Physics

Chapter 19 Review

Magnets and Magnetic Fields 10. You have two iron bars and a ball of string in your
possession; one iron bar is magnetized, and one iron
Reviewing Main Ideas bar is not. How can you determine which iron bar is
magnetized?
1. What is the minimum number of poles for a magnet?
11. Why does a very strong magnet attract both poles of a
2. When you break a magnet in half, how many poles weak magnet?
does each piece have?
12. A magnet attracts a piece of iron. The iron can then
3. The north pole of a magnet is attracted to the attract another piece of iron. Explain, on the basis of
geographic North Pole of Earth, yet like poles repel. alignment of domains, what happens in each piece
Can you explain this? of iron.

4. W hich way would a compass needle point if you were 13. W hen a small magnet is repeatedly dropped, it
at the magnetic north pole? becomes demagnetized. Explain what happens to
the magnet at the atomic level.
5. What is a magnetic domain?
Magnetism from Electricity
6. W hy are iron atoms so strongly affected by mag­netic
fields? Reviewing Main Ideas

7. W hen a magnetized steel needle is strongly heated in 14. A conductor carrying a current is arranged so that
a Bunsen burner flame, it becomes demagn­ etized. electrons flow in one segment from east to west. If a
Explain why. compass is held over this segment of the wire, in what
direction is the needle deflected? (Hint: Recall that
8. I f an unmagnetized piece of iron is attracted to current is defined as the motion of positive charges.)
one pole of a magnet, will it be repelled by the
opposite pole? 15. What factors does the strength of the magnetic field
of a solenoid depend on?
Conceptual Questions
Conceptual Questions
9. I n the figure below, two permanent magnets with
holes bored through their centers are placed one 16. A solenoid with ends marked A and B is suspended
over the other. Because the by a thread so that the core can rotate in the horizon-
poles of the upper magnet tal plane. A current is maintained in the coil so that
are the reverse of those of the electrons move clockwise when viewed from end
the lower, the upper magnet A toward end B. How will the coil align itself in Earth’s
levitates above the lower magnetic field?
magnet. If the upper magnet
were displaced slightly, 17. Is it possible to orient a current-carrying loop of wire
either up or down, what in a uniform magnetic field so that the loop will not
would be the resulting tend to rotate?
motion? Explain. What
would happen if the upper
magnet were inverted?

Chapter Review 681

Chapter review 26. For each situation below, use the movement of the
positively charged particle and the direction of the
18. I f a solenoid were suspended by a string so that it magnetic force acting on it to find the direction of the
could rotate freely, could it be used as a compass magnetic field.
when it carried a direct current? Could it also be used
if the current were alternating in direction? (a) F (b) F (c)
F
Magnetic Force v
vout vin
Reviewing Main Ideas
Conceptual Questions
19. Two charged particles are projected into a region
where there is a magnetic field perpendicular to their HRW • Holt Physics
velocities. If the particles are deflected in opposite
directions, what can you say about them? 27. A stream of electrPoHn9s9iPsEp-rCo2j1e-cCtHedR-h0o08r-izAontally to the
right. A straight conductor carrying a current is
20. S uppose an electron is chasing a proton up this page supported parallel to and above the electron stream.
when suddenly a magnetic field pointing into the a. What is the effect on the electron stream if the
page is applied. What would happen to the particles? current in the conductor is left to right?
b. What is the effect if the current is reversed?
21. W hy does the picture on a television screen become
distorted when a magnet is brought near the screen? 28. If the conductor in item 27 is replaced by a magnet
with a downward magnetic field, what is the effect on
22. A proton moving horizontally enters a region where the electron stream?
there is a uniform magnetic field perpendicular to the
proton’s velocity, as shown below. Describe the 29. Two wires carrying equal but opposite currents are
proton’s subsequent motion. How would an electron twisted together in the construction of a circuit. Why
behave under the same circumstances? does this technique reduce stray magnetic fields?

Bin Practice Problems

+v For problems 30–31, see Sample Problem A.

23. Explain why two parallel wires carrying currents in 30. A duck flying due east passes over Atlanta, where the
opposite direPcHtH9io9RnPWEs-•rCeH2p1oe-ltlCPeHhaRyc-sh0ic0os6t-hAer. magnetic field of Earth is 5.0 × 10-5 T directed north.
The duck has a positive charge of 4.0 × 10-8 C. If the
24. Can a stationary magnetic field set a resting electron magnetic force acting on the duck is 3.0 × 10-11 N
in motion? Explain. upward, what is the duck’s velocity?

25. At a given instant, a proton moves in the positive x 31. A proton moves eastward in the plane of Earth’s
direction in a region where there is a magnetic field in magnetic equator, where Earth’s magnetic field points
the negative z direction. What is the direction of the north and has a magnitude of 5.0 × 10–5 T. What
magnetic force? Does the proton cont­ inue to move velocity must the proton have for the magnetic force
along the x‑axis? Explain. to just cancel the gravitational force?

For problems 32–33, see Sample Problem B.

32. A wire carries a 10.0 A current at an angle 90.0° from
the direction of a magnetic field. If the magnitude of
the magnetic force on a 5.00 m length of the wire is
15.0 N, what is the strength of the magnetic field?

682 Chapter 19

33. A thin 1.00 m long copper rod in a uniform magnet­ ic Chapter review
field has a mass of 50.0 g. When the rod carries a
current of 0.245 A, it floats in the magnetic field. What 40. A proton travels with a speed of 3.0 × 106 m/s at an
is the field strength of the magnetic field? angle of 37° west of north. A magnetic field of 0.30 T
points to the north. Determine the following:
Mixed Review a. t he magnitude of the magnetic force on the proton
b. t he direction of the magnetic force on the proton
Reviewing Main Ideas c. the proton’s acceleration as it moves through the
magnetic field
34. A proton moves at 2.50 × 106 m/s horizontally at a
(Hint: The magnetic force experienced by the proton
right angle to a magnetic field. in the magnetic field is proportional to the compo-
a. What is the strength of the magnetic field required nent of the proton’s velocity that is perpendicular to
the magnetic field.)
to exactly balance the weight of the proton and
41. I n the figure below, a 15 cm length of conducting wire
keep it moving horizontally? that is free to move is held in place between two thin
b. Should the direction of the magnetic field be in a conducting wires. All the wires are in a magnetic field.
When a 5.0 A current is in the wire, as shown in the
horizontal or a vertical plane? figure, the wire segment moves upward at a constant
velocity. Assuming the wire slides without friction on
35. Find the direction of the force on a proton moving the two vertical conductors and has a mass of 0.15 kg,
through each magnetic field in the four figures below. find the magnitude and direction of the minimum
magnetic field that is required to move the wire.
(a) v (b) v B

Bin

15 cm

(c) (d) Bout 5.0 A

HRvW • Holt Physics HRW • Holt Physics 5.0 A 5.0 A
PH99PE-C21-CHR-002-A PH99PvE-C21-CHR-003-A

B

36. Find the direction of the force on an electron moving 42. A current, I = 15 A, is directed along the positive
x-axis and perpeHnRdWic•uHlaorlttoPhaysuicnsiform magnetic field.
through each magnetic field in the four figures in The conductoPrHe9x9pPeEr-iCe2n1c-eCsHaRm-00a7g-nAetic force per unit
itPeHmH99 R3PW5Ea-•CbH2o1ov-lteCP.HhRy-s0ic0s4-A HRW • Holt Physics length of 0.12 N/m in the negative y direction.
PH99PE-C21-CHR-005-A Calculate the magnitude and direction of the
magnetic field in the region through which the
37. I n the four figures in item 35, assume that in each current passes.

case the velocity vector shown is replaced with a wire

carrying a current in the direction of the velocity

vector. Find the direction of the magnetic force acting 43. A proton moving perpendicular to a magnetic field of

on each wire. strength 3.5 mT experiences a force due to the field of
4.5 × 10-21 N. Calculate the following:
38. A proton moves at a speed of 2.0 × 107 m/s at right a. the speed of the proton
angles to a magnetic field with a magnitude of 0.10 T. b. the kinetic energy of the proton
Find the magnitude of the acceleration of the proton. Recall that a proton has a charge of 1.60 × 10-19 C
and a mass of 1.67 × 10-27 kg.
39. A proton moves perpendicularly to a uniform
magn­ etic field, B, with a speed of 1.0 × 107 m/s and
experiences an acceleration of 2.0 × 1013 m/s2 in the

positive x direction when its velocity is in the positive

z direction. Determine the magnitude and direction

of the field.

