Class 12 Physics NCERT Solutions: Electromagnetic Induction Important Questions

Electromagnetic Induction is a crucial chapter in the Class 12 Physics curriculum as prescribed by the NCERT (National Council of Educational Research and Training) in India. This chapter covers the fundamental principles and applications of Faraday's Law of Electromagnetic Induction, Lenz's Law, eddy currents, and self and mutual induction. These concepts are essential for understanding various phenomena in electromagnetism and form the foundation for advanced topics in physics and engineering.

In this comprehensive article, we will explore the important questions from the chapter on Electromagnetic Induction, providing detailed solutions and explanations. The content will help students prepare effectively for their Class 12 board exams and competitive entrance exams like JEE Main and NEET.

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1. What is Electromagnetic Induction?

Electromagnetic Induction refers to the process by which a changing magnetic field within a conductor induces an electromotive force (EMF). This phenomenon was discovered by Michael Faraday in 1831, and it has two fundamental laws:

1. Faraday's First Law: When the magnetic flux linked with a circuit changes, an EMF is induced in the circuit.
2. Faraday's Second Law: The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux.

Mathematically, the induced EMF ($\varepsilon$) can be expressed as:

$$\varepsilon = -\frac{d\Phi}{dt}$$

where $\Phi$ is the magnetic flux and $\frac{d\Phi}{dt}$ represents the rate of change of magnetic flux.

2. Important Questions and Solutions on Electromagnetic Induction

Let's dive into some of the most important questions from the chapter "Electromagnetic Induction" for Class 12 Physics. These questions are often asked in board exams and competitive entrance tests. We will provide detailed answers to help you grasp the underlying concepts better.

Question 1: Explain Lenz's Law of Electromagnetic Induction with an Example.

Solution:

Lenz's Law states that the direction of the induced current is such that it opposes the change in magnetic flux that caused it. This law is a consequence of the law of conservation of energy.

Example:

Consider a coil connected to a galvanometer. When a bar magnet is moved towards the coil, an EMF is induced, and a current flows through the coil. The direction of the induced current will be such that it creates a magnetic field opposing the motion of the magnet. If the north pole of the magnet is moved towards the coil, the end of the coil facing the magnet will develop a north pole to repel it.

This opposing nature of the induced current is due to Lenz's Law and ensures that energy is conserved in the process.

Question 2: Derive the Expression for the Induced EMF in a Rotating Coil in a Magnetic Field.

Solution:

Consider a rectangular coil of $N$ turns, area $A$, rotating with angular velocity $\omega$ in a uniform magnetic field $B$. The magnetic flux ($\Phi$) through the coil at any time $t$ is given by:

$$\Phi = B \cdot A \cdot \cos(\omega t)$$

According to Faraday's Law, the induced EMF is:

$$\varepsilon = -\frac{d\Phi}{dt}$$

Substituting the value of $\Phi$:

$$\varepsilon = -\frac{d}{dt} (B \cdot A \cdot \cos(\omega t))$$ $$\varepsilon = B \cdot A \cdot \omega \cdot \sin(\omega t)$$

Therefore, the maximum induced EMF ($\varepsilon_0$) is:

$$\varepsilon_0 = B \cdot A \cdot \omega$$

Thus, the induced EMF varies sinusoidally with time, and its expression is:

$$\varepsilon = \varepsilon_0 \cdot \sin(\omega t)$$

This equation describes an alternating current (AC) generator.

Question 3: What are Eddy Currents? Explain Their Applications and Disadvantages.

Solution:

Eddy Currents are circulating currents that are induced in a conductor when it is exposed to a changing magnetic field. These currents flow in closed loops within the conductor, perpendicular to the magnetic field.

Applications of Eddy Currents:

1. Magnetic Braking in Trains: Eddy currents are used in magnetic brakes where a magnetic field induces eddy currents in the wheels, producing a force that opposes the motion and slows down the train.

2. Induction Heating: Used in induction cooktops, where eddy currents heat the cooking vessel.

3. Energy Meters: In electric energy meters, the rotating disk's motion is slowed down using eddy currents, allowing accurate measurement of energy consumption.

Disadvantages of Eddy Currents:

1. Energy Losses: Eddy currents cause energy losses in the form of heat, especially in transformers, electric motors, and other AC machinery.

2. Overheating: The unwanted heat generated by eddy currents can cause overheating of electrical components.

To minimize eddy currents, laminated cores are used in transformers and motors, which increase the resistance to current flow, thereby reducing eddy currents.

Question 4: Explain the Concept of Self-Induction and Derive the Expression for Self-Inductance.

