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Electromagnetic Induction – CBSE NCERT Study Resources

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12th

12th - Physics

Electromagnetic Induction

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Chapter Overview: Electromagnetic Induction

Electromagnetic Induction is a fundamental concept in Physics that explains how a changing magnetic field can induce an electric current in a conductor. This chapter explores Faraday's laws, Lenz's law, self and mutual induction, and applications like transformers and AC generators.

Electromagnetic Induction: The phenomenon of generating an electromotive force (emf) or current in a conductor due to a changing magnetic field.

Key Concepts

  • Faraday's Laws of Electromagnetic Induction
  • Lenz's Law and Conservation of Energy
  • Self-Induction and Mutual Induction
  • Eddy Currents and their Applications
  • AC Generator and Transformer Principles

Faraday's Laws of Electromagnetic Induction

Faraday's experiments led to two key laws:

  1. First Law: An emf is induced in a circuit whenever the magnetic flux linked with the circuit changes.
  2. Second Law: The magnitude of the induced emf is proportional to the rate of change of magnetic flux.

Magnetic Flux (Φ): The product of the magnetic field (B) and the area (A) perpendicular to the field, given by Φ = B·A·cosθ.

Lenz's Law

Lenz's law states that the direction of the induced current opposes the change in magnetic flux that produced it, in accordance with the law of conservation of energy.

Self and Mutual Induction

Self-induction occurs when a changing current in a coil induces an emf in the same coil. Mutual induction occurs when a changing current in one coil induces an emf in a nearby coil.

Inductance (L): The property of a coil that opposes the change in current flowing through it, measured in Henry (H).

Eddy Currents

Eddy currents are loops of induced current formed in bulk conductors due to changing magnetic flux. They are utilized in applications like electromagnetic braking and induction furnaces.

AC Generator and Transformer

An AC generator converts mechanical energy into electrical energy using electromagnetic induction. A transformer works on mutual induction to change AC voltage levels efficiently.

All Question Types with Solutions – CBSE Exam Pattern

Explore a complete set of CBSE-style questions with detailed solutions, categorized by marks and question types. Ideal for exam preparation, revision and practice.

Very Short Answer (1 Mark) – with Solutions (CBSE Pattern)

These are 1-mark questions requiring direct, concise answers. Ideal for quick recall and concept clarity.

Question 1:
Define magnetic flux.
Answer:

Magnetic flux is the product of magnetic field and area perpendicular to the field.

Question 2:
State Faraday's first law of electromagnetic induction.
Answer:

An emf is induced when magnetic flux linked with a circuit changes.

Question 3:
What is the SI unit of self-inductance?
Answer:

The SI unit is henry (H).

Question 4:
Name the phenomenon where a changing current induces emf in the same coil.
Answer:

Self-induction.

Question 5:
What does Lenz's law state about induced current direction?
Answer:

Induced current opposes the change in magnetic flux.

Question 6:
How does eddy current affect energy loss in transformers?
Answer:

Eddy currents cause heat dissipation, reducing efficiency.

Question 7:
What is the role of a commutator in a DC generator?
Answer:

It converts AC to DC in the output.

Question 8:
Define mutual inductance between two coils.
Answer:

It is the flux linkage in one coil per unit current in the other.

Question 9:
Why is a laminated core used in transformers?
Answer:

To reduce eddy current losses.

Question 10:
What happens to induced emf if the rate of change of flux doubles?
Answer:

Induced emf also doubles.

Question 11:
Name the device that converts mechanical energy into electrical energy.
Answer:

Electric generator.

Question 12:
What is the direction of induced current in a loop moving away from a magnet?
Answer:

Clockwise (as per Lenz's law).

Question 13:
State the principle behind electromagnetic induction.
Answer:

Changing magnetic flux induces an emf.

Question 14:
What is the significance of the negative sign in Faraday's law?
Answer:

It indicates opposition to flux change (Lenz's law).

Question 15:
Define electromagnetic induction.
Answer:

The phenomenon of generating an electromotive force (emf) or current in a conductor when it is exposed to a changing magnetic field is called electromagnetic induction. This was discovered by Michael Faraday.

Question 16:
State Faraday's first law of electromagnetic induction.
Answer:

Faraday's first law states that whenever there is a change in the magnetic flux linked with a circuit, an emf is induced. The induced emf lasts only as long as the change in flux is occurring.

Question 17:
What is the SI unit of magnetic flux?
Answer:

The SI unit of magnetic flux is the Weber (Wb). It is equivalent to Tesla-meter² (Tm²).

Question 18:
Write the formula for induced emf in a moving conductor in a magnetic field.
Answer:

The induced emf (ε) in a conductor of length l moving with velocity v perpendicular to a magnetic field B is given by:
ε = B l v.

Question 19:
What is the significance of Lenz's law in electromagnetic induction?
Answer:

Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it. This ensures the conservation of energy in electromagnetic processes.

Question 20:
Differentiate between self-induction and mutual induction.
Answer:
  • Self-induction occurs when a changing current in a coil induces an emf in the same coil.
  • Mutual induction occurs when a changing current in one coil induces an emf in a nearby coil.
Question 21:
What is the role of a soft iron core in a transformer?
Answer:

The soft iron core in a transformer increases the magnetic flux linkage between the primary and secondary coils, improving efficiency by reducing energy losses.

Question 22:
Explain why eddy currents are produced in a metallic conductor.
Answer:

Eddy currents are induced currents in a conductor due to a changing magnetic field. They circulate within the conductor and cause energy dissipation as heat.