Chapter Review 683

Chapter review 46. C alculate the force on an electron in each of the

44. A singly charged positive ion that has a mass of following situations:
6.68 × 10-27 kg moves clockwise with a speed of a. moving at 2.0 percent the speed of light and
1.00 × 104 m/s. The positively charged ion moves in a
circular path that has a radius of 3.00 cm. Find the perpendicular to a 3.0 T magnetic field
direction and strength of the uniform magnetic field b. 3 .0 × 10-6 m from a proton
through which the charge is moving. (Hint: The c. in Earth’s gravitational field at the surface of Earth
magnetic force exerted on the positive ion is the Use the following: qe = -1.6 × 10-19 C;
centripetal force, and the speed given for the positive me = 9.1 × 10-31 kg; qp = 1.6 × 10-19 C;
ion is its tangential speed.) c = 3.0 × 108 m/s; kC = 9.0 × 109 N•m2/C2

45. W hat speed would a proton need to achieve in order
to circle Earth 1000.0 km above the magne­tic
equator? Assume that Earth’s magnetic field is
everywhere perpendicular to the path of the proton
and that Earth’s magnetic field has an intensity of
4.00 × 10-8 T. (Hint: The magnetic force exerted on
the proton is equal to the centripetal force, and the
speed needed by the proton is its tangential speed.
Remember that the radius of the circular orbit
should also include the radius of Earth. Ignore
relativistic effects.)

Solenoids known at two different currents. Once you determine a and b,
you can predict the magnetic field strength of a solenoid for
A solenoid consists of a long, helically wound coil of insulated various currents.
wire. When it carries a current, a solenoid acts as a magnet.
The magnetic field strength (B) increases linearly with the The graphing calculator program that accompanies this
current (I ) and with the number of coils per unit length. activity uses this procedure. You will be given the magnetic
Because there is a direct relation between B and I, the field and current data for various solenoids. You will then use
following equation applies to any solenoid: this information and the program to predict the magnetic field
strength of each solenoid.
B = aI + b
Go online to HMDScience.com to find this graphing
In this equation, the parameters a and b are different for calculator activity.
different solenoids. The a and b parameters can be
determined if the magnetic field strength of the solenoid is

684 Chapter 19

ALTERNATIVE ASSESSMENT Chapter review

1. D uring a field investigation with your class, you find a 3. Research phenomena related to one of the following
roundish chunk of metal that attracts iron objects. topics, and prepare a report or presentation with
Design a procedure to determine whether the object pictures and data.
is magnetic and, if so, to locate its poles. Describe the a. H ow does Earth’s magnetic field vary with latitude,
limitations of your method. What materials would with longitude, with the distance from Earth, and
you need? How would you draw your conclusions? in time?
List all the possible results you can anticipate and the b. How do people who rely on compasses account for
conclusions you could draw from each result. these differences in Earth’s magnetic field?
c. What is the Van Allen belt?
2. I magine you have been hired by a manufacturer d. H ow do solar flares occur?
interested in making kitchen magnets. The manufac- e. How do solar flares affect Earth?
turer wants you to determine how to combine several
magnets to get a very strong magnet. He also wants to 4. Obtain old buzzers, bells, telephone receivers,
know what protective material to use to cover the speakers, motors from power or kitchen tools, and so
magnets. Develop a method for measuring the on to take apart. Identify the mechanical and electro-
strength of different magnets by recording the magnetic components. Examine their connections.
maximum number of paper clips they can hold under How do they produce magnetic fields? Work in a
various conditions. First open a paper clip to use as a cooperative group to describe and organize your
hook. Test the strength of different magnets and findings about several devices for a display entitled
combinations of magnets by holding up the magnet, “Anatomy of Electromagnetic Devices.”
placing the open clip on the magnet, and hooking the
rest of the paper clips so that they hang below the 5. Magnetic force was first described by the ancient
magnet. Examine the effect of layering different Greeks, who mined a magnetic mineral called
materials between the magnet and the clips. Organize magnetite. Magnetite was used in early experiments
your data in tables and graphs to present your on magnetic force. Research the historical develop-
conclusions. ment of the concept of magnetic force. Describe the
work of Peregrinus, William Gilbert, Oersted,
Faraday, and other scientists.

Chapter Review 685

Standards-Based Assessment

mulTiple choice 4. How can you increase the strength of a magnetic
field inside a solenoid?
1. Which of the following statements best describes F. increase the number of coils per unit length
the domains in unmagnetized iron? G. increase the current
A. There are no domains. H. place an iron rod inside the solenoid
B. There are domains, but the domains are smaller J. all of the above
than in magnetized iron.
C. There are domains, but the domains are Use the diagram below to answer questions 5–6.
oriented randomly.
D. There are domains, but the domains are B in
not magnetized.
v
2. Which of the following statements is most correct? –
F. The north pole of a freely rotating magnet points
north because the magnetic pole near the 5. How will the electron move once it passes into the
geographic North Pole is like the north pole of magnetic field?
a magnet. A. It will curve to the right and then continue
G. The north pole of a freely rotating magnet points moving in a straight line to the right.
north because the magnetic pole near the B. It will curve to the left and then continue moving
geographic North Pole is like the south pole of in a straight line to the left.
a magnet. C. It will move in a clockwise circle.
H. The north pole of a freely rotating magnet points D. It will move in a counterclockwise circle.
south because the magnetic pole near the
geographic South Pole is like the north pole of 6. What will be the magnitude of the force on the
a magnet. electron once it passes into the magnetic field?
J. The north pole of a freely rotating magnet points F. qvB
south because the magnetic pole near the G. -qvB
geographic South Pole is like the south pole of H. ​_ qBv  ​ 
a magnet. J. BIℓ

3. If you are standing at Earth’s magnetic north pole 7. An alpha particle (q = 3.2 × 10-19 C) moves at a
and holding a bar magnet that is free to rotate in speed of 2.5 × 106 m/s perpendicular to a magn­ etic
three dimensions, which direction will the south field of strength 2.0 × 10-4 T. What is the magnitude
pole of the magnet point? of the magnetic force on the particle?
A. straight up A. 1.6 × 10-16 N
B. straight down B. -1.6 × 10-16 N
C. parallel to the ground, toward the north C. 4.0 × 10-9 N
D. parallel to the ground, toward the south D. zero

686 Chapter 19

Test Prep

Use the passage below to answer questions 8–9. 11. What is the direction of the force on wire 2 as a
A wire 25 cm long carries a 12 A current from east to result of B1?
west. Earth’s magnetic field at the wire’s location has a A. to the left
magnitude of 4.8 × 10-5 T and is directed from south B. to the right
to north. C. into the page
8. What is the magnitude of the magnetic force on D. out of the page

the wire? 12. What is the magnitude of the magnetic force on
F. 2.3 × 10-5 N wire 2?
G. 1.4 × 10-4 N F. B1I1ℓ1
H. 2.3 × 10-3 N G. B1I1ℓ2
J. 1.4 × 10-2 N H. B1I2ℓ2
9. What is the direction of the magnetic force on J. B2I2ℓ2
the wire?
A. north SHORT RESPONSE
B. south
C. up, away from Earth 13. Sketch the magnetic field lines around a
D. down, toward Earth bar magnet.

