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Chapter Analysis
Advanced22 pages • EnglishQuick Summary
In this chapter, the concept of electromagnetic induction, as discovered by Faraday and Henry, is explored. It discusses how electric currents are generated by changing magnetic fields and introduces key principles such as Faraday’s law of electromagnetic induction and Lenz’s law. The chapter covers the mathematical formulations of magnetic flux and induced emf, explains the workings of ac generators, and highlights the practical applications of these principles in devices like transformers. It touches on the role of mutual and self-inductance in electromagnetic systems.
Key Topics
- •Faraday's law of electromagnetic induction
- •Lenz's law
- •Motional electromotive force
- •Mutual inductance
- •Self-inductance
- •AC generators
- •Magnetic flux
- •Induced electromotive force
Learning Objectives
- ✓Understand Faraday’s law and its implications.
- ✓Explain Lenz's law and its relation to energy conservation.
- ✓Describe the process of electromagnetic induction in generating electrical energy.
- ✓Analyse the concepts of mutual and self-inductance and their applications.
- ✓Evaluate the operation principles of AC generators.
- ✓Apply mathematical expressions to calculate induced emf and inductance.
Questions in Chapter
Predict the direction of induced current in the situations described by the following Figs. 6.15(a) to (f).
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Use Lenz’s law to determine the direction of induced current in the situations described by Fig. 6.16.
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A long solenoid with 15 turns per cm has a small loop of area 2.0 cm² placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?
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A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm s–1 in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case?
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A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s–1 about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.
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A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 m s–1, at right angles to the horizontal component of the earth’s magnetic field, 0.30 × 10–4 Wb m–2. (a) What is the instantaneous value of the emf induced in the wire? (b) What is the direction of the emf? (c) Which end of the wire is at the higher electrical potential?
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Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V induced, give an estimate of the self-inductance of the circuit.
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A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?
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Additional Practice Questions
What is the significance of Lenz's Law in electromagnetic induction?
mediumAnswer: Lenz’s Law states that the direction of induced current is such that it opposes the change in magnetic flux that produces it. It is derived from the law of conservation of energy and ensures that energy is conserved within the system.
Explain how an AC generator converts mechanical energy into electrical energy.
hardAnswer: An AC generator consists of a coil rotated in a magnetic field, which induces an electromotive force due to the changing magnetic flux. Slip rings and brushes are used to connect the rotating coil to an external circuit. The mechanical rotation results in a sinusoidal output of voltage, converting mechanical energy to electrical energy.
Describe mutual inductance and its practical implications.
mediumAnswer: Mutual inductance occurs when a change in current in one coil induces a voltage in a neighboring coil. It is utilized in transformers and other electromagnetic devices to transfer energy between circuits.
How does self-inductance affect a circuit?
mediumAnswer: Self-inductance is the property of a circuit (or coil) to oppose a change in current due to its own magnetic field. It causes a back emf which can affect the timing of circuits and is crucial in the design of inductive components.
Explain the concept of motional emf and the Lorentz force.
hardAnswer: Motional emf is generated when a conductor moves through a magnetic field, inducing a voltage due to the Lorentz force acting on the charge carriers. This principle is fundamental in devices where mechanical motion is converted into electrical energy.
What are the primary components of an AC generator, and how do they function?
hardAnswer: The main components of an AC generator include the armature, magnetic field, slip rings, and brushes. The armature rotates within a magnetic field, altering the magnetic flux and inducing an emf. Slip rings and brushes transmit this induced current to an external circuit.
List the factors affecting the strength of the induced emf in a coil.
mediumAnswer: The strength of the induced emf in a coil depends on the rate of change of magnetic flux, the number of turns in the coil, the area of the coil, and the magnetic field strength.
What role does the angle between the coil and magnetic field play in electromagnetic induction?
easyAnswer: The angle between the coil and the magnetic field affects the component of the magnetic flux that acts through the coil. Changes in this angle, as the coil rotates, directly impact the amount of induced emf according to the cosine function.