Electromagnetic Induction Class 12 Physics Notes | Laws, Derivations & Questions

Electromagnetic Induction (EMI) is one of the most important topics in Class 12 Physics. It deals with the phenomenon of producing electric current using a changing magnetic field. This concept was first discovered by Michael Faraday in 1831, and it laid the foundation for modern-day electrical engineering, including generators, transformers, and induction motors.

In simple terms:

Electromagnetic induction is the process of generating an electric current in a conductor by changing the magnetic field around it.

This chapter covers concepts like Faraday’s Laws, Lenz’s Law, Eddy Currents, Self and Mutual Induction, Energy in Inductor, and practical applications.

Electromagnetic Induction Class 12 Physics Notes | Laws, Derivations & Questions

Faraday’s Experiments and Laws

Faraday’s First Experiment

• Faraday took a coil of wire connected to a galvanometer.

• When a bar magnet was moved towards the coil, the galvanometer showed a deflection, indicating that current was induced in the coil.

• When the magnet was taken away, deflection occurred in the opposite direction.

• If the magnet was at rest, there was no current.

Conclusion: A changing magnetic field induces current in the circuit.

Faraday’s Laws of Electromagnetic Induction

Faraday’s First Law

Whenever the magnetic flux linked with a circuit changes, an electromotive force (EMF) is induced in the circuit.

Mathematically,

Induced EMF (ε)∝dΦBdt\text{Induced EMF (ε)} \propto \frac{d\Phi_B}{dt}Induced EMF (ε)∝dtdΦB​​

Where ΦB = Magnetic flux.

Faraday’s Second Law

The magnitude of induced EMF is directly proportional to the rate of change of magnetic flux through the circuit.

ε=−dΦBdtε = -\frac{d\Phi_B}{dt}ε=−dtdΦB​​

The negative sign is due to Lenz’s law, indicating that induced EMF always opposes the change in magnetic flux.

Lenz’s Law

Lenz’s law states that:

The direction of the induced current is such that it always opposes the cause that produces it.

Mathematically represented by the negative sign in Faraday’s law.

Example: If the magnetic flux through a coil increases, the induced current will create a magnetic field opposing this increase.

Motional EMF

When a conductor moves in a magnetic field, charges inside experience a force and accumulate at the ends, producing an EMF.

• Formula:

$$\epsilon =Blv$$

Where
B = Magnetic field, l = length of conductor, v = velocity of conductor.

Induced EMF Types

1. Static EMF

• Produced when the magnetic field changes with time, but conductor remains stationary.

2. Motional EMF

• Produced when the conductor moves in a uniform magnetic field.

Eddy Currents

When a changing magnetic field passes through a solid conductor, circulating currents known as eddy currents are induced.

• Applications:

  • Electromagnetic brakes in trains.

  • Induction furnace.

  • Speedometers in vehicles.

  • Energy meters.

• Disadvantage: Energy loss in the form of heat.

Self-Induction

When the current in a coil changes, the magnetic flux linked with it also changes, inducing EMF in the same coil.

• Formula:

ε=−LdIdtε = -L \frac{dI}{dt}ε=−LdtdI​

Where L is the self-inductance.

Unit of L: Henry (H)

Mutual Induction

When current in one coil changes, it induces EMF in a nearby coil.

• Formula:

ε2=−MdI1dtε_2 = -M \frac{dI_1}{dt}ε2​=−MdtdI1​​

Where M is the mutual inductance between two coils.

Energy Stored in an Inductor

When current flows through an inductor, energy is stored in its magnetic field:

U=12LI2U = \frac{1}{2} L I^2U=21​LI2

Practical Applications of Electromagnetic Induction

• Electric Generators: Convert mechanical energy into electrical energy.

• Transformers: Step-up or step-down AC voltages.

• Induction Motors: Work on the principle of EMI.

• Wireless Charging: Uses changing magnetic fields to transfer power.

• Metal Detectors: Detect metallic objects using induced currents.

Important Derivations in Electromagnetic Induction

1. Derivation of EMF for a Rotating Coil in Magnetic Field

• Consider a coil with N turns rotating in a uniform magnetic field.

• Magnetic flux at time t:

  $$\Phi =BA\cos \theta$$

  Where $\theta =\omega t$.