Use the diagram below to answer questions 10–12. 14. Describe how to use the right-hand rule to deter-
I1 mine the direction of a magnetic field around a
current-carrying wire.
I2
15. Draw a diagram showing the path of a positively
Wire 1 carries current I1 and creates magnetic field B1. charged particle moving in the plane of a piece of
Wire 2 carries current I2 and creates magnetic field B2. paper if a uniform magnetic field is coming out of
10. What is the direction of the magnetic field B1 at the the page.

location of wire 2? EXTENDED RESPONSE
F. to the left
G. to the right 16. A proton (q = 1.6 × 10-19 C; m = 1.7 × 10-27 kg) is
H. into the page in a uniform 0.25 T magnetic field. The proton
J. out of the page moves in a clockwise circle with a tangential speed
of 2.8 × 105 m/s.
a. What is the direction of the magnetic field?
Explain how you determined this.
b. What is the radius of the circle? Show your work.

11 12 1 Test Tip
10 2 If you are asked to write out an answer,
93 to show your calculations, or to draw
a diagram, be sure to write clearly, to
84 show all steps of your work, and to add
76 5 clear labels to your diagrams. You may
receive some credit for using the right
approach to a problem, even if you do
not arrive at the correct final answer.

Standards-Based Assessment 687

  engineering and technology
Can Cell Phones
Cause Cancer?

Cell phones transfer messages by sending and receiving Cell-phone usage has become increasingly popular among ©BananaStock/Jupiterimages
electromagnetic waves. The electromagnetic spectrum children, adolescents, and adults. Little is known, however,
includes low-energy waves, such as radio waves, and high- about its long-term health effects.
energy waves, such as X rays and gamma rays. High-energy
electromagnetic waves are ionizing, which means they have people to determine if there are any health issues linked to
enough energy to remove an electron from its orbit. Ionizing prolonged exposure to radio frequency energy from cell phone
electromagnetic radiation can damage living tissue and use. The COSMOS study will follow approximately 250 000 cell
cause DNA mutations, which is why exposure to X rays should phone users in Europe for over 25 years.
be limited.
MOBI-KIDS is another international study investigating the
Cell phones use radio frequencies (RFs) ranging from about relationship between exposure to radio frequency energy
800 to 900 MHz. These nonionizing waves do not alter the from communication technologies, including cell phones, and
molecular structure of living tissue. Though they can cause the brain cancer in young people. This study, which involves
atoms in a molecule to vibrate, they do not have enough 13 countries, began in 2010 and will continue for 5 years.
energy to remove electrons from their orbits. At high enough
levels, however, nonionizing radiation can cause biological Interphone is still another international study designed to
damage by heating living tissue. But the amount of heat that a determine whether cell phones increase the risk of head and
cell phone’s radiation generates is very small and is much neck cancer. In this study, scientists compared cell phone
smaller than the energy generated in a microwave oven. usage for more than 5000 people with brain tumors and a
similar number of healthy controls.
Identify the Problem: Effects of Nonionizing
Radiation Results of this study did not conclusively show that cell
The effects of nonionizing radiation on the human body are not phones caused brain cancer. However, the study did suggest
fully known. Several studies have been conducted to determine that people who used cell phones an average of more than a
whether there is a link between cell phone use and brain half hour per day, every day, for over 10 years had a slight
cancer. Scientists conducting these studies have attempted to increase in brain cancer. But the scientists cautioned that the
determine whether the risk of brain cancer is greater for cell increase was not significant enough to determine a relationship
phone users than for nonusers. Even if a link is found, it is not between heavy use of cell phones and brain cancer.
necessarily a cause-and-effect link. In other words, even if cell
phone users do have a higher risk of cancer, cell phone use is However, a December 2010 report questioned the findings of
not necessarily the cause. the Interphone study. In this latest report, scientists examined
the findings of the earlier report to include a wider age group
Other issues complicate research into the issue. Cell phones
were not widely available until the 1990s, and brain tumors
develop over many years. Therefore, long-range studies are
required to assess the effects of nonionizing radiation from cell
phones. One such study is now underway.

Conduct Research
The International Cohort Study on Mobile Phone Users (COSMOS)
aims to conduct long-term health monitoring of a large group of

688

and redefine how users were classified. Based on their results, and thinner skulls, they should limit cell phone use. Some
the scientists concluded that there was a significant link scientists also warn against using a cell phone in areas with a
between heavy cell phone use and brain cancer. weak signal, because the phones emit more radiation during
those times. Finally, researchers caution to not go to sleep with
Select a Solution a cell phone turned on and placed next to your bedside or
While researchers continue their investigation of nonionizing under your pillow.
radiation, concerned cell phone users can take measures to
limit their exposure to RFs. Exposure depends on a number of Design Your Own
factors, including the amount of time spent using the phone,
the amount of cell phone traffic in the area, and the distance Conduct Research
between the antenna and the user’s head. One way to reduce As cell phones have grown in popularity, concerns have arisen
exposure is to minimize the time spent on cellular calls. not only about brain cancer, but also about the safety of driving
Another option is to use a hands-free device that puts the while using a cell phone. Several countries and many states in
antenna farther from the head. the United States have banned the use of cell phones while
driving. Conduct research to find out about studies conducted
Additionally, pregnant women should avoid carrying a cell on this issue. Is it hazardous? Should laws be passed in all
phone next to their abdomen. Because children have smaller states that prevent the use of a cell phone while driving in a
school zone? Write a paper summarizing your findings.
Radio towers, such as the one in this image, send out radio
signals that are picked up by cell phones and translated Test and Evaluate
into sounds and images. Cell phone makers are now required to report the specific
absorption rate (SAR), the amount of RF energy absorbed by
©PictureNet/Corbis the user. The maximum allowed SAR is 1.6 watts per kilogram.
Find the SAR of several top models of phones. If you own a cell
phone, see if you can determine the SAR of your phone.

Communicate
Use the Internet to research one of the recent studies done on
cell phone use and brain cancer. Write a short report describing
the study, including the subjects and control group, the method
of obtaining data, and the conclusions reached by the
researchers. Share your report with the class.

689

The vibrations of the strings in an (bg) ©Aaron Jones Studio/Getty Images
electric guitar change the magnetic
field near a coil of wire called the
pickup. In turn, this induces an
electric current in the coil, which is
then amplified to create the unique
sound of an electric guitar.

NNNNNN
I

SI

690

CHAPTER 20

Electromagnetic
Induction

Why It Matters Section 1

Electric guitars have Electricity from
many different types of Magnetism
pickups, but all generate
electric current by the Section 2
process of induction. An
understanding of the Generators,
induction of electromag- Motors,
netic fields is essential and Mutual
to the good design of Inductance
an electric guitar.
Section 3

AC Circuits and
Transformers

Section 4

Electromagnetic
Waves

Online Physics Premium
Content
HMDScience.com
Physics
Online Labs
Electricity and Magnetism HMDScience.com
Electromagnetic Induction
Motors Ways of Inducing Current

691

Section 1 Electricity from
Magnetism
Objectives
Key Term
Recognize that relative motion
between a conductor and a electromagnetic induction
magnetic field induces an emf
in the conductor. Electromagnetic Induction
Describe how the change in the
number of magnetic field lines Recall that when you were studying circuits, you were asked if it was
through a circuit loop affects possible to produce an electric current using only wires and no battery.
the magnitude and direction of So far, all electric circuits that you have studied have used a battery or an
the induced electric current. electrical power supply to create a potential difference within a circuit.
Apply Lenz’s law and Faraday’s The electric field associated with that potential difference causes charges
law of induction to solve to move through the circuit and to create a current.
problems involving induced emf
and current. It is also possible to induce a current in a circuit without the use of a
battery or an electrical power supply. You have learned that a current in a
electromagnetic induction  the circuit is the source of a magnetic field. Conversely, a current results
process of creating a current in a circuit when a closed electric circuit moves with respect to a magnetic field, as
loop by changing the magnetic flux in shown in Figure 1.1. The process of inducing a current in a circuit by
the loop changing the magnetic field that passes through the circuit is called

electromagnetic induction.

Consider a closed circuit consisting of only a resistor that is in the
vicinity of a magnet. There is no battery to supply a current. If neither the
magnet nor the circuit is moving with respect to the other, no current will
be present in the circuit. But, if the circuit moves toward or away from the
magnet or the magnet moves toward or away from the circuit, a current is
induced. As long as there is relative motion between the two, a current is
created in the circuit.

The separation of charges by the magnetic force induces an emf.

