/2, 0, {sin(\x*pi/2*180/pi r)}) node[below right] { }; } \end{tikzpicture} \end{center} Diagram Explanation: The wave is propagating along the positive X-axis. The electric field vector (in red) oscillates along the Y-axis. The magnetic field vector (in blue) oscillates along the Z-axis. At every point and every instant, is perpendicular to , and both are perpendicular to the direction of propagation. The vectors , , and the propagation vector form a right-handed system ( points in the direction of propagation).$

11

PYQ 2025

medium

physics ID: up-board

$Electro-magnetic wave of minimum frequency is :$

1

$Ultraviolet rays$

2

$X-rays$

3

$Gamma (-) rays$

4

$Micro waves$

Official Solution

Correct Option: (4)

$Step 1: Understanding the Concept: The electromagnetic (EM) spectrum is the range of all types of EM radiation. Radiation is ordered by frequency (or wavelength). We need to identify which of the given options has the lowest frequency. Step 2: Key Formula or Approach: Recall the order of the electromagnetic spectrum. The standard order from lowest frequency (longest wavelength) to highest frequency (shortest wavelength) is: Radio waves Microwaves Infrared Visible Light Ultraviolet X-rays Gamma rays. Step 3: Detailed Explanation: We are given the following options: (A) Ultraviolet rays (B) X-rays (C) Gamma rays (D) Micro waves Comparing their positions in the electromagnetic spectrum: Gamma rays have the highest frequency. X-rays have a lower frequency than gamma rays. Ultraviolet rays have a lower frequency than X-rays. Microwaves have a lower frequency than ultraviolet rays. Therefore, among the given choices, microwaves have the minimum frequency. Step 4: Final Answer: The electromagnetic wave with the minimum frequency among the options is Micro waves.$

12

PYQ 2025

medium

physics ID: up-board

$Name the waves of longest wavelength and highest frequency in the given electromagnetic waves — microwaves, X-rays, radio waves, and -rays. What is meant by displacement current?$

Official Solution

Correct Option: (1)

$In the given set of electromagnetic waves — microwaves, X-rays, radio waves, and -rays — the following observations are made: - Longest Wavelength: Radio waves have the longest wavelength among the given electromagnetic waves. The wavelength of radio waves can range from a few millimeters to several kilometers, which is significantly longer compared to the other waves. - Highest Frequency: -rays (gamma rays) have the highest frequency in the given list. Gamma rays have frequencies greater than Hz, much higher than X-rays, microwaves, or radio waves. Next, the term displacement current refers to a term used in Maxwell’s equations to extend the concept of current to situations involving time-varying electric fields. It is defined as: Where: - is the displacement current, - is the permittivity of free space, - is the time rate of change of the electric flux . Displacement current arises in situations like capacitors in an AC circuit where a changing electric field creates a current in the absence of actual charge movement.$

13

PYQ 2025

medium

physics ID: up-board

$On which principle does the transformer work? What are step-up and step-down transformers? Mention two main losses occurring in transformers. In an ideal transformer, the ratio of turns in primary and secondary coils is 10 : 1. Supply in primary is of 220 V and secondary is connected with a resistance of 220 . Find the value of current flowing in the primary.$

Official Solution

Correct Option: (1)

$A transformer works on the principle of electromagnetic induction and Faraday's law of induction. The voltage induced in the secondary coil is proportional to the ratio of the number of turns in the secondary coil to the number of turns in the primary coil. This relationship is given by the equation: Where and are the voltages in the secondary and primary coils, and and are the number of turns in the secondary and primary coils. In a step-up transformer, the number of turns in the secondary coil is greater than the primary coil, which increases the voltage. In a step-down transformer, the number of turns in the secondary coil is less than the primary coil, which decreases the voltage. Given that, the ratio of turns is, and the resistance in the secondary coil is, we can calculate the current flowing in the secondary coil using Ohm's law: Since the transformer is ideal, the voltage ratio is equal to the turns ratio: Now, calculate the current in the secondary: By conservation of energy and assuming an ideal transformer, the current in the primary coil is related to the current in the secondary by the inverse of the turns ratio:$