Question 23:
State the principle of a DC generator.
Answer:

A DC generator works on the principle of electromagnetic induction, converting mechanical energy into electrical energy by rotating a coil in a magnetic field, producing a direct current via a split-ring commutator.

Question 24:
What is the function of a commutator in a DC motor?
Answer:

The commutator reverses the direction of current in the coil every half rotation, ensuring continuous rotation of the coil in the same direction.

Question 25:
How does the number of turns in the secondary coil affect the voltage in a step-up transformer?
Answer:

In a step-up transformer, increasing the number of turns in the secondary coil increases the output voltage proportionally, as per the turns ratio (Ns/Np).

Question 26:
Why is laminated iron core used in transformers?
Answer:

A laminated iron core reduces eddy current losses by breaking the path of induced currents, thereby improving the transformer's efficiency.

Very Short Answer (2 Marks) – with Solutions (CBSE Pattern)

These 2-mark questions test key concepts in a brief format. Answers are expected to be accurate and slightly descriptive.

Question 1:
Differentiate between self-induction and mutual induction.
Answer:
  • Self-induction occurs when the changing current in a coil induces an emf in the same coil.
  • Mutual induction occurs when the changing current in one coil induces an emf in a nearby coil.
Question 2:
Explain why eddy currents are considered undesirable in some electrical devices.
Answer:

Eddy currents cause energy loss in the form of heat due to resistance in the core material. This reduces the efficiency of devices like transformers and motors. To minimize them, laminated cores are used.

Question 3:
What is the SI unit of mutual inductance?
Answer:

The SI unit of mutual inductance is the henry (H). One henry is the mutual inductance between two coils when a change in current of 1 ampere per second in one coil induces an emf of 1 volt in the other coil.

Question 4:
How does the number of turns in a coil affect the induced emf?
Answer:

The induced emf is directly proportional to the number of turns in the coil. More turns mean a greater change in magnetic flux, resulting in a higher induced emf according to Faraday's law.

Question 5:
Describe one application of electromagnetic induction in daily life.
Answer:

One common application is in electric generators, where mechanical energy is converted to electrical energy by rotating a coil in a magnetic field, inducing an emf due to electromagnetic induction.

Question 6:
What happens to the induced current if the rate of change of magnetic flux is doubled?
Answer:

According to Faraday's law, the induced emf (and hence current) is directly proportional to the rate of change of magnetic flux. If the rate doubles, the induced current also doubles.

Question 7:
State Faraday's first law of electromagnetic induction.
Answer:

Faraday's first law states that whenever there is a change in the magnetic flux linked with a circuit, an emf is induced in the circuit. The induced emf lasts only as long as the change in flux is occurring.

Question 8:
Write the expression for the induced emf in a moving conductor in a magnetic field.
Answer:

The induced emf (ε) in a conductor of length l moving with velocity v perpendicular to a magnetic field B is given by:
ε = B l v

Short Answer (3 Marks) – with Solutions (CBSE Pattern)

These 3-mark questions require brief explanations and help assess understanding and application of concepts.

Question 1:
Explain the phenomenon of electromagnetic induction and state Faraday's law of electromagnetic induction.
Answer:

Electromagnetic induction is the process of generating an electromotive force (emf) in a conductor when it is exposed to a changing magnetic field. This phenomenon was discovered by Michael Faraday.

Faraday's law states that the induced emf in a closed loop is equal to the negative rate of change of the magnetic flux through the loop. Mathematically, it is expressed as:
emf = -dΦ/dt
where Φ is the magnetic flux.

This law forms the basis for the working of generators, transformers, and many electrical devices.

Question 2:
Differentiate between self-induction and mutual induction with suitable examples.
Answer:

Self-induction occurs when the changing current in a coil induces an emf in the same coil. It depends on the coil's geometry and the core material. Example: The back emf generated in an inductor when the current through it changes.

Mutual induction occurs when the changing current in one coil induces an emf in a nearby coil. Example: A transformer where the primary coil induces a voltage in the secondary coil.

Key differences:

  • Self-induction involves a single coil, while mutual induction involves two coils.
  • Self-inductance (L) is the property of a single coil, while mutual inductance (M) depends on both coils.

Question 3:
Describe how Lenz's law is a consequence of the principle of conservation of energy in electromagnetic induction.
Answer:

Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it. This law ensures the conservation of energy in electromagnetic induction.

For example, when a magnet is pushed into a coil, the induced current creates a magnetic field opposing the magnet's motion. This requires work to be done against the opposing force, converting mechanical energy into electrical energy.

If Lenz's law didn't hold, the induced current would aid the change in flux, leading to a perpetual increase in energy, violating the conservation of energy principle.

Question 4:
Explain the working principle of an AC generator with a labeled diagram.
Answer:

An AC generator converts mechanical energy into alternating current electricity using electromagnetic induction. The key components are:

  • Armature coil (rotates in magnetic field)
  • Strong field magnet
  • Slip rings and brushes

Working principle:
1. The coil rotates in the magnetic field, changing the magnetic flux through it.
2. According to Faraday's law, this changing flux induces an alternating emf in the coil.
3. The slip rings maintain contact with the brushes, allowing the AC output to be tapped.

The diagram would show:
- Rotating coil between pole pieces of magnet
- Axis of rotation perpendicular to magnetic field
- Slip rings connected to coil ends
- Brushes touching slip rings
- Output terminals connected to brushes

Question 5:
Derive the expression for the instantaneous value of induced emf in a rotating coil in a uniform magnetic field.
Answer:

Consider a rectangular coil of N turns, area A, rotating with angular velocity ω in a uniform magnetic field B.