It may seem strange that there can be an induced emf and a correspond-
ing induced current without a battery or similar source of electrical

Figure 1.1 Galvanometer Magnetic eld

Electromagnetic 0 S N
Induction  When the circuit
100 100 Current
loop crosses the lines of the 200 200
magnetic field, a current is 300 300
induced in the circuit, as 400 400
indicated by the movement of 500 500
the galvanometer needle. 600 600
700 700
800 800
900 900

1000

692 Chapter 20

energy. Recall from that a moving charge can be deflected by a magnetic Figure 1.2
field. This deflection can be used to explain how an emf occurs in a wire
that moves through a magnetic field. Potential Difference in a
Wire  The separation of positive
Consider a conducting wire pulled through a magnetic field, as shown
on the left in Figure 1.2. You learned when studying magnetism that and negative moving charges by the
charged particles moving with a velocity at an angle to the magnetic field magnetic force creates a potential
will experience a magnetic force. According to the right-hand rule, this difference (emf) between the ends of
force will be perpendicular to both the magnetic field and the motion of the conductor.
the charges. For free positive charges in the wire, the force is directed
downward along the wire. For negative charges, the force is upward. This -
effect is equivalent to replacing the segment of wire and the magnetic
field with a battery that has a potential difference, or emf, between its v = –
terminals, as shown on the right in Figure 1.2. As long as the conducting +
wire moves through the magnetic field, the emf will be maintained.
+
The polarity of the induced emf depends on the direction in which the
wire is moved through the magnetic field. For instance, if the wire in B (out of page)
Figure 1.2 is moved to the right, the right-hand rule predicts that the
negative charges will be pushed upward. If the wire is moved to the left, HRW • Holt Physics
the negative charges will be pushed downward. The magnitude of the PH99PE-C22-001-002-A
induced emf depends on the velocity with which the wire is moving
through the magnetic field, on the length of the wire in the field, and on
the strength of the magnetic field.

The angle between a magnetic field and a circuit affects induction.

One way to induce an emf in a closed loop of wire is to move all or part of
the loop into or out of a constant magnetic field. No emf is induced if the
loop is static and the magnetic field is constant.

The magnitude of the induced emf and current depend partly on how
the loop is oriented to the magnetic field, as shown in Figure 1.3. The
induced current is largest if the plane of the loop is perpendicular to the
magnetic field, as in (a); it is smaller if the plane is tilted into the field, as
in (b); and it is zero if the plane is parallel to the field, as in (c).

The role that the orientation of the loop plays in inducing the current can
be explained by the force that the magnetic field exerts on the charges in the
moving loop. Only the component of the magnetic field perpendicular to

Figure 1.3 v vv
(a) (b) (c)
Orientation of a Loop in a
Magnetic Field  These three loops of

wire are moving out of a region that has a
constant magnetic field. The induced emf
and current are largest when the plane of
the loop is perpendicular to the magnetic
field (a), smaller when the plane of the loop
is tilted (b), and zero when the plane of the
loop and the magnetic field are parallel (c).

HRW • Holt Physics 693
PH99PE-C22-001-004-A

Electromagnetic Induction

Did YOU Know? both the plane and the motion of the loop exerts a magnetic force on the
In 1996, the space shuttle Columbia charges in the loop. If the area of the loop is moved parallel to the magnetic
attempted to use a 20.7 km conducting field, there is no magnetic field component perpendicular to the plane of the
tether to study Earth’s magnetic field in loop and therefore no induced emf to move the charges around the circuit.
space. The plan was to drag the tether
through the magnetic field, inducing Change in the number of magnetic field lines induces a current.
an emf in the tether. The magnitude
of the emf would directly vary with So far, you have learned that moving a circuit loop into or out of a mag-
the strength of the magnetic field. netic field can induce an emf and a current in the circuit. Changing the
Unfortunately, the tether broke before it size of the loop or the strength of the magnetic field also will induce an
was fully extended, so the experiment emf in the circuit.
was abandoned.
One way to predict whether a current will be induced in a given
694 Chapter 20 situation is to consider how many magnetic field lines cut through the
loop. For example, moving the circuit into the magnetic field causes some
lines to move into the loop. Changing the size of the circuit loop or
rotating the loop changes the number of field lines passing through the
loop, as does changing the magnetic field’s strength or direction. Figure 1.4
summarizes these three ways of inducing a current.

Characteristics of Induced Current

Suppose a bar magnet is pushed into a coil of wire. As the magnet moves
into the coil, the strength of the magnetic field within the coil increases,
and a current is induced in the circuit. This induced current in turn
produces its own magnetic field, whose direction can be found by using
the right-hand rule. If you were to apply this rule for several cases, you
would notice that the induced magnetic field direction depends on the
change in the applied field.

Figure 1.4

Ways of Inducing a Current in a Circuit

Description Before After

Circuit is moved into or out of vv vv
magnetic field (either circuit or
magnet moving). I B
I B
Circuit is rotated in the magnetic
field (angle between area of HRW • Holt Physics
circuit and magnetic field PH99PPEH-H9CR92PW2E-0•-C0H12o-20l-t00P50h-1yA-s0i0c5s-A
changes).
BB I I BB
Intensity and/or direction of
magnetic field is varied. HRHWRW• H•oHltoPlthPyshiycssics
PHP9H9P99EP-CE2-C2-2020-10-0010-60-0A6-A

BB II BB

HHRRWW••HHoollttPPhhyyssiiccss
PPHH9999PPEE--CC2222--000011--000077--AA

Figure 1.5 Conceptual Challenge

Magnet Moving Toward Coil  When a bar magnet Falling Magnet  A bar magnet
is dropped toward the floor,
is moved toward a coil, the induced magnetic field is similar on which lies a large ring
to the field of a bar magnet with the orientation shown. of conducting metal. The
magnet’s length—and thus the
Wire poles of the magnet—is parallel
to the direction of motion.
SN NS Disregarding air resistance,
does the magnet fall toward the
v ring with the constant accel-
eration of a freely falling body?
Magnetic field from Approaching Explain your answer.
Induced current induced current magnetic field
Induction in a Bracelet 
HRW • Holt Physics Suppose you are wearing a
As the magnet approPaHc9h9ePs,Et-hCe2m2-a0g0n1e-0ti0c8f-iAeld passing through the coil bracelet that is an unbroken
increases in strength. The induced current in the coil is in a direction that ring of copper. If you walk
produces a magnetic field that opposes the increasing strength of the briskly into a strong magnetic
approaching field. So, the induced magnetic field is in the opposite field while wearing the bracelet,
direction of the increasing magnetic field. how would you hold your wrist
with respect to the magnetic
The induced magnetic field is similar to the field of a bar magnet that field in order to avoid inducing
is oriented as shown in Figure 1.5. The coil and the approaching magnet a current in the bracelet?
create a pair of forces that repel each other.

If the magnet is moved away from the coil, the magnetic field passing
through the coil decreases in strength. Again, the current induced in the
coil produces a magnetic field that opposes the decreasing strength of the
receding field. This means that the magnetic field that the coil sets up is
in the same direction as the receding magnetic field.

The induced magnetic field is similar to the field of a bar magnet
oriented as shown in Figure 1.6. In this case the coil and magnet attract
each other.

Figure 1.6

Magnet Moving Away from Coil  When a bar magnet

is moved away from a coil, the induced magnetic field is similar
to the field of a bar magnet with the orientation shown.