14

PYQ 2025

medium

physics ID: up-board

$In electromagnetic waves, phase difference between electric and magnetic field vectors is:$

1

2

3

4

Official Solution

Correct Option: (4)

$Step 1: Relation between and .} In an electromagnetic (EM) wave, the electric field vector, magnetic field vector, and the direction of propagation are all mutually perpendicular. Step 2: Phase relation. The and vectors oscillate in the same phase (they reach maximum and minimum together). Step 3: Conclusion. Therefore, the phase difference between and is .$

15

PYQ 2025

medium

physics ID: up-board

$Show the electromagnetic wave by a diagram and write down its three important properties. Which radiation has the least wavelength in the spectrum of electromagnetic waves?$

Official Solution

Correct Option: (1)

$An electromagnetic wave consists of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation of the wave. These waves travel at the speed of light () in a vacuum. The electric field and magnetic field oscillate in phase, and their energy is transferred through the space. The diagram for an electromagnetic wave is shown below: In the diagram: - The electric field () oscillates in one plane (perpendicular to the direction of wave propagation). - The magnetic field () oscillates in a plane perpendicular to the electric field, and also perpendicular to the direction of wave propagation. - The wave propagates in the direction perpendicular to both the electric and magnetic fields. Three Important Properties of Electromagnetic Waves: 1. Transverse Nature: Electromagnetic waves are transverse waves, meaning the oscillations of the electric and magnetic fields are perpendicular to the direction of wave propagation. 2. Speed of Light: In a vacuum, electromagnetic waves travel at a constant speed of . 3. Electromagnetic Spectrum: Electromagnetic waves encompass a wide range of wavelengths and frequencies, forming the electromagnetic spectrum, which includes radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. The frequency and wavelength of an electromagnetic wave are related by: Where: - is the speed of light (), - is the wavelength, - is the frequency. Which Radiation Has the Least Wavelength? Gamma rays have the least wavelength in the electromagnetic spectrum. They have the highest frequency and the most energy compared to other types of electromagnetic radiation. The wavelength of gamma rays can be as small as, making them the most penetrating form of electromagnetic radiation.$

16

PYQ 2025

medium

physics ID: up-board

$1 GHz frequency corresponds to which region of the electromagnetic spectrum?$

1

$Ultraviolet rays$

2

$Radio waves$

3

$Visible rays$

4

$X-rays$

Official Solution

Correct Option: (2)

$The frequency of electromagnetic waves determines their position in the electromagnetic spectrum. The different regions of the spectrum are associated with different ranges of frequency and wavelength. 1 GHz (gigahertz) corresponds to a frequency of Hz. This frequency is within the range of radio waves in the electromagnetic spectrum, which typically spans from 3 kHz to 300 GHz. Radio waves are used for communication purposes, including television and radio broadcasting. Frequencies around 1 GHz are commonly used in modern communication technologies. Hence, the correct answer is option (B) Radio waves.$

17

PYQ 2025

medium

physics ID: up-board

$What are electromagnetic waves? Give a brief description of the main properties of electromagnetic waves. The equation for oscillation of the magnetic field of an electromagnetic wave is . Find the wavelength and equation for the oscillating electric field. Mention the direction of propagation of the wave also.$

Official Solution

Correct Option: (1)

$Electromagnetic waves are a combination of electric and magnetic fields that oscillate perpendicular to each other and to the direction of propagation. They travel at the speed of light,, and do not require a medium for propagation. The general equation for a magnetic field in an electromagnetic wave is given by: Where: - is the magnetic field, - is the maximum magnetic field (amplitude), - is the wave number, - is the angular frequency, - is the position along the x-axis, and - is time. From the given equation, we can compare the terms with the standard wave equation. Here: -, - The angular frequency, - The wave number . Now, the wavelength is related to the wave number by the equation: Substitute : Next, the electric field oscillates in the same direction as the magnetic field but is perpendicular to it. The magnitude of the electric field is related to the magnetic field by the equation: Substitute and : Thus, the equation for the oscillating electric field is: Where . The direction of propagation is along the -axis, which is determined by the cross-product of the electric field and magnetic field vectors. Thus, the wave is traveling in the positive -direction.$

