Book cover for Physics

Physics

Alan Giambattista, Betty McCarthy Richardson, Robert C. Richardson

ISBN #9780073404530

2nd Edition

2,795 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter on electromagnetic induction covers the principles governing the generation of an emf through the motion of conductors in magnetic fields and changing magnetic flux. Central to the discussion are Faraday’s law, which quantitatively relates the induced emf to the rate of change of flux, and Lenz’s law, which determines the direction of induced currents. Applications such as electric generators, transformers, and motors illustrate how these principles are harnessed in technology. Additional topics include back emf, eddy currents, and inductance, which are essential for understanding transient behaviors in LR circuits and energy storage in magnetic fields.

Learning Objectives

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Key Concepts

CONCEPT

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Example Problems

Example 1

In Fig. $20.2,$ a metal rod of length $L$ moves to the right at speed $v .$ (a) What is the current in the rod, in terms of $v, B, L,$ and $R ?$ (b) In what direction does the current flow? (c) What is the direction of the magnetic force on the rod? (d) What is the magnitude of the magnetic force on the rod (in terms of $v, B, L,$ and $R$ )?

Example 2

Suppose that the current were to flow in the direction opposite to that found in Problem 1. (a) In what direction would the magnetic force on the rod be? (b) In the absence of an external force, what would happen to the rod's kinetic energy? (c) Why is this not possible? Returning to the correct direction of the current, sketch a rough graph of the kinetic energy of the rod as a function of time.

Example 3

To maintain a constant emf, the moving rod of Fig. 20.2 must maintain a constant velocity. In order to maintain a constant velocity, some external force must pull it to the right. (a) What is the magnitude of the external force required, in terms of $v, B, L,$ and $R ?$ (See Problem 1.) (b) At what rate does this force do work on the rod? (c) What is the power dissipated in the resistor? (d) Overall, is energy conserved? Explain.

Example 4

In Fig. $20.2,$ what would the magnitude (in terms of $v$ $L, R, \text { and } B)$ and direction (CW or CCW) of the current be if the direction of the magnetic field were: (a) into the page; (b) to the right (in the plane of the page); (c) up (in the plane of the page); (d) such that it has components both out of the page and to the right, with a $20.0^{\circ}$ angle between the field and the plane of the page?

Example 5

A 15.0 -g conducting rod of length $1.30 \mathrm{m}$ is free to slide downward between two vertical rails without friction. The rails are connected to an $8.00-\Omega$ resistor, and the entire apparatus is placed in a $0.450-$ T uniform magnetic field. Ignore the resistance of the rod and rails. (a) What is the terminal velocity of the rod? (b) At this terminal velocity, compare the magnitude of the change in gravitational potential energy per second with the power dissipated in the resistor. (FIGURE CANNOT COPY)
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