• Induced EMF:

  ε=−dΦdt=NBAωsin⁡(ωt)ε = -\frac{d\Phi}{dt} = NBA\omega \sin(\omega t)ε=−dtdΦ​=NBAωsin(ωt)

Maximum EMF: εmax=NBAωε_{max} = NBA\omegaεmax​=NBAω

Points to Remember

• EMI is due to change in magnetic flux.

• Direction of induced EMF is given by Lenz’s Law.

• Self-inductance depends on the coil’s geometry and material.

• Eddy currents can cause energy losses.

Electromagnetic Induction – Objective Questions with Options

Q1. Who discovered electromagnetic induction?

• a) Newton

• b) Maxwell

• c) Faraday

• d) Tesla

Answer:
The phenomenon of electromagnetic induction was discovered by Michael Faraday in 1831.

Q2. The unit of magnetic flux is:

• a) Tesla

• b) Weber

• c) Henry

• d) Newton

Answer:
The SI unit of magnetic flux is Weber (Wb).

Q3. Which law gives the direction of induced EMF?

• a) Faraday’s first law

• b) Coulomb’s law

• c) Lenz’s law

• d) Gauss’s law

Answer:
The direction of induced EMF is given by Lenz’s Law.

Q4. The formula for motional EMF is:

• a) ε = Blv

• b) ε = IR

• c) ε = Q/V

• d) ε = mv²/2

Answer:
The correct formula for motional EMF is ε = B l v.

Q5. The SI unit of self-inductance is:

• a) Tesla

• b) Henry

• c) Weber

• d) Newton

Answer:
Self-inductance is measured in Henry (H).

Q6. Eddy currents cause:

• a) Cooling effect

• b) Heating losses

• c) Light emission

• d) Magnetic field removal

Answer:
Eddy currents produce heating losses in conductors.

Q7. Faraday’s first law states that:

• a) Induced current depends on voltage

• b) Current is directly proportional to power

• c) EMF is induced when magnetic flux changes

• d) No EMF is produced without current

Answer:
It states that EMF is induced when the magnetic flux linked with a circuit changes.

Q8. Which device works on mutual induction?

• a) Electric bulb

• b) Transformer

• c) Battery

• d) Solar cell

Answer:
Transformers work on the principle of mutual induction.

Q9. Energy stored in an inductor is given by:

• a) U = ½ C V²

• b) U = ½ L I²

• c) U = ½ m v²

• d) U = ½ Q²/C

Answer:
The energy stored in an inductor is U = ½ L I².

Q10. Lenz’s law is based on which principle?

• a) Conservation of energy

• b) Conservation of charge

• c) Conservation of mass

• d) Conservation of momentum

Answer:
Lenz’s law obeys the law of conservation of energy.

Q11. Eddy currents are reduced by:

• a) Increasing resistance

• b) Using laminated cores

• c) Increasing conductor thickness

• d) Decreasing voltage

Answer:
They are minimized by using laminated cores in electrical machines.

Q12. The direction of induced current is given by:

• a) Faraday’s second law

• b) Coulomb’s law

• c) Lenz’s law

• d) Ampere’s law

Answer:
The direction is given by Lenz’s law.

Q13. Induced current in a conductor depends on:

• a) Speed of motion

• b) Strength of magnetic field

• c) Length of conductor

• d) All of these

Answer:
It depends on all of these factors.

Q14. In a moving conductor, EMF is induced because:

• a) Magnetic force on charges

• b) Electric field is constant

• c) Motion is perpendicular to force

• d) Resistance decreases

Answer:
It is because magnetic force acts on moving charges in the conductor.

Q15. Which of the following uses electromagnetic induction?

• a) Generator

• b) Transformer

• c) Induction motor

• d) All of these

Answer:
All of these devices work on the principle of electromagnetic induction.

Q16. Mutual induction is measured in:

• a) Weber

• b) Henry

• c) Tesla

• d) Coulomb

Answer:
It is measured in Henry (H).

Q17. The EMF induced in a circuit is maximum when:

• a) Flux changes slowly

• b) Flux remains constant

• c) Flux changes rapidly

• d) Flux is zero

Answer:
It is maximum when flux changes rapidly.

Q18. Which is a disadvantage of eddy currents?

• a) Heating losses

• b) Power gain

• c) Reduced efficiency

• d) Both a and c

Answer:
Both heating losses and reduced efficiency are disadvantages.