18

PYQ 2025

medium

physics ID: up-board

$Show the electromagnetic wave by a diagram and write down its three important properties. Which radiation has the least wavelength in the spectrum of electromagnetic waves?$

Official Solution

Correct Option: (1)

$An electromagnetic wave consists of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation of the wave. These waves travel at the speed of light () in a vacuum. The electric field and magnetic field oscillate in phase, and their energy is transferred through the space. The diagram for an electromagnetic wave is shown below: In the diagram: - The electric field () oscillates in one plane (perpendicular to the direction of wave propagation). - The magnetic field () oscillates in a plane perpendicular to the electric field, and also perpendicular to the direction of wave propagation. - The wave propagates in the direction perpendicular to both the electric and magnetic fields. Three Important Properties of Electromagnetic Waves: 1. Transverse Nature: Electromagnetic waves are transverse waves, meaning the oscillations of the electric and magnetic fields are perpendicular to the direction of wave propagation. 2. Speed of Light: In a vacuum, electromagnetic waves travel at a constant speed of . 3. Electromagnetic Spectrum: Electromagnetic waves encompass a wide range of wavelengths and frequencies, forming the electromagnetic spectrum, which includes radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. The frequency and wavelength of an electromagnetic wave are related by: Where: - is the speed of light (), - is the wavelength, - is the frequency. Which Radiation Has the Least Wavelength? Gamma rays have the least wavelength in the electromagnetic spectrum. They have the highest frequency and the most energy compared to other types of electromagnetic radiation. The wavelength of gamma rays can be as small as, making them the most penetrating form of electromagnetic radiation.$

19

PYQ 2025

medium

physics ID: up-board

$Name the waves of longest wavelength and highest frequency in the given electromagnetic waves — microwaves, X-rays, radio waves, and -rays. What is meant by displacement current?$

Official Solution

Correct Option: (1)

$In the given set of electromagnetic waves — microwaves, X-rays, radio waves, and -rays — the following observations are made: - Longest Wavelength: Radio waves have the longest wavelength among the given electromagnetic waves. The wavelength of radio waves can range from a few millimeters to several kilometers, which is significantly longer compared to the other waves. - Highest Frequency: -rays (gamma rays) have the highest frequency in the given list. Gamma rays have frequencies greater than Hz, much higher than X-rays, microwaves, or radio waves. Next, the term displacement current refers to a term used in Maxwell's equations to extend the concept of current to situations involving time-varying electric fields. It is defined as: Where: - is the displacement current, - is the permittivity of free space, - is the time rate of change of the electric flux . Displacement current arises in situations like capacitors in an AC circuit where a changing electric field creates a current in the absence of actual charge movement.$

20

PYQ 2025

medium

physics ID: up-board

$Equation of electric field of a plane electromagnetic wave is given as: Write the equation for the magnetic field of the wave.$

Official Solution

Correct Option: (1)

$To find the magnetic field of the electromagnetic wave, we need to utilize the relationship between the electric and magnetic fields in a plane electromagnetic wave. In such a wave, the electric field and the magnetic field are related by the speed of light, and they are perpendicular to each other, as well as to the direction of propagation of the wave. For an electromagnetic wave traveling along the -axis, the electric and magnetic fields are related by the following equation: Where: - is the electric field, - is the magnetic field, - is the speed of light in a vacuum, which is . Thus, the magnetic field can be written as: Given that the electric field is: we can substitute this into the equation for : Now, simplifying the expression: We can calculate the constant factor: Thus, the equation for the magnetic field becomes: Interpretation of the Result: - The magnetic field has the same functional form as the electric field, since they are both sinusoidal waves with the same frequency and wavevector. - The only difference is the amplitude, which is scaled by a factor of, due to the relationship between the electric and magnetic fields in an electromagnetic wave. - The phase of the wave, as well as the wavevector and angular frequency, remain unchanged. - The magnetic field oscillates in sync with the electric field but is scaled by the factor related to the speed of light.$

