Book cover for Physics

Physics

John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler

ISBN #9781118486894

10th Edition

2,562 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

Electromagnetic induction is the foundation for modern electrical technology, describing how a changing magnetic field produces an induced emf which, in a closed circuit, causes a current. Central to this topic are the concepts of motional emf, magnetic flux, Faraday’s law, and Lenz’s law. These ideas not only explain fundamental phenomena such as the operation of generators and transformers, but also underpin everyday applications from audio devices to vehicle cruise control systems. A careful application of the mathematical relationships, along with an understanding of energy conservation, is crucial for correctly analyzing and designing inductive circuits.

Learning Objectives

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Key Concepts

CONCEPT

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Example Problems

Example 1

A $0.80-\mathrm{m}$ aluminum bar is held with its length parallel to the east-west direction and dropped from a bridge. Just before the bar hits the river below, its speed is $22 \mathrm{m} / \mathrm{s},$ and the emf induced across its length is $6.5 \times 10^{-4} \mathrm{V} .$ Assuming the horizontal component of the earth's magnetic field at the location of the bar points directly north, (a) determine the magnitude of the horizontal component of the earth's magnetic field, and (b) state whether the east end or the west end of the bar is positive.

Example 2

Near San Francisco, where the vertically downward component of the earth's magnetic field is $4.8 \times 10^{-5} \mathrm{T}, \mathrm{a}$ car is traveling forward at $25 \mathrm{m} / \mathrm{s}$ The width of the car is $2.0 \mathrm{m}$. (a) Find the emf induced between the two sides of the car. (b) Which side of the car is positive - the driver's side or the passenger's side?

Example 3

In 1996, NASA performed an experiment called the Tethered Satellite experiment. In this experiment a $2.0 \times 10^{4}-\mathrm{m}$ length of wire was let out by the space shuttle Atlantis to generate a motional emf. The shuttle had an orbital speed of $7.6 \times 10^{3} \mathrm{m} / \mathrm{s},$ and the magnitude of the earth's magnetic field at the location of the wire was $5.1 \times 10^{-5} \mathrm{T}$. If the wire had moved perpendicular to the earth's magnetic field, what would have been the motional emf generated between the ends of the wire?

Example 4

The drawing shows a type of flow meter that can be used to measure the speed of blood in situations when a blood vessel is sufficiently exposed (e.g., during surgery). Blood is conductive enough that it can be treated as a moving conductor. When it flows perpendicularly with respect to a magnetic field, as in the drawing, electrodes can be used to measure the small voltage that develops across the vessel. Suppose that the speed of the blood is $0.30 \mathrm{m} / \mathrm{s}$ and the diameter of the vessel is $5.6 \mathrm{mm} .$ In a $0.60-\mathrm{T}$ magnetic field what is the magnitude of the voltage that is measured with the electrodes in the drawing?

Example 5

The drawing shows three identical rods $(\mathrm{A}, \mathrm{B}, \mathrm{and}\space \mathrm{C}$) moving in different planes. A constant magnetic field of magnitude $0.45 \mathrm{T}$ is directed along the $+y$ axis. The length of each rod is $L=1.3 \mathrm{m},$ and the rods each have the same speed, $v_{\mathrm{A}}=v_{\mathrm{B}}=v_{\mathrm{C}}=2.7 \mathrm{m} / \mathrm{s} .$ For each rod, find the magnitude of the motional emf, and indicate which end (1 or 2) of the rod is positive.
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