Q19. The EMF produced without motion is called:

• a) Motional EMF

• b) Static EMF

• c) Induced EMF

• d) Potential difference

Answer:
It is called Static EMF.

Q20. In AC generators, EMF is induced because:

• a) Magnetic flux changes with time

• b) Resistance increases

• c) Voltage is constant

• d) Current is zero

Answer:
It is induced because magnetic flux linked with the coil changes with time.

Short Answer Questions (3 Marks)

Q1. Define electromagnetic induction with an example.

Electromagnetic induction is the process of producing an electromotive force (EMF) or current in a conductor when the magnetic flux linked with it changes. For example, when a bar magnet moves toward a coil connected to a galvanometer, current flows through the coil due to change in magnetic flux.

Q2. State Faraday’s laws of electromagnetic induction.

Faraday’s first law states that whenever the magnetic flux linked with a circuit changes, an induced EMF is produced in the circuit. Faraday’s second law states that the magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux through the circuit.

Q3. Write any two applications of eddy currents.

Eddy currents are used in electromagnetic brakes of trains and roller coasters to provide a smooth braking system. They are also used in induction furnaces for heating metals uniformly in industries.

Q4. What is self-induction? Write its formula.

Self-induction is the property of a coil by which it opposes the change in current flowing through it by inducing an EMF in itself. The formula for self-induced EMF is

ε=−LdIdtε = -L \frac{dI}{dt}ε=−LdtdI​

where L is the self-inductance of the coil.

Q5. Explain Lenz’s law.

Lenz’s law states that the direction of the induced current is such that it always opposes the change in magnetic flux that produced it. This is represented by the negative sign in Faraday’s second law and ensures the law of conservation of energy is followed.

Long Answer Questions (5 Marks)

Q1. Derive the expression for EMF induced in a rotating coil in a uniform magnetic field.

Consider a rectangular coil of N turns rotating with angular velocity ω in a uniform magnetic field B. The magnetic flux at any time t is

$$\Phi =BA\cos (\omega t)$$

The induced EMF is the negative rate of change of magnetic flux:

ε=−dΦdt=NBAωsin⁡(ωt)ε = -\frac{d\Phi}{dt} = NBA\omega \sin(\omega t)ε=−dtdΦ​=NBAωsin(ωt)

Hence, the maximum EMF is

εmax=NBAωε_{max} = NBA\omegaεmax​=NBAω

This derivation explains the working principle of AC generators.

Q2. Explain mutual induction with a neat diagram and formula.

Mutual induction is the phenomenon where a change in current in one coil induces an EMF in a nearby coil due to the change in magnetic flux linked with it. The induced EMF in the second coil is given by

ε2=−MdI1dtε_2 = -M\frac{dI_1}{dt}ε2​=−MdtdI1​​

where M is the mutual inductance between the two coils. Transformers and wireless chargers work on this principle.

Q3. What are eddy currents? Explain their uses and disadvantages.

When a solid conductor is placed in a changing magnetic field, circulating currents called eddy currents are induced in it.

Uses:

• Electromagnetic brakes in trains

• Induction furnaces for melting metals

• Speedometers in vehicles

Disadvantages:

• Energy loss due to heat

• Reduced efficiency of electrical devices

Laminating the core minimizes eddy current losses in machines.

Q4. Describe the principle and working of an AC generator.

An AC generator works on the principle of electromagnetic induction. A rectangular coil rotates in a uniform magnetic field, changing the magnetic flux linked with it. This produces an alternating EMF according to Faraday’s laws. The output voltage varies sinusoidally with time, producing alternating current.

Q5. What is self-inductance? Derive an expression for energy stored in an inductor.

Self-inductance is the property of a coil to oppose the change in current flowing through it. When current flows through an inductor of inductance L, energy is stored in its magnetic field.

The energy stored is

U=12LI2U = \frac{1}{2}LI^2U=21​LI2

This energy can be released when the current decreases to zero.

Conclusion

Electromagnetic induction is the backbone of modern electrical technology. From power generation to wireless communication, the concepts of Faraday’s laws, Lenz’s law, and inductance form the theoretical basis of numerous applications. Mastering these concepts not only helps in Class 12 exams but also builds a strong foundation for higher studies in physics and engineering.

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