21

PYQ 2025

easy

physics ID: up-board

$The amplitude of electric field vector of a plane electromagnetic wave is N/C and frequency MHz. Find out (i) Amplitude of magnetic field () (ii) Angular frequency () (iii) Wavelength ()$

Official Solution

Correct Option: (1)

22

PYQ 2025

medium

physics ID: up-board

$What is meant by 'displacement current' and write modified equation of Ampere's law.$

Official Solution

Correct Option: (1)

$Step 1: Understanding the Concept: James Clerk Maxwell discovered an inconsistency in Ampere's Circuital Law, particularly when applied to situations with time-varying electric fields, such as the charging or discharging of a capacitor. To resolve this, he introduced the concept of displacement current. Step 2: Explanation of Displacement Current: Displacement current () is not a current in the traditional sense of flowing charges (which is conduction current,). Instead, it is a theoretical current that is associated with a changing electric field. Consider the gap between the plates of a capacitor being charged. While charges flow in the connecting wires (), no charge actually crosses the gap. However, as charge accumulates on the plates, the electric field () between the plates changes with time. This changing electric field produces a magnetic field in the gap, just as a real current would. Maxwell defined this displacement current as being proportional to the rate of change of electric flux () through a surface. The displacement current is given by the formula: where is the electric flux and is the permittivity of free space. The existence of displacement current implies that a changing electric field is a source of a magnetic field. Step 3: Modified Ampere's Law (Ampere-Maxwell Law): The original Ampere's law was . Maxwell modified this by adding the displacement current term to the total current. The modified law, known as the Ampere-Maxwell Law, states that the line integral of the magnetic field around a closed loop is proportional to the sum of the conduction current () and the displacement current () passing through the surface enclosed by the loop. The equation is: Substituting the expression for, we get:$

23

PYQ 2025

medium

physics ID: up-board

$The frequency range of ultraviolet radiation in electromagnetic radiation spectrum is$

1

$Hz$

2

$Hz$

3

$Hz$

4

$and above$

Official Solution

Correct Option: (3)

$Step 1: Understanding the Concept: The electromagnetic (EM) spectrum is the range of all types of EM radiation. Radiation is classified by wavelength or frequency. The order of the spectrum in terms of increasing frequency (and decreasing wavelength) is: Radio waves, Microwaves, Infrared, Visible light, Ultraviolet, X-rays, Gamma rays. Step 2: Detailed Explanation: Let's analyze the given frequency ranges: \begin{itemize} \item Visible Light: The visible spectrum, which our eyes can see, ranges from approximately Hz (red) to Hz (violet). \item Ultraviolet (UV) Radiation: UV radiation has a frequency just higher than that of violet light. Its range typically starts from the end of the visible spectrum and extends upwards. The accepted range for UV is roughly Hz to Hz. \end{itemize} (A) Hz: This corresponds to the microwave and far-infrared region. (B) Hz: This corresponds to the infrared region. (C) Hz: This range begins at the boundary of infrared/visible light and extends through the entire ultraviolet region, up to the start of the X-ray region. This is the most appropriate range among the choices. (D) and above: Frequencies above Hz are generally classified as X-rays and Gamma rays. Step 3: Final Answer: The frequency range that best represents ultraviolet radiation from the given options is Hz. Therefore, option (C) is correct.$

24

PYQ 2025

medium

physics ID: up-board

$1 GHz frequency corresponds to which region of the electromagnetic spectrum?$

1

$Ultraviolet rays$

2

$Radio waves$

3

$Visible rays$

4

$X-rays$

Official Solution

Correct Option: (2)