Wire

NS NS

Induced current Magnetic field from v
induced current
Receding
magnetic field

HRW • Holt Physics Electromagnetic Induction 695
PH99PE-C22-001-009-A

Figure 1.7 The rule for finding the direction of the induced current is called
Lenz’s law and is expressed as follows:
Magnetic Field of a
Conducting Loop at an The magnetic field of the induced current is in a direction to produce a
Angle  The angle θ is defined as field that opposes the change causing it.

the angle between the magnetic field Note that the field of the induced current does not oppose the applied
and the normal to the plane of the field but rather the change in the applied field. If the applied field
loop. B cos θ equals the strength of changes, the induced field tends to keep the total field strength constant.
the magnetic field perpendicular to
the plane of the loop. Faraday’s law of induction predicts the magnitude of the
induced emf.
B cos
B Lenz’s law allows you to determine the direction of an induced
current in a circuit. Lenz’s law does not provide information on the
Normal to magnitude of the induced current or the induced emf. To calculate the
plane of loop magnitude of the induced emf, you must use Faraday’s law of magnetic
Loop induction. For a single loop of a circuit, this may be expressed as follows:

HRW • Holt Physics emf = −​_∆  ∆ΦtM ​  
PH99PE-C22-001-010-A
Recall from the chapter on magnetism that the magnetic flux, ΦM,
696 Chapter 20 can be written as AB cos θ. This equation means that a change with time
of any of the three variables—applied magnetic field strength, B;
circuit area, A; or angle of orientation, θ—can give rise to an induced emf.
The term B cos θ represents the component of the magnetic field perpen-
dicular to the plane of the loop. The angle θ is measured between the
applied magnetic field and the normal to the plane of the loop, as
indicated in Figure 1.7.

The minus sign in front of the equation is included to indicate the
polarity of the induced emf. The sign indicates that the induced magnetic
field opposes the change in the applied magnetic field as stated by Lenz’s
law.

If a circuit contains a number, N, of tightly wound loops, the average
induced emf is simply N times the induced emf for a single loop. The
equation thus takes the general form of Faraday’s law of magnetic induction.

Faraday’s Law of Magnetic Induction

emf = −N ​_ ∆∆ΦtM ​  

average induced emf = −the number of loops in the circuit ×
the time rate of change of the magnetic flux

In this chapter, N is always assumed to be a whole number.

Recall that the SI unit for magnetic field strength is the tesla (T), which
equals one newton per ampere-meter, or N/(A•m). The tesla can also be
expressed in the equivalent units of one volt-second per meter squared,
or (V•s)/m2. Thus, the unit for emf, as for electric potential, is the volt.

Induced emf and Current Premium Content

Sample Problem A  A coil with 25 turns of wire is wrapped Interactive Demo
around a hollow tube with an area of 1.8 m2. Each turn has the
same area as the tube. A uniform magnetic field is applied at a HMDScience.com
right angle to the plane of the coil. If the field increases uniformly
from 0.00 T to 0.55 T in 0.85 s, find the magnitude of the induced
emf in the coil. If the resistance in the coil is 2.5 Ω, find the
magnitude of the induced current in the coil.

Analyze Given: ∆t = 0.85 s    A = 1.8 m2    θ = 0.0°    N = 25 turns

Bi = 0.00 T = 0.00 V•s/m2
Bf = 0.55 T = 0.55 V•s/m2
R = 2.5 Ω

Unknown: emf = ?    I = ?

Diagram: Show the coil before and after the change in the
magnetic field.

N = 25 turns N = 25 turns
A = 1.8 m2 A = 1.8 m2

R = 2.5 Ω R = 2.5 Ω
B = 0.00 T at t = 0.00 s B = 0.55 T at t = 0.85 s

Plan Choose an equation or situationH:RUWse•FaHroaldtaPyh’sylsaicwsof magnetic
induction to find the induced ePmHf9i9nPtEhe-Cc2o2il-.001-011-A
Continued
emf = −N_​∆  ∆ΦtM ​ = −N ​_ ∆[AB∆_cto s θ​]  

Substitute the induced emf into the definition of resistance to deter-
mine the induced current in the coil.

I = _​e  mR f​ 

Rearrange the equation to isolate the unknown: In this example,
only the magnetic field strength changes with time. The other compo-
nents (the coil area and the angle between the magnetic field and the
coil) remain constant.

emf = -NA cos θ _​∆ ∆Bt ​  

Electromagnetic Induction 697

Induced emf and Current  (continued)

solve Substitute the values into the equation and solve:
( )emf = −(25)(1.8 m2)(cos 0.0°) ​ ​_(  0.55(−0.80_5.0s0 )) _​V m ​•2 s  ​  ​= −29 V
Tips and Tricks
Because the minimum number
of significant figures for the
data is two, the calculator I = ​− _2.259ΩV  ​= −12 A
answer, 29.11764706, should be
rounded to two digits.

emf = −29 V

I = −12 A

check your The induced emf, and therefore the induced current, is directed
work through the coil so that the magnetic field produced by the induced
current opposes the change in the applied magnetic field. For the
diagram shown on the previous page, the induced magnetic field is
directed to the right and the current that produces it is directed from
left to right through the resistor.

1.  A single circular loop with a radius of 22 cm is placed in a uniform external
magnetic field with a strength of 0.50 T so that the plane of the coil is
perpendicular to the field. The coil is pulled steadily out of the field in 0.25 s. Find
the average induced emf during this interval.

2.  A coil with 205 turns of wire, a total resistance of 23 Ω, and a cross-sectional area
of 0.25 m2 is positioned with its plane perpendicular to the field of a powerful
electromagnet. What average current is induced in the coil during the 0.25 s that
the magnetic field drops from 1.6 T to 0.0 T?

3.  A circular wire loop with a radius of 0.33 m is located in an external magnetic field
of strength +0.35 T that is perpendicular to the plane of the loop. The field
strength changes to −0.25 T in 1.5 s. (The plus and minus signs for a magnetic
field refer to opposite directions through the coil.) Find the magnitude of the
average induced emf during this interval.

4.  A 505-turn circular-loop coil with a diameter of 15.5 cm is initially aligned so that
its plane is perpendicular to Earth’s magnetic field. In 2.77 ms the coil is rotated
90.0° so that its plane is parallel to Earth’s magnetic field. If an average emf of
0.166 V is induced in the coil, what is the value of Earth’s magnetic field?

698 Chapter 20

Electric Guitar Pickups

T he word pickup refers to a device that “picks up” shapes the magnetic field. Because guitar
the sound of an instrument and turns the sound strings are made from magnetic
into an electrical signal. The most common type of materials (steel and/or
electric guitar pickup uses electromagnetic induction to nickel), a vibrating guitar
convert string vibrations into electrical energy. string causes a change in the
magnetic field above the pickup. This
In their most basic form, magnetic pickups consist changing magnetic field induces a
simply of a permanent magnet and a coil of copper wire. current in the pickup coil.
A pole piece under each guitar string concentrates and
Many turns of very fine gauge wire
Magnets Strings —finer than the hair on your head—
Wire coil are wound around each pole piece.
The number of turns determines the
Vibrating string current that the pickup produces, with
more windings resulting in a larger current.

Electrical signal
to amplifier

Secspt08iseo_mnagw1im2F8boa rmative ASSESSMENT
1st Pass
Re6ve.2vrn2in.e0b6wt ing Main Ideas

1. A circular current loop made of flexible wire is located in a magnetic field.
Describe three ways an emf can be induced in the loop.

2. A bar magnet is positioned near a coil of wire, as shown to the

right. What is the direction of the current in the resistor when S N
the magnet is moved to the left, as in (a)? to the right, as in (b)?
(a) v
3. A 256-turn coil with a cross-sectional area of 0.0025 m2 is (b)
placed in a uniform external magnetic field of strength 0.25 T vR

so that the plane of the coil is perpendicular to the field. The HRW • Holt Physics
PH99PE-C22-001-014-A
coil is pulled steadily out of the field in 0.75 s. Find the average induced

emf during this interval.

(tr) ©SW Productions/Photodisc/Getty Images Critical Thinking

4. E lectric guitar strings are made of ferromagn­ etic materials that can be
magnetized. The strings lie closely over and perpendicular to a coil of wire.
Inside the coil are permanent magnets that magnetize the segments of the
strings overhead. Using this arrangement, explain how the vibrations of a
plucked string produce an electrical signal at the same frequency as the
vibration of the string.