1. The magnetic flux through the coil at time t is:
Φ = NBAcosθ
where θ = ωt is the angle between B and normal to the coil.

2. The induced emf is given by Faraday's law:
e = -dΦ/dt = -d(NBAcosωt)/dt

3. Differentiating:
e = NBAωsinωt

4. The maximum emf (e0) occurs when sinωt = 1:
e0 = NBAω

5. Therefore, the instantaneous emf is:
e = e0sinωt

This shows the emf varies sinusoidally with time, characteristic of AC generation.

Question 6:
What are eddy currents? Explain two applications and one method to reduce their undesirable effects.
Answer:

Eddy currents are circulating currents induced in bulk conductors when exposed to changing magnetic fields. They flow in closed loops within the conductor.

Applications:
1. Induction heating: Eddy currents generate heat used in induction furnaces for melting metals.
2. Electromagnetic braking: In trains, eddy currents oppose motion, providing smooth braking.

Reduction method:
Using laminated cores in transformers and motors:
- The core is made of thin insulated sheets
- This increases resistance to eddy current paths
- Reduces energy losses as heat

Question 7:
Define electromagnetic induction and state Faraday's Law of electromagnetic induction.
Answer:

Electromagnetic induction is the process of generating an electromotive force (emf) in a conductor when it is exposed to a changing magnetic field.

Faraday's Law states that the induced emf in a closed loop is equal to the negative rate of change of the magnetic flux through the loop. Mathematically, it is expressed as:
emf = -dΦ/dt, where Φ is the magnetic flux.

Question 8:
Explain Lenz's Law and how it relates to the conservation of energy.
Answer:

Lenz's Law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it.

This law is a consequence of the conservation of energy. If the induced current were to support the change in flux, it would lead to a perpetual increase in energy, violating energy conservation. Thus, Lenz's Law ensures energy balance in electromagnetic systems.

Question 9:
Differentiate between self-induction and mutual induction with examples.
Answer:

Self-induction occurs when a changing current in a coil induces an emf in the same coil. Example: A solenoid's back emf when current changes.

Mutual induction occurs when a changing current in one coil induces an emf in a nearby coil. Example: A transformer where primary and secondary coils are linked magnetically.

Question 10:
Describe the working principle of an AC generator with a labeled diagram.
Answer:

An AC generator works on the principle of electromagnetic induction.

Working:

  • A coil rotates in a magnetic field, changing the magnetic flux.
  • This induces an alternating emf according to Faraday's Law.
  • Slip rings and brushes collect the alternating current.

Diagram: (Imagine a rectangular coil rotating between magnet poles, connected to slip rings and brushes.)

Question 11:
What is eddy current? Explain one application and one disadvantage of eddy currents.
Answer:

Eddy currents are circulating currents induced in a conductor when exposed to a changing magnetic field.

Application: Used in induction furnaces for heating metals efficiently.

Disadvantage: They cause energy loss in transformers due to unwanted heating, reduced by laminating the core.

Question 12:
Derive the expression for the induced emf in a straight conductor moving perpendicular to a uniform magnetic field.
Answer:

Consider a conductor of length l moving with velocity v perpendicular to a magnetic field B.

The force on free electrons: F = qvB.

This creates an electric field E = F/q = vB.

The induced emf is: emf = E × l = Bvl.

Thus, emf = Bvl (where B, v, and l are mutually perpendicular).

Long Answer (5 Marks) – with Solutions (CBSE Pattern)

These 5-mark questions are descriptive and require detailed, structured answers with proper explanation and examples.

Question 1:
Explain the phenomenon of electromagnetic induction and state Faraday's Law and Lenz's Law. Derive the expression for induced emf in a straight conductor moving in a uniform magnetic field.
Answer:

Electromagnetic induction is the process of generating an electromotive force (emf) in a conductor when it is exposed to a changing magnetic field. This phenomenon was discovered by Michael Faraday and forms the basis of many electrical devices like generators and transformers.

Faraday's Law states that the induced emf in a coil is equal to the negative rate of change of magnetic flux through the coil. Mathematically, it is expressed as:
emf = -dΦ/dt
where Φ is the magnetic flux (Φ = B.A.cosθ).

Lenz's Law gives the direction of the induced emf and states that the induced current will flow in such a direction that it opposes the change in magnetic flux that produced it. This law ensures the conservation of energy.

For a straight conductor of length l moving with velocity v perpendicular to a uniform magnetic field B, the induced emf is derived as follows:
1. The force on a charge q moving in the conductor is F = qvB.
2. Work done to move the charge along the conductor is W = F.l = qvBl.
3. The emf (ε) is the work done per unit charge: ε = W/q = vBl.
Thus, the induced emf is ε = Bvl.

Question 2:
Describe the working principle of an AC generator with a labeled diagram. Derive the expression for the instantaneous emf produced in it.
Answer:

An AC generator converts mechanical energy into electrical energy using the principle of electromagnetic induction. It consists of a rotating coil (armature) placed in a magnetic field, slip rings, and brushes to collect the current.

Working Principle:
1. The coil rotates in a magnetic field, causing the magnetic flux through it to change continuously.
2. According to Faraday's Law, this changing flux induces an alternating emf in the coil.
3. The slip rings and brushes ensure the alternating current is transmitted to the external circuit.

Derivation of Instantaneous emf:
1. Let the coil have N turns and area A, rotating with angular velocity ω in a magnetic field B.
2. The flux through the coil at time t is Φ = NBAcosθ, where θ = ωt.
3. The induced emf is ε = -dΦ/dt = -d(NBAcosωt)/dt = NBAωsinωt.
4. The maximum emf (ε0) occurs when sinωt = 1, so ε0 = NBAω.
5. Thus, the instantaneous emf is ε = ε0sinωt.