$The frequency of electromagnetic waves determines their position in the electromagnetic spectrum. The different regions of the spectrum are associated with different ranges of frequency and wavelength. 1 GHz (gigahertz) corresponds to a frequency of Hz. This frequency is within the range of radio waves in the electromagnetic spectrum, which typically spans from 3 kHz to 300 GHz. Radio waves are used for communication purposes, including television and radio broadcasting. Frequencies around 1 GHz are commonly used in modern communication technologies. Hence, the correct answer is option (B) Radio waves.$

25

PYQ 2025

medium

physics ID: up-board

$What is meant by displacement current? The amplitude of electric field of an electromagnetic wave is and frequency is . Find out: i) Amplitude of the magnetic field ii) Wavelength of the electromagnetic wave.$

Official Solution

Correct Option: (1)

$Displacement Current: Displacement current is a term introduced by James Clerk Maxwell to extend Ampère's law to situations involving time-varying electric fields. The displacement current density is given by: where: - is the displacement current density, - is the permittivity of free space, - is the rate of change of the electric field with respect to time. The displacement current plays a crucial role in explaining how electric fields can generate magnetic fields in a vacuum or in materials with varying electric fields, forming the foundation of electromagnetic wave propagation. i) Amplitude of the Magnetic Field : The electric field and the magnetic field in an electromagnetic wave are related by the speed of light . The relationship between the electric and magnetic field amplitudes in an electromagnetic wave is: where: - is the speed of light in vacuum (), - is the amplitude of the magnetic field. Rearranging the formula to solve for : Substituting the given values and : So, the amplitude of the magnetic field is . ii) Wavelength of the Electromagnetic Wave: The wavelength of an electromagnetic wave is related to its frequency by the equation: where: - is the speed of light in vacuum (), - is the frequency of the wave. Substituting the given value of frequency : So, the wavelength of the electromagnetic wave is .$

26

PYQ 2025

medium

physics ID: up-board

$Explain the difference between self-inductance and mutual inductance. Define the coefficient of self-inductance and coefficient of mutual inductance. A plane coil of area 100 cm is rotating in a magnetic field of 2 weber/m with angular velocity 20 rad/s. What will be the maximum induced electromotive force in the coil?$

Official Solution

Correct Option: (1)

$Self-inductance () is a property of a coil (or any conductor) that opposes the change in current flowing through it. When the current in a coil changes, it induces an electromotive force (emf) in the coil itself, as given by the equation: Where: - is the self-inductance of the coil, - is the rate of change of current. Mutual inductance () is the property of two coils where a change in current in one coil induces an emf in the other coil. The induced emf is proportional to the rate of change of current in the first coil and the mutual inductance between them. The equation is given by: Where: - is the induced emf in the second coil, - is the mutual inductance, - is the rate of change of current in the first coil. For the second part of the question, the induced electromotive force () in a rotating coil in a magnetic field is given by: Where: - is the magnetic field strength, - is the area of the coil, - is the angular velocity. Given: -, -, - . Substituting the values into the formula: Thus, the maximum induced electromotive force in the coil is .$

27

PYQ 2025

medium

physics ID: up-board

$Self-inductance of a coil is 6 mH and the rate of flow of current in it is A/s. Find the induced emf produced in the coil.$

Official Solution

Correct Option: (1)

$The induced emf in a coil is given by where = self-inductance, and = rate of change of current. Substituting the given values: Final Answer: The induced emf produced in the coil is .$

28

PYQ 2025

medium

physics ID: up-board

$In electromagnetic waves, phase difference between electric and magnetic field vectors is:$

1

2

3

4

Official Solution

Correct Option: (4)

$Step 1: Relation between and .} In an electromagnetic (EM) wave, the electric field vector, magnetic field vector, and the direction of propagation are all mutually perpendicular. Step 2: Phase relation. The and vectors oscillate in the same phase (they reach maximum and minimum together). Step 3: Conclusion. Therefore, the phase difference between and is .$

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Chapter Questions
28 MCQs

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Electromagnetic Wave

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Chapter Questions 28 MCQs

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Chapter Questions
28 MCQs