Electromagnetic Induction 699

Section 2 Generators,
Motors, and Mutual
Objectives Inductance

Describe how generators and Key Terms alternating current
motors operate. mutual inductance
Explain the energy conversions generator
that take place in generators back emf
and motors.
Describe how mutual induction Generators and Alternating Current
occurs in circuits.
In the previous section, you learned that a current can be induced in a
generator  a machine that converts circuit either by changing the magnetic field strength or by moving the
mechanical energy into electrical energy circuit loop in or out of the magnetic field. Another way to induce a current
is to change the orientation of the loop with respect to the magnetic field.
Figure 2.1
This second approach to inducing a current represents a practical
A Simple Generator  In a means of generating electrical energy. In effect, the mechanical energy
used to turn the loop is converted to electrical energy. A device that does
simple generator, the rotation of this conversion is called an electric generator.
conducting loops through a constant
magnetic field induces an alternating In most commercial power plants, mechanical energy is provided in
current in the loops. the form of rotational motion. For example, in a hydroelectric plant,
falling water di­rected against the blades of a turbine causes the turbine to
turn. In a coal or natural-gas-burning plant, energy produced by burning
fuel is used to convert water to steam, and this steam is directed against
the turbine blades to turn the turbine.

Basically, a generator uses the turbine’s rotary motion to turn a wire
loop in a magnetic field. A simple generator is shown in Figure 2.1. As the
loop rotates, the effective area of the loop changes with time, inducing an
emf and a current in an external circuit connected to the ends of the loop.

A generator produces a continuously changing emf.

Consider a single loop of wire that is rotated with a constant angular
fre­quency in a uniform magnetic field. The loop can be thought of as four
conducting wires. In this example, the loop is rotating counterclockwise
within a magnetic field directed to the left.

When the area of the loop is perpendicular to the magnetic field lines,
as shown in Figure 2.2(a) on the next page, every segment of wire in the
loop is moving parallel to the magnetic field lines. At this instant, the
magnetic field does not exert force on the charges in any part of the wire,
so the induced emf in each segment is therefore zero.

700 Chapter 20

As the loop rotates away from this position, segments a and c cross
magnetic field lines, so the magnetic force on the charges in these
segments, and thus the induced emf, increases. The magnetic force on
the charges in segments b and d cancel each other, so the motion of these
segments does not contribute to the emf or the current. The greatest
magnetic force on the charges and the greatest induced emf occur at the
instant when segments a and c move perpendicularly to the magnetic
field lines, as in Figure 2.2(b). This occurs when the plane of the loop is
parallel to the field lines.

Because segment a moves downward through the field while segment
c moves upward, their emfs are in opposite directions, but both produce a
counterclockwise current. As the loop continues to rotate, segments a
and c cross fewer lines, and the emf decreases. When the plane of the
loop is perpendicular to the magnetic field, the motion of segments a and
c is again parallel to the magnetic lines and the induced emf is again zero,
as shown in Figure 2.2(c). Segments a and c now move in directions
opposite those in which they moved from their positions in (a) to those in
(b). As a result, the polarity of the induced emf and the direction of the
current are reversed, as shown in Figure 2.2(d).

Figure 2.2 Ba B d
d a
Induction of an emf in an
ac Generator  For a rotating Induced emf b Induced emf c
– 0+ c b
loop in a magnetic field, the – 0+
induced emf is zero when the loop
is perpendicular to the magnetic
field, as in (a) and (c), and is at a
maximum when the loop is parallel
to the field, as in (b) and (d).

(a) (b)

Bc PHYSICS PHYS
b BSpoestco. nNGuBmrabpehricPsH,cIn9c9. PE Cd22-002-002-SApec
a d Bosto

617.523.1333 617.5
Induced emf
Induced emf – 0+ a
– 0+ b

(c) (d)

PEHleYcStrIoCmSagnetic Induction 701 PHYS
Spec. Number PH 99 PE C22-002-004-ASpec.

Figure 2.3 A graph of the change in emf versus time as the loop rotates is shown
in Figure 2.3. Note the similarities between this graph and a sine curve.
Alternating emf  The change The four locations marked on the curve correspond to the orientation of
the loop with respect to the magnetic field in Figure 2.2. At locations a and
with time of the induced emf in c, the emf is zero. These locations correspond to the instants when the
a rotating loop is depicted by a plane of the loop is parallel to the direction of the magnetic field. At
sine wave. The letters on the plot locations b and d, the emf is at its maximum and minimum, respectively.
correspond to the coil locations in These locations correspond to the instants when the plane of the loop is
perpendicular to the magnetic field.
Figure 2.2.
The induced emf is the result of the steady change in the angle θ
emf versus Time between the magnetic field lines and the normal to the loop. The
emf following equation for the emf produced by a generator can be derived
from Faraday’s law of induction. The derivation is not shown here
Maximum b because it requires the use of calculus. In this equation, the angle of
emf orientation, θ, has been replaced with the equivalent expression ωt,
where ω is the angular frequency of rotation (2πf  ).
ac
emf = NABω sin ωt
Time
The equation describes the sinusoidal variation of emf with time, as
d graphed in Figure 2.3.

alternating current  an electric The maximum emf strength can be easily calculated for a sinusoidal
current that changes direction at function. The emf has a maximum value when the plane of a loop is
regular intervals parallel to a magnetic field, that is, when sin ωt = 1, which occurs when
ωt = θ = 90°. In this case, the expression above reduces to the following:
702 Chapter 20
maximum emf = NABω

Note that the maximum emf is a function of four things: the number of
loops, N; the area of the loop, A; the magnetic field strength, B; and the
angular frequency of the rotation of the loop, ω.

Alternating current changes direction at a constant frequency.

Note in Figure 2.3 that the emf alternates from positive to negative. As a
result, the output current from the generator changes its direction at
regular intervals. This variety of current is called alternating current, or,
more commonly, ac.

The rate at which the coil in an ac generator rotates determines the
maximum generated emf. The frequency of the alternating current can
differ from country to country. In the United States, Canada, and Central
America, the frequency of rotation for commercial generators is 60 Hz.
This means that the emf undergoes one full cycle of changing direction 60
times each second. In the United Kingdom, Europe, and most of Asia and
Africa, 50 Hz is used. (Recall that ω = 2πf, where f  is the frequency in Hz.)

Resistors can be used in either alternating- or direct-current
applications. A resistor resists the motion of charges regardless of
whether they move in one continuous direction or shift direction
periodically. Thus, if the definition for resistance holds for circuit
elements in a dc circuit, it will also hold for the same circuit elements
with alternating currents and emfs.

Figure 2.4 dc Generator

ac versus dc Generators  A simple dc generator (shCow2n2-o0n02-011-A

the right) employs the same design as an ac generator (shown on
the left). A split slip ring converts alternating current to direct current.

ac Generator

Slip rings

N N

S S

Brush Brush Brush
Commutator
Brush

Alternating current can be converted to direct current. Figure 2.5Current

The conducting loop in an ac generator must be free to rotate through the Current Output for a dc
magnetic field. Yet it must also be part of an electric circuit at all times. To Generator  The output current for
accomplish this, the ends of the loop are connected to conducting rings,
called slip rings, that rotate with the loop. Connections to the external a dc generator with a single loop is a
circuit are made by stationary graphite strips, called brushes, that make sine wave with the negative parts of
continuous contact with the slip rings. Because the current changes the curve made positive.
direction in the loop, the output current through the brushes alternates
direction as well. Output Current versus
Time for dc Generator
By varying this arrangement slightly, an ac generator can be converted
to a dc generator. Note in Figure 2.4 that the components of a dc generator Time
are essentially the same as those of the ac generator except that the
contacts to the rotating loop are made by a single split slip ring, called HRW • Holt Physics
a commutator. PH99PE-C22-002-012-A
Electromagnetic Induction 703
At the point in the loop’s rotation when the current has dropped to
zero and is about to change direction, each half of the commutator
comes into contact with the brush that was previously in contact with the
other half of the commutator. The reversed current in the loop changes
directions again so that the output current has the same direction as it
originally had, although it still changes from a maximum value to zero.
A plot of this pulsating direct current is shown in Figure 2.5.