Diagram: (A labeled diagram would show the coil, magnetic field, slip rings, brushes, and the direction of rotation and current.)

Question 3:
Explain the phenomenon of electromagnetic induction and derive the expression for the induced emf in a conductor moving perpendicular to a uniform magnetic field. Also, state Lenz's Law and its significance.
Answer:

Electromagnetic induction is the process of generating an electromotive force (emf) in a conductor when it is exposed to a changing magnetic field. This phenomenon was discovered by Michael Faraday and forms the basis of generators and transformers.


To derive the expression for induced emf in a conductor moving perpendicular to a uniform magnetic field:


1. Consider a straight conductor of length l moving with velocity v perpendicular to a uniform magnetic field B.
2. The magnetic force on free electrons in the conductor is given by F = qvB, where q is the charge of an electron.
3. This force causes electrons to accumulate at one end, creating an electric field E inside the conductor.
4. In equilibrium, the electric force balances the magnetic force: qE = qvB ⇒ E = vB.
5. The potential difference (emf) across the conductor is ε = El = Bvl.


Lenz's Law states that the direction of the induced current is such that it opposes the change in magnetic flux producing it. This law is a consequence of the conservation of energy, ensuring that energy is not created out of nothing in electromagnetic processes.


Significance of Lenz's Law:
- It determines the direction of induced emf/current.
- It ensures energy conservation by opposing the cause of induction.
- It explains the 'back emf' in motors and generators.

Question 4:
Explain the phenomenon of electromagnetic induction and derive the expression for the induced emf in a straight conductor moving in a uniform magnetic field perpendicular to its length. Also, state Lenz's Law and its significance.
Answer:

Electromagnetic induction is the process of generating an electromotive force (emf) in a conductor when it is exposed to a changing magnetic field. This phenomenon was discovered by Michael Faraday and forms the basis of many electrical devices like generators and transformers.


Derivation of induced emf in a straight conductor:
Consider a straight conductor of length l moving with velocity v perpendicular to a uniform magnetic field B. The force on a charge q in the conductor is given by:
F = qvB
This force causes charges to accumulate at the ends, creating an electric field E such that:
F = qE
Equating the two forces:
qvB = qE ⇒ E = vB
The potential difference (emf) between the ends is:
ε = El = Bvl


Lenz's Law: The direction of the induced emf is such that it opposes the change in magnetic flux that produced it. This law is a consequence of the conservation of energy, ensuring that energy is not created or destroyed in the process.


Significance of Lenz's Law:

  • It determines the direction of induced current.
  • It ensures energy conservation by opposing the change causing induction.
  • It is crucial in designing electrical machines like motors and generators.

Question 5:
Explain the phenomenon of electromagnetic induction and derive the expression for the induced emf in a coil rotating in a uniform magnetic field. Discuss its significance in real-world applications.
Answer:

Electromagnetic induction is the process of generating an electromotive force (emf) in a conductor when it is exposed to a changing magnetic field. This phenomenon was discovered by Michael Faraday and forms the basis of many electrical devices.


Consider a coil of N turns rotating with an angular velocity ω in a uniform magnetic field B. The magnetic flux (Φ) through the coil is given by:
Φ = NBA cosθ
where A is the area of the coil and θ is the angle between the magnetic field and the normal to the coil.

As the coil rotates, θ changes with time as θ = ωt. Thus, the flux becomes:
Φ = NBA cos(ωt)

According to Faraday's law of induction, the induced emf (ε) is the negative rate of change of flux:
ε = -dΦ/dt = -d/dt [NBA cos(ωt)]
ε = NBAω sin(ωt)

This shows that the induced emf varies sinusoidally with time, which is the principle behind AC generators.


Significance in real-world applications:

  • AC Generators: Convert mechanical energy into electrical energy using electromagnetic induction.
  • Transformers: Step-up or step-down voltages for efficient power transmission.
  • Induction Cooktops: Use eddy currents generated by alternating magnetic fields to heat cookware.
  • Wireless Charging: Employs electromagnetic induction to transfer energy without physical connections.

Question 6:
Explain the phenomenon of self-induction and derive an expression for the self-inductance of a long solenoid. How does self-inductance depend on the number of turns and the area of the solenoid?
Answer:

Self-induction is the phenomenon where a changing current in a coil induces an emf in the same coil, opposing the change in current. This is due to the magnetic flux linked with the coil changing as the current varies.


For a long solenoid of length l, area A, and N turns carrying current I, the magnetic field inside is given by:
B = μ₀nI, where n = N/l (turns per unit length).


The total flux linkage is:
Φ = NBA = μ₀nI × N × A.
Substituting n = N/l, we get:
Φ = μ₀(N²/l)IA.


By definition, self-inductance (L) = Φ/I:
L = μ₀(N²/l)A.


Dependence:

  • Self-inductance L ∝ N² (square of turns).
  • L ∝ A (cross-sectional area).

Thus, increasing turns or area enhances self-inductance.

Question 7:
Describe Faraday's law of electromagnetic induction and derive the expression for induced emf in a rotating coil in a uniform magnetic field. State how the magnitude of emf changes with the speed of rotation.
Answer:

Faraday's law states that the induced emf in a coil is equal to the negative rate of change of magnetic flux linkage:
emf = −dΦ/dt.


For a coil of N turns, area A, rotating at angular speed ω in a uniform magnetic field B, the flux linkage at time t is:
Φ = NBA cosθ, where θ = ωt.