Solution:

Self-Induction is the phenomenon by which a changing current in a coil induces an EMF in the same coil. This EMF opposes the change in current, as per Lenz's Law.

The self-induced EMF ($\varepsilon$) is given by:

$$\varepsilon = -L \frac{dI}{dt}$$

where $L$ is the self-inductance of the coil and $\frac{dI}{dt}$ is the rate of change of current.

Expression for Self-Inductance (L):

For a solenoid of length $l$, number of turns $N$, and cross-sectional area $A$, the magnetic flux ($\Phi$) is:

$$\Phi = B \cdot A = \mu_0 \frac{N}{l} I \cdot A$$

The total flux linked with the coil is:

$$N \Phi = \mu_0 \frac{N^2 A}{l} I$$

The self-inductance $L$ is defined as:

$$L = \frac{N \Phi}{I} = \mu_0 \frac{N^2 A}{l}$$

Thus, the self-inductance of a solenoid depends on the number of turns, the area of the cross-section, and the length of the solenoid.

Question 5: Describe Mutual Induction and its Application in Transformers.

Solution:

Mutual Induction is the phenomenon by which a change in current in one coil induces an EMF in a neighboring coil. It is the basic working principle of transformers, which are used to step up or step down AC voltages.

Mutual Inductance (M):

The mutual inductance between two coils is given by:

$$\varepsilon_2 = -M \frac{dI_1}{dt}$$

where $M$ is the mutual inductance, $\varepsilon_2$ is the induced EMF in the second coil, and $\frac{dI_1}{dt}$ is the rate of change of current in the first coil.

Application in Transformers:

A transformer consists of a primary coil and a secondary coil wound on a common magnetic core. When an alternating current flows through the primary coil, it creates a changing magnetic field, which induces an EMF in the secondary coil. The voltage induced in the secondary coil depends on the turn ratio between the coils:

$$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$

where $V_s$ and $V_p$ are the voltages in the secondary and primary coils, respectively, and $N_s$ and $N_p$ are the number of turns in the secondary and primary coils, respectively.

Transformers are used in power distribution systems to step up voltage for transmission and step it down for domestic or industrial use.

Question 6: Calculate the Induced EMF When a Rod of Length 1 m Moves Perpendicularly Through a Magnetic Field of 0.5 T with a Velocity of 2 m/s.

Solution:

The induced EMF in a moving conductor in a magnetic field can be calculated using the formula:

$$\varepsilon = B \cdot l \cdot v$$

where:

• $B = 0.5 \, \text{T}$ (magnetic field strength)
• $l = 1 \, \text{m}$ (length of the rod)
• $v = 2 \, \text{m/s}$ (velocity of the rod)

Substituting the values:

$$\varepsilon = 0.5 \times 1 \times 2 = 1 \, \text{V}$$

Therefore, the induced EMF is 1 volt.

Question 7: A Coil of 100 Turns and an Area of $0.01 \, \text{m}^2$ is Placed in a Magnetic Field Which Changes from 0.1 T to 0.5 T in 2 Seconds. Calculate the Induced EMF.

Solution:

The induced EMF for a coil is given by Faraday's Law:

$$\varepsilon = -N \frac{d\Phi}{dt}$$

where:

• $N = 100$ turns
• Change in magnetic field ($\Delta B$) = $0.5 - 0.1 = 0.4 \, \text{T}$
• Area ($A$) = $0.01 \, \text{m}^2$
• Time ($\Delta t$) = 2 seconds

Magnetic flux ($\Phi$) is $B \cdot A$, so:

$$\varepsilon = -N \frac{\Delta (B \cdot A)}{\Delta t}$$ $$\varepsilon = -100 \times \frac{0.4 \times 0.01}{2}$$ $$\varepsilon = -100 \times \frac{0.004}{2}$$ $$\varepsilon = -100 \times 0.002 = -0.2 \, \text{V}$$

The negative sign indicates that the induced EMF opposes the change in magnetic flux according to Lenz's Law. The magnitude of the induced EMF is 0.2 V.

Conclusion

The chapter on Electromagnetic Induction is a pivotal topic in Class 12 Physics, providing the foundation for understanding various applications in electromagnetism, electrical engineering, and technology. The questions discussed above cover a range of concepts from Lenz's Law and eddy currents to self and mutual induction. A solid understanding of these topics is essential for performing well in board exams and competitive entrance tests like JEE Main and NEET.

By practicing these questions and thoroughly understanding the solutions, students can gain a deep understanding of Electromagnetic Induction, enhance their problem-solving skills, and prepare effectively for their exams.