20.1 Introduction

In this chapter, we will explore Faraday’s law of electromagnetic induction and Lenz’s law. Faraday’s law states that a change in the magnetic field within a closed loop induces an electromotive force (EMF) in the loop. Lenz’s law describes the direction of the induced EMF and helps us understand the principle of energy conservation in electromagnetic induction.

20.2 Faraday’s Law of Electromagnetic Induction

Faraday’s law states that the electromotive force (EMF) induced in a closed loop is equal to the negative rate of change of the magnetic flux passing through the loop:

where is the magnetic flux and is time.

20.3 Magnetic Flux

Magnetic flux () is a measure of the magnetic field passing through a given area. It is defined as the product of the magnetic field (), the area (), and the cosine of the angle () between the magnetic field and the normal to the area:

20.4 Lenz’s Law

Lenz’s law states that the direction of the induced EMF and the resulting current are such that they oppose the change in magnetic flux that produced them. This opposition can be understood through the conservation of energy, as it prevents the perpetual generation of energy from an induced current.

20.5 Applications of Electromagnetic Induction

Electromagnetic induction is the principle behind many devices and technologies, including:

• Transformers: These devices use varying magnetic fields to transfer electrical energy between two coils with different numbers of turns, allowing voltage to be stepped up or down as needed.
• Generators: In a generator, mechanical energy is converted into electrical energy by rotating a coil within a magnetic field, inducing an EMF and producing a current.
• Induction motors: An induction motor operates on the principle of electromagnetic induction, where an alternating current in a primary coil creates a varying magnetic field that induces a current in a secondary coil, producing torque and causing rotation.

20.6 Eddy Currents

Eddy currents are circular currents induced in a conductive material by a changing magnetic field. These currents can generate heat and cause energy loss in some applications, such as transformers and motors. Techniques such as laminating the cores or using materials with high electrical resistance can help minimize eddy current losses.

Chapter Summary

In this chapter, we discussed Faraday’s law of electromagnetic induction, which states that a change in the magnetic field within a closed loop induces an electromotive force. We also explored Lenz’s law, which helps us understand the direction of the induced EMF and how it opposes the change in magnetic flux. Electromagnetic induction plays a crucial role in many technologies, including transformers, generators, and induction motors. Understanding these principles allows us to harness and manipulate electromagnetic energy more efficiently.

Contine to Chapter 21: Superconductivity

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