Differentiating Φ w.r.t. time:
emf = −d/dt (NBA cosωt) = NBAω sinωt.
Thus, emf = emf₀ sinωt, where emf₀ = NBAω (peak emf).


Dependence on speed: Since emf₀ ∝ ω, faster rotation (higher ω) increases the induced emf proportionally. This principle is used in AC generators to produce higher voltages.

Question 8:
Explain the phenomenon of self-induction and derive an expression for the self-inductance of a long solenoid. How does it depend on the number of turns and the area of the solenoid?
Answer:

Self-induction is the phenomenon where a changing current in a coil induces an emf in the same coil, opposing the change in current. This occurs due to the varying magnetic flux linked with the coil itself.


For a long solenoid of length l, cross-sectional area A, and N turns carrying current I, the magnetic field inside is given by:
B = μ₀nI, where n = N/l (turns per unit length).


The total magnetic flux linked with the solenoid is:
Φ = NBA = (μ₀nI)(N)(A).
Substituting n = N/l, we get:
Φ = μ₀(N²/l)IA.


By definition, self-inductance (L) = Φ/I:
L = μ₀(N²/l)A.


Thus, self-inductance depends on:

  • Square of the number of turns (N²): More turns increase flux linkage.
  • Area (A): Larger area enhances magnetic flux.
  • Length (l): Longer solenoids reduce inductance.

This principle is crucial in designing inductors for circuits.

Question 9:
Describe Faraday's law of electromagnetic induction and Lenz's law with an example. How do these laws explain energy conservation in electromagnetic processes?
Answer:

Faraday's law states that the induced emf in a coil is equal to the negative rate of change of magnetic flux through it:
ε = -dΦ/dt.
For example, moving a magnet toward a coil increases flux, inducing a current opposing the motion.


Lenz's law specifies the direction of the induced current: it always opposes the change causing it. In the magnet-coil example, the induced current creates a magnetic field repelling the magnet, resisting its motion.


These laws conserve energy:

  • Work done to move the magnet against the opposing force converts into electrical energy via the induced current.
  • Without Lenz's law, perpetual motion would violate energy conservation.

Thus, Faraday's and Lenz's laws ensure energy balance in electromagnetic systems, aligning with the principle of conservation of energy.

Question 10:
Explain the principle of electromagnetic induction and derive the expression for the induced emf in a straight conductor moving perpendicular to a uniform magnetic field. Also, state Fleming's right-hand rule and its significance.
Answer:

The principle of electromagnetic induction states that whenever there is a change in the magnetic flux linked with a conductor, an electromotive force (emf) is induced in the conductor. This phenomenon was discovered by Michael Faraday.

For a straight conductor of length l moving with velocity v perpendicular to a uniform magnetic field B, the induced emf (ε) is given by:
ε = B l v
This is derived from the fact that the magnetic force on the free electrons in the conductor causes them to accumulate at one end, creating a potential difference.

Fleming's right-hand rule is used to determine the direction of the induced current:

  • Thumb: Direction of motion of the conductor
  • Forefinger: Direction of the magnetic field
  • Middle finger: Direction of the induced current
This rule is significant as it helps in understanding the direction of current in generators and other applications of electromagnetic induction.

Question 11:
Describe the working of an AC generator with a labeled diagram. Derive the expression for the instantaneous emf induced in the coil and explain the factors affecting its magnitude.
Answer:

An AC generator converts mechanical energy into electrical energy using the principle of electromagnetic induction. It consists of a rectangular coil rotating in a uniform magnetic field.

Working:
The coil rotates in the magnetic field, causing the magnetic flux through it to change continuously. This change induces an alternating emf in the coil, which is tapped using slip rings and brushes.

Instantaneous emf (ε):
If the coil has N turns, area A, and rotates with angular velocity ω in a magnetic field B, the emf induced at time t is:
ε = NBAω sin(ωt)
This shows that the emf varies sinusoidally with time.

Factors affecting magnitude:

  • Number of turns (N) in the coil
  • Strength of the magnetic field (B)
  • Area of the coil (A)
  • Angular velocity (ω) of rotation

Case-based Questions (4 Marks) – with Solutions (CBSE Pattern)

These 4-mark case-based questions assess analytical skills through real-life scenarios. Answers must be based on the case study provided.

Question 1:
A student observes that when a bar magnet is quickly moved towards a coil connected to a galvanometer, the needle deflects. However, no deflection occurs when the magnet is held stationary. Explain the phenomenon and analyze how the speed of the magnet affects the deflection.
Answer:
Case Deconstruction

The deflection occurs due to electromagnetic induction, where a changing magnetic flux induces an emf in the coil. Our textbook shows that Faraday's Law states the induced emf is proportional to the rate of change of flux.

Theoretical Application
  • Faster movement increases the rate of flux change, causing higher emf and greater deflection.
  • No deflection when stationary confirms that steady flux induces no emf.
Critical Evaluation

This aligns with Lenz's Law, where the induced current opposes the magnet's motion. Example: A stronger magnet moved at the same speed produces larger deflection due to greater flux change.

Question 2:
A circular loop of radius 0.1m is placed perpendicular to a uniform magnetic field of 0.5T. If the loop is rotated about its diameter at 120 rpm, derive the expression for induced emf and calculate its peak value.
Answer:
Case Deconstruction

We studied that emf is induced due to change in flux linkage. Here, flux Φ = BAcosθ, where θ = ωt.

Theoretical Application
  • Angular velocity ω = 2π × (120/60) = 4π rad/s.
  • Induced emf ε = -dΦ/dt = BAωsinωt.
Critical Evaluation

Peak emf (ε0) = BAω = 0.5 × π(0.1)2 × 4π = 0.02π2 V. Example: Doubling ω doubles ε0, as seen in generators.