A steady direct current can be produced by using many loops and
commutators distributed around the rotation axis of the dc generator.
This generator uses slip rings to continually switch the output of the
generator to the commutator that is producing its maximum emf.
This switching produces an output that has a slight ripple but is
nearly constant.

back emf  the emf induced in a Motors
motor’s coil that tends to reduce the
current in the coil of the motor Motors are machines that convert electrical energy to mechanical energy.
Instead of a current being generated by a rotating loop in a magnetic
field, a current is supplied to the loop by an emf source, and the magnetic
force on the current loop causes it to rotate (see Figure 2.6).

A motor is almost identical in construction to a dc generator. The coil
of wire is mounted on a rotating shaft and is positioned between the poles
of a magnet. Brushes make contact with a commutator, which alternates
the current in the coil. This alternation of the current causes the magnetic
field produced by the current to regularly reverse and thus always be
repelled by the fixed magnetic field. Thus, the coil and the shaft are kept
in continuous rotational motion.

A motor can perform mechanical work when a shaft connected to its
rotating coil is attached to some external device. As the coil in the motor
rotates, however, the changing normal component of the magnetic field
through it induces an emf that acts to reduce the current in the coil. If this
were not the case, Lenz’s law would be violated. This induced emf is
called the back emf.

The back emf increases in magnitude as the magnetic field changes at
a higher rate. In other words, the faster the coil rotates, the greater the
back emf becomes. The potential difference available to supply current to
the motor equals the difference between the applied potential difference
and the back emf. Consequently, the current in the coil is also reduced
because of the presence of back emf. As the motor turns faster, both the
net emf across the motor and the net current in the coil become smaller.

Figure 2.6 C22-002-013-A

Components of a dc Motor  In a

motor, the current in the coil interacts with
the magnetic field, causing the coil and the
shaft on which the coil is mounted to turn.

Commutator S

N Brush

Brush

dc Motor +

emf

704 Chapter 20

Mutual Inductance mutual inductance  the ability of one
circuit to induce an emf in a nearby
The basic principle of electromagnetic induction was first demonstrated circuit in the presence of a changing
by Michael Faraday. His experimental apparatus, which resembled the current
arrangement shown in Figure 2.7, used a coil connected to a switch and a
battery instead of a magnet to produce a magnetic field. This coil is called Galvanometer
the primary coil, and its circuit is called the primary circuit. The magnetic
field is strengthened by the magnetic properties of the iron ring around 0+
which the primary coil is wrapped.
100 100
A second coil is wrapped around another part of the iron ring and is 200 200
connected to a galvanometer. An emf is induced in this coil, called the 300 300
secondary coil, when the magnetic field of the primary coil is changed. 400 400
When the switch in the primary circuit is closed, the galvanometer in the 500 500
secondary circuit deflects in one direction and then returns to zero. When 600 600
the switch is opened, the galvanometer deflects in the opposite direction 700 700
and again returns to zero. When there is a steady current in the primary 800 800
circuit, the galvanometer reads zero. 900 900

The magnitude of this emf is predicted by Faraday’s law of induction. 1000
However, Faraday’s law can be rewritten so that the induced emf is
proportional to the changing current in the primary coil. This can be
done because of the direct proportionality between the magnetic field
produced by a current in a coil, or solenoid, and the current itself. The
form of Faraday’s law in terms of changing primary current is as follows:

emf = −N ​_ ∆∆ΦtM ​  = −M ​_ ∆∆It   ​

The constant, M, is called the mutual inductance of the two-coil system.
The mutual inductance depends on the geometrical properties of the
coils and their orientation to each other. A changing current in the
secondary coil can also induce an emf in the primary circuit. In fact,
when the current through the second coil varies, the induced emf in the
first coil is governed by an analo­gous equation with the same value of M.

The induced emf in the secondary circuit can be changed by changing
the number of turns of wire in the secondary coil. This arrangement is the
basis of an extremely useful electrical device: the transformer.

Figure 2.7 C22-003-001-A

Induction of Current by a Switch
Fluctuating Current 
+
Faraday’s electromagnetic-induction
experiment used a changing current
in one circuit to induce a current in
another circuit.

Battery Primary Iron Secondary
coil ring coil

Electromagnetic Induction 705

Avoiding Electrocution

A person can receive an electric shock by touching outlets and individual appliances to prevent further
something that is at a different electric potential electrocution.
than your body. For example, you might touch a
high electric potential object while in contact with a GFCIs and GFIs provide protection by comparing the
cold-water pipe (normally at zero potential) or while current in one side of the electrical outlet socket to the
standing on the floor with wet feet (because impure water current in the other socket. The two currents are
is a good conductor). compared by induction in a device called a differential
transformer. If there is even a 5 mA difference, the
Electric shock can result in fatal burns or can cause the interrupter opens the circuit in a few milliseconds
muscles of vital organs, such as the heart, to malfunction. (thousandths of a second). The quick motion needed to
The degree of damage to the body depends on the open the circuit is again provided by induction, with the
magnitude of the current, the length of time it acts, and use of a solenoid switch.
the part of the body through which it passes. A current of
100 milliamps (mA) can be fatal. If the current is larger Despite these safety devices, you can still be electrocuted.
than about 10 mA, the hand muscles contract and the Never use electrical appliances near water or with wet
person may be unable to let go of the wire. hands. Use a battery-powered radio near water because
batteries cannot supply enough current to harm you. It is
Any wires designed to have such currents in them are also a good idea to replace old outlets with GFCI-equipped
wrapped in insulation, usually plastic or rubber, to prevent units or to install GFI-equipped circuit breakers.
electrocution. However, with frequent use, electrical cords
can fray, exposing some of the conductors. In these and
other situations in which electrical contact can be made,
devices called a ground fault circuit interrupter (GFCI) and
a ground fault interrupter (GFI) are mounted in electrical

Section 2 Formative ASSESSMENT

Reviewing Main Ideas

1. A loop with 37 turns and an area of 0.33 m2 is rotating at 281 rad/s. The
loop’s axis of rotation is perpendicular to a uniform magnetic field with a
strength of 0.035 T. What is the maximum emf induced?

2. A generator coil has 25 turns of wire and a cross-sectional area of 36 cm2.
The maximum emf developed in the generator is 2.8 V at 60 Hz. What is
the strength of the magnetic field in which the coil rotates?

3. E xplain what would happen if a commutator were not used in a motor.

Critical Thinking

4. Suppose a fixed distance separates the centers of two circular loops. What
relative orientation of the loops will give the maximum mutual induc-
tance? What orientation will give the minimum mutual inductance?

706 Chapter 20

AC Circuits and Section 3
Transformers
Objectives
Key Terms transformer
Distinguish between rms values
rms current and maximum values of current
and potential difference.
Effective Current
Solve problems involving rms
In the previous section, you learned that an electrical generator could and maximum values of current
produce an alternating current that varies as a sine wave with respect to and emf for ac circuits.
time. Commercial power plants use generators to provide electrical
energy to power the many electrical devices in our homes and busi- Apply the transformer equation
nesses. In this section, we will investigate the characteristics of simple to solve problems involving
ac circuits. step-up and step-down
transformers.
As with the discussion about direct-current circuits, the resistance, the
current, and the potential difference in a circuit are all relevant to a discus- Figure 3.1
sion about alternating-current circuits. The emf in ac circuits is analogous
to the potential difference in dc circuits. One way to measure these three A Digital Multimeter 
important circuit parameters is with a digital multimeter, as shown in
Figure 3.1. The resistance, current, or emf can be measured by choosing the The effective current and emf of an
proper settings on the multimeter and locations in the circuit. electric circuit can be measured
using a digital multimeter.