Question 3:
Two identical coils A and B are placed close to each other. Coil A is connected to an AC source, while coil B is connected to a bulb. Analyze why the bulb lights up and how the brightness depends on the frequency of the AC source.
Answer:
Case Deconstruction

The bulb lights due to mutual induction, where AC in coil A induces a changing flux in coil B.

Theoretical Application
  • Faraday's Law: Induced emf in B depends on the rate of flux change from A.
  • Higher frequency increases emf, brightening the bulb.
Critical Evaluation

Example: At 50Hz, brightness is lower than at 100Hz. This principle is used in transformers, where frequency affects output voltage.

Question 4:
A metallic rod of length 1m is moved at 2m/s perpendicular to a magnetic field of 0.3T. Compare the induced emf when the rod is moved (a) straight (b) at 45° to the field. Justify with calculations.
Answer:
Case Deconstruction

Emf is induced due to motional emf (ε = Blvsinθ). Our textbook shows θ is the angle between v and B.

Theoretical Application
  • (a) θ = 90°: ε = 0.3 × 1 × 2 × 1 = 0.6V.
  • (b) θ = 45°: ε = 0.3 × 1 × 2 × sin45° = 0.42V.
Critical Evaluation

Example: In generators, maximum emf occurs when θ = 90°. The 45° case shows reduced efficiency due to vector components.

Question 5:
A student observes that a magnetic flux through a coil changes from 0.02 Wb to 0.08 Wb in 0.5 seconds. Using Faraday's Law, calculate the induced emf. Discuss how Lenz's Law determines the direction of the induced current.
Answer:
Case Deconstruction

We studied that Faraday's Law states emf = -dΦ/dt. Here, ΔΦ = 0.08 - 0.02 = 0.06 Wb, Δt = 0.5 s. Thus, emf = -0.06/0.5 = -0.12 V.

Theoretical Application
  • Magnitude: 0.12 V (ignoring sign)
  • Direction: Lenz's Law opposes the increase in flux, so current creates a field opposing the original.
Critical Evaluation

Negative sign confirms Lenz's Law. Example: Moving a magnet toward a coil induces opposing current.

Question 6:
A rectangular loop moves with constant velocity into a uniform magnetic field perpendicular to its plane. Analyze the induced current direction and magnitude using Fleming's Right-Hand Rule and energy considerations.
Answer:
Case Deconstruction

Our textbook shows that motion-induced emf follows Fleming's Rule. Thumb = motion, fingers = field, palm = current.

Theoretical Application
  • Direction: Current flows to oppose entry (Lenz's Law).
  • Magnitude: I = Bvl/R (v = velocity, l = length, R = resistance).
Critical Evaluation

Energy is conserved as work done equals thermal energy dissipated. Example: Eddy currents in braking systems.

Question 7:
Compare self-inductance and mutual inductance with two examples each. Derive the expression for energy stored in an inductor (E = ½LI²).
Answer:
Case Deconstruction

Self-inductance (L) opposes current change in single coil (e.g., solenoid). Mutual inductance (M) links two coils (e.g., transformer).

Theoretical Application
  • Energy derivation: Integrate power P = VI = L(dI/dt)I from 0 to I.
  • Result: E = ½LI².
Critical Evaluation

Examples: Self-inductance in LR circuits, mutual inductance in wireless chargers. Energy stored is magnetic potential energy.

Question 8:
A metallic rod rotates at angular velocity ω in a magnetic field B about one end. Calculate the induced emf between its ends. Justify if this setup can act as a DC generator.
Answer:
Case Deconstruction

We use motional emf: de = Bvdr. For rod, v = ωr, so emf = ∫Bωrdr = ½BωL² (L = length).

Theoretical Application
  • Magnitude: ½BωL².
  • DC output? No, polarity reverses every half-rotation (AC).
Critical Evaluation

Example: Faraday's disk generator. Commutators are needed for DC conversion, unlike this setup.

Question 9:
A student observes that moving a magnet quickly through a coil induces a higher emf than moving it slowly. Using Faraday's Law, explain this phenomenon and discuss how Lenz's Law ensures energy conservation.
Answer:
Case Deconstruction

We studied that Faraday's Law states emf is induced due to the rate of change of magnetic flux. Faster magnet movement increases flux change, raising emf.

Theoretical Application
  • Lenz's Law opposes the change causing emf, ensuring energy conservation.
  • Example: Rapid magnet motion induces higher current, but work done against opposition matches energy dissipated.
Critical Evaluation

Our textbook shows that energy conservation is maintained as mechanical work converts to electrical energy, validated by Joule heating in the coil.

Question 10:
A solenoid connected to an AC source is placed near a circular conducting loop. Analyze why the loop experiences an induced current and predict the effect of doubling the AC frequency.
Answer:
Case Deconstruction

AC in the solenoid creates a time-varying magnetic field, inducing emf in the loop via electromagnetic induction.

Theoretical Application
  • Doubling frequency increases the rate of flux change, doubling induced emf (Faraday's Law).
  • Example: 50 Hz AC induces lower emf than 100 Hz for the same loop.
Critical Evaluation

Our textbook confirms proportionality between frequency and emf, supported by experiments with oscilloscopes.

Question 11:
Compare self-induction and mutual induction using two scenarios: (a) a coil with varying current, (b) two coils sharing a core. Highlight their roles in transformers.
Answer:
Case Deconstruction

Self-induction occurs when a coil's own current change induces emf, while mutual induction involves emf in a nearby coil.

Theoretical Application
  • Example (a): A choke coil uses self-induction to stabilize current.
  • Example (b): Transformers rely on mutual induction for voltage regulation.
Critical Evaluation

Our textbook shows mutual induction is efficient in energy transfer, whereas self-induction resists current changes, critical for circuit safety.

Question 12:
A metallic rod rotates at angular velocity ω in a uniform magnetic field perpendicular to its axis. Derive the expression for induced emf and discuss how eddy currents affect its motion.
Answer:
Case Deconstruction

Emf is induced due to Lorentz force on free electrons: ε = ½BωL², where L is rod length.

Theoretical Application
  • Eddy currents oppose rotation (Lenz's Law), causing damping.
  • Example: Power loss in generators due to eddy currents reduces efficiency.
Critical Evaluation

Our textbook confirms laminated cores minimize eddy currents, validating the need for design optimization in rotating systems.

Question 13:

A student sets up an experiment to study electromagnetic induction using a solenoid and a bar magnet. The solenoid is connected to a galvanometer. The student moves the bar magnet towards the solenoid and observes the deflection in the galvanometer.

(i) State the principle behind the observed deflection.

(ii) What happens to the deflection if the magnet is moved faster? Justify your answer.

(iii) How will the deflection change if the number of turns in the solenoid is increased? Explain.

Answer:

(i) The deflection is based on Faraday's Law of Electromagnetic Induction, which states that a changing magnetic flux through a coil induces an emf (electromotive force) in the coil.


(ii) The deflection increases because the rate of change of magnetic flux increases with faster movement, leading to a higher induced emf (as per Faraday's Law: emf = -dΦ/dt).


(iii) The deflection increases because the induced emf is directly proportional to the number of turns (N) in the solenoid (emf = -N(dΦ/dt)). More turns mean greater flux linkage and hence a stronger induced current.

Question 14:

A rectangular loop of wire is placed perpendicular to a uniform magnetic field. The loop is then rotated about one of its sides with a constant angular velocity.

(i) What is the direction of the induced current when the loop is rotated clockwise? Explain using Lenz's Law.

(ii) Derive the expression for the instantaneous induced emf in the loop.

(iii) How does the induced emf vary with time? Sketch a graph showing this relationship.

Answer:

(i) The induced current opposes the change in flux. For clockwise rotation, the magnetic flux decreases, so the current flows in a direction to oppose the decrease (counter-clockwise when viewed from the rotation axis).


(ii) The induced emf is given by: emf = -dΦ/dt.
For a loop of area A and magnetic field B, Φ = BAcosθ, where θ = ωt.
Thus, emf = -d(BAcosωt)/dt = BAωsinωt.


(iii) The emf varies sinusoidally with time (emf = BAωsinωt). The graph is a sine wave with amplitude BAω and angular frequency ω.

Question 15:

A student sets up an experiment to study electromagnetic induction using a solenoid, a bar magnet, and a galvanometer. The student moves the bar magnet towards the solenoid and observes the deflection in the galvanometer.

Question: Explain the principle behind the observed deflection and describe how the direction of the induced current can be determined using Lenz's Law. Also, state one practical application of this phenomenon.

Answer:

The deflection in the galvanometer is due to electromagnetic induction, where a changing magnetic field induces an emf (electromotive force) in the solenoid. According to Faraday's Law, the magnitude of the induced emf is proportional to the rate of change of magnetic flux.


The direction of the induced current is determined by Lenz's Law, which states that the induced current will flow in such a direction as to oppose the change producing it. For example:

  • If the north pole of the magnet moves towards the solenoid, the induced current will create a magnetic field that repels the magnet.
  • If the magnet is moved away, the induced current will create a field that attracts the magnet.


A practical application of this phenomenon is in electric generators, where mechanical energy is converted into electrical energy by rotating a coil in a magnetic field, inducing a current.

Question 16:

A rectangular loop of wire is moved at a constant velocity through a uniform magnetic field directed perpendicular to the plane of the loop. The loop has dimensions 10 cm × 20 cm and a resistance of 2 Ω. The magnetic field strength is 0.5 T.

Question: Calculate the induced emf when the loop is moved at a speed of 5 m/s. Also, determine the direction of the induced current and the power dissipated in the loop.

Answer:

The induced emf (ε) is calculated using the formula: ε = B × l × v, where:

  • B = magnetic field strength (0.5 T)
  • l = length of the conductor perpendicular to motion (20 cm = 0.2 m)
  • v = velocity (5 m/s)

Substituting the values: ε = 0.5 × 0.2 × 5 = 0.5 V.


The direction of the induced current is determined by Fleming's Right-Hand Rule. Since the loop is moving to the right and the magnetic field is into the plane, the current will flow clockwise.


The power dissipated (P) is given by: P = ε² / R, where R = resistance (2 Ω).
Thus, P = (0.5)² / 2 = 0.125 W.

Question 17:

A circular loop of radius 10 cm is placed in a uniform magnetic field of 0.5 T directed perpendicular to the plane of the loop. The loop is rotated about its diameter at a constant angular velocity of 100 rad/s.

(i) Calculate the maximum induced emf in the loop.

(ii) If the loop has a resistance of 2 Ω, find the maximum current induced.

Answer:

Given: Radius (r) = 10 cm = 0.1 m, Magnetic field (B) = 0.5 T, Angular velocity (ω) = 100 rad/s, Resistance (R) = 2 Ω

(i) Maximum induced emf (εmax):

The formula for induced emf in a rotating loop is ε = NBAω sin(ωt).

For maximum emf, sin(ωt) = 1 ⇒ εmax = NBAω.

Here, N = 1 (single loop), A = πr² = π × (0.1)² = 0.0314 m².


εmax = (1)(0.5)(0.0314)(100) = 1.57 V.


(ii) Maximum current (Imax):

Using Ohm's Law, Imax = εmax/R = 1.57/2 = 0.785 A.

Note: The direction of current changes periodically due to rotation, following Faraday's Law of Electromagnetic Induction.

Question 18:

A rectangular coil of 50 turns, each of area 0.02 m², is placed perpendicular to a magnetic field of 0.4 T. The coil is pulled out of the field in 0.1 seconds.

(i) Calculate the change in magnetic flux.

(ii) Determine the average induced emf in the coil during this interval.

Answer:

Given: Number of turns (N) = 50, Area (A) = 0.02 m², Magnetic field (B) = 0.4 T, Time (Δt) = 0.1 s.

(i) Change in magnetic flux (ΔΦ):

Initial flux (Φinitial) = B × A = 0.4 × 0.02 = 0.008 Wb.

Final flux (Φfinal) = 0 (since coil is pulled out).


ΔΦ = Φfinal - Φinitial = 0 - 0.008 = -0.008 Wb.


(ii) Average induced emf (εavg):

Using Faraday's Law, εavg = -N × (ΔΦ/Δt).

εavg = -50 × (-0.008)/0.1 = 4 V.

Explanation: The negative sign indicates opposition to the change (Lenz's Law), but magnitude is considered for average emf.

Question 19:
A student sets up an experiment to study electromagnetic induction. She uses a solenoid connected to a galvanometer and moves a bar magnet towards and away from the solenoid.

Explain the observations made by the student and the underlying principle involved. Also, state how the deflection in the galvanometer would change if the number of turns in the solenoid is increased.

Answer:

The student observes that the galvanometer shows a deflection when the bar magnet is moved towards or away from the solenoid. This happens because the magnetic flux linked with the solenoid changes, inducing an emf (electromotive force) and hence a current in the circuit, as per Faraday's Law of Electromagnetic Induction.


When the magnet moves towards the solenoid, the deflection is in one direction, and when moved away, it is in the opposite direction. The magnitude of deflection depends on the speed of the magnet's motion.


If the number of turns in the solenoid is increased, the deflection in the galvanometer increases because the induced emf is directly proportional to the number of turns (N) as per the formula: emf = -N(dΦ/dt).

Question 20:
A rectangular loop of wire is placed perpendicular to a uniform magnetic field. The loop is then rotated about one of its sides with a constant angular velocity.

Explain the phenomenon of electromagnetic induction occurring in this scenario. Derive the expression for the induced emf in the loop.

Answer:

When the loop is rotated in the magnetic field, the magnetic flux through the loop changes continuously, leading to the generation of an induced emf as per Faraday's Law.


The flux through the loop at any instant is given by: Φ = BAcosθ, where θ = ωt (since the loop rotates with angular velocity ω).


Using Faraday's Law, the induced emf is: emf = -dΦ/dt = -d(BAcosωt)/dt
This simplifies to: emf = BAωsinωt
Thus, the induced emf varies sinusoidally with time, which is the principle behind an AC generator.


The maximum emf (emfmax) occurs when sinωt = 1, giving emfmax = BAω.

Question 21:
A student sets up an experiment to study electromagnetic induction. She uses a bar magnet, a coil connected to a galvanometer, and a wooden stand. When she moves the magnet towards the coil, the galvanometer shows a deflection. However, when she moves the magnet away at the same speed, the deflection is in the opposite direction but of the same magnitude.

Explain the underlying principle behind this observation and state the factors on which the magnitude of the induced current depends.

Answer:

The observation is based on Faraday's Law of Electromagnetic Induction, which states that a changing magnetic flux through a coil induces an emf (and hence current) in the coil. The direction of the induced current is given by Lenz's Law, which states that the induced current opposes the change in magnetic flux causing it.


When the magnet moves towards the coil, the magnetic flux increases, and the induced current flows in a direction to oppose this increase (e.g., creating a repulsive pole). When the magnet moves away, the flux decreases, and the current reverses to oppose this decrease (e.g., creating an attractive pole).


The magnitude of the induced current depends on:

  • The rate of change of magnetic flux (faster movement = greater deflection).
  • The number of turns in the coil (more turns = higher emf).
  • The strength of the magnet (stronger magnet = greater flux change).
Question 22:
A rectangular loop of wire is placed perpendicular to a uniform magnetic field. The loop is then rotated about an axis parallel to one of its sides.

Describe how an emf is induced in the loop during rotation. Derive the expression for the instantaneous emf induced and explain the significance of the angle between the magnetic field and the normal to the loop.

Answer:

When the loop rotates, the magnetic flux through it changes continuously due to the variation in the angle (θ) between the magnetic field (B) and the normal to the loop. According to Faraday's Law, this changing flux induces an emf in the loop.


The magnetic flux (Φ) through the loop is given by:
Φ = BA cosθ, where A is the area of the loop.


For a loop rotating with angular velocity ω, θ = ωt. The induced emf (ε) is:
ε = -dΦ/dt = -d(BA cosωt)/dt
= BAω sinωt (since the derivative of cosωt is -ω sinωt).


The angle θ determines the component of the magnetic field perpendicular to the loop. When θ = 0°, flux is maximum (Φ = BA), and when θ = 90°, flux is zero. The induced emf is maximum when θ = 90° (sinωt = 1) and zero when θ = 0°, showing the dependence on orientation.

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