Effective current and effective emf are measured in ac circuits. Figure 3.2

An ac circuit consists of combinations of circuit elements and an ac A Schematic of an ac
generator or an ac power supply, which provides the alternating current. Circuit  An ac circuit represented
As shown earlier, the emf produced by a typical ac generator is sinusoidal
and varies with time. The induced emf as a function of time (∆v) can be sche­matically consists of an ac
written in terms of the maximum emf (∆Vmax), and the emf produced by source and an equivalent resistance.
a generator can be expressed as follows:
Req
∆v = ∆Vmax sin ωt
∆v
A simple ac circuit can be treated as an equivalent resistance and an
ac source. In a circuit diagram, the ac source is represented by the symbol ac source

, as shown in Figure 3.2. HRW • Holt Physics
ElectProHm9a9gPnEe-Ctic22In-0d0u2c-t0io0n8-A 707
The instantaneous current that changes with the potential difference
can be determined using the definition for resistance. The instantaneous
PHH9R9PWE•-CH2co2ul-tr0rP0ehn2y-ts0,ii1c,4sis-Arelated to maximum current by the following expression:

i = Imax sin ωt

The rate at which electrical energy is converted to internal energy in
the resistor (the power, P) has the same form as in the case of direct
current. The electrical energy converted to internal energy at some point
in time in a resistor is proportional to the square of the instantaneous
current and is independent of the direction of the current. However, the

energy produced by an alternating current with a maximum value of Imax
is not the same as that produced by a direct current of the same value.
The energies are different because during a cycle, the alternating current
is at its maximum value for only an instant.

rms current  the value of alternating An important measure of the current in an ac circuit is the rms current.
current that gives the same heating The rms (or root-mean-square) current is the same as the amount of
effect that the corresponding value of direct current that would dissipate the same energy in a resistor as is
direct current does dissipated by the instantaneous alternating current over a complete cycle.
Figure 3.3 shows a graph in which instantaneous and rms currents are
Figure 3.3 compared. Figure 3.4 summarizes the notations used in this chapter for
these and other ac quantities.
Alternating Current  The rms
The equation for the average power dissipated in an ac circuit has the
current is a little more than two-thirds same form as the equation for power dissipated in a dc circuit except that
as large as the maximum current. the dc current I is replaced by the rms current (Irms).

Current versus Time P = (Irms)2R
in an ac Circuit
Current This equation is identical in form to the one for direct current.
Imax However, the power dissipated in the ac circuit equals half the power
Irms dissipated in a dc circuit when the dc current equals Imax.

Time P = (Irms)2 R = _​12 _ ​(Imax)2R

HRW • Holt Physics From this equation, you may note that the rms current is related to the
PH99PE-C22-002-009-A maximum value of the alternating current by the following equation:

708 Chapter 20 (Irms)2 = _​(  Im2a x)​2  

Solving the above equation for Irms leads to the following:

Irms = _​I ​ √ m  2 ax  ​   ​= 0.707 Imax
This equation says that an alternating current with a maximum value of
5 A produces the same heating effect in a resistor as a direct current of
(5/​√    2    )​ A, or about 3.5 A.

Alternating emfs are also best discussed in terms of their rms values,

with the relationship between rms and maximum values analogous to the

one for currents. The rms and maximum values are related as follows:

_ ∆Vrms
= ​ ∆Vma x​ = 0.707 Vmax
​ √    2    ​

Figure 3.4

Notation Used for ac Circuits

Induced or Applied emf Current

instantaneous values ∆v i

maximum values ∆Vmax Imax
rms values Irms = _​​ I  √r m  2 s    ​ ​
∆Vrms = _​∆  Vm a​x 
​√    2    ​

rms Current and emf Premium Content

Sample Problem B  A generator with a maximum output emf Interactive Demo
of 205 V is connected to a 115 Ω resistor. Calculate the rms
potential difference. Find the rms current through the resistor. HMDScience.com
Find the maximum ac current in the circuit.

Analyze Given: ∆Vmax = 205 V    R = 115 Ω
Unknown: ∆Vrms = ?    Irms = ?    Imax = ?

Diagram: ∆Vmax = 205 V

R = 115 Ω

Plan Cpohtoeonstieaal dnieffqerueantcioePntHooH9frRi9nsPWidtEuƥ-aCHVt2iroo2mln-ts0.:P0Uh2sy-es0it1ch0se-Aequation for the rms
Tips
solve ∆Vrms = 0.707 ∆Vmax and Tricks

check your Because emf is measured
work in volts, maximum emf is
Rearrange the definition for resistance to calculate Irms. frequently abbreviated as
Continued
Irms = _​∆  VRr m​s   aΔbVbmreavxi,aatendd rms emf can be
as ΔVrms.

Use the equation for rms current to find Imax.

Irms = 0.707 Imax

Rearrange the equation to isolate the unknown:

Rearrange the equation relating rms current to maximum current so

that maximum current is calculated.

Imax = _​0  I.r7m0s7   ​

Substitute the values into the equation and solve:

∆Vrms = (0.707)(205 V) = 145 V

Irms = ​ _114155 VΩ   ​= 1.26 A
Imax = ​1 _0.2.760A7   ​= 1.78 A
∆Vrms = 145 V

Irms = 1.26 A
Imax = 1.78 A

The rms values for the emf and current are a little more than two-thirds
the maximum values, as expected.

Electromagnetic Induction 709

rms Current and emf  (continued)

1.  What is the rms current in a light bulb that has a resistance of 25 Ω and an rms emf
of 120 V? What are the maximum values for current and emf?

2.  T he current in an ac circuit is measured with an ammeter. The meter gives a
reading of 5.5 A. Calculate the maximum ac current.

3.  A toaster is plugged into a source of alternating emf with an rms value of 110 V.
The heating element is designed to convey a current with a peak value of 10.5 A.
Find the following:
a.  the rms current in the heating element
b.  the resistance of the heating element

4.  An audio amplifier provides an alternating rms emf of 15.0 V. A loudspeaker
connected to the amplifier has a resistance of 10.4 Ω. What is the rms current in
the speaker? What are the maximum values of the current and the emf?

5.  An ac generator has a maximum emf output of 155 V.
a.  Find the rms emf output.
b.  Find the rms current in the circuit when the generator is connected to a
53 Ω resistor.

6.  T he largest emf that can be placed across a certain capacitor at any instant is
451 V. What is the largest rms emf that can be placed across the capacitor without
damaging it?

Resistance influences current in an ac circuit.

The ac potential difference (commonly called the voltage) of 120 V
measured from an electrical outlet is actually an rms emf of 120 V. (This,
too, is a simplification that assumes that the voltmeter has infinite
resistance.) A quick calculation shows that such an emf has a maximum
value of about 170 V.

The resistance of a circuit modifies the current in an ac circuit just as it
does in a dc circuit. If the definition of resistance is valid for an ac circuit,
the rms emf across a resistor equals the rms current multiplied by the
resistance. Thus, all maximum and rms values can be calculated if only
one current or emf value and the circuit resistance are known.

Ammeters and voltmeters that measure alternating current are
calibrated to measure rms values. In this chapter, all values of alternating
current and emf will be given as rms values unless otherwise noted. The
equations for ac circuits have the same form as those for dc circuits when
rms values are used.

710 Chapter 20

Transformers transformer  a device that increases
or decreases the emf of alternating
It is often desirable or necessary to change a small ac applied emf to a current
larger one or to change a large applied emf to a smaller one. The device
that makes these conversions possible is the transformer. Figure 3.5

In its simplest form, an ac transformer consists of two coils of wire Basic Components of an ac
wound around a core of soft iron, like the apparatus for the Faraday Transformer  A transformer uses
experiment. The coil on the left in Figure 3.5 has N1 turns and is connected
to the input ac potential difference source. This coil is called the primary the alternating current in the primary
winding, or the primary. The coil on the right, which is connected to a circuit to induce an alternating
resistor R and consists of N2 turns, is the secondary. As in Faraday’s current in the secondary circuit.
experiment, the iron core “guides” the magnetic field lines so that nearly
all of the field lines pass through both of the coils. Soft iron core

Because the strength of the magnetic field in the iron core and the ∆V1 N1 N2 R ∆V2
cross-sectional area of the core are the same for both the primary and
secondary windings, the measured ac potential differences across the two Primary Secondary
windings differ only because of the different number of turns of wire for (input) (output)
each. The applied emf that gives rise to the changing magnetic field in the
primary is related to that changing field by Faraday’s law of induction. HRW • Holt Physics
PH99PE-C22-003-002-A
∆V1 = −N1 ​_∆  ∆ΦtM ​  

Similarly, the induced emf across the secondary coil is

∆V2 = −N2 _​∆  ∆ΦtM ​  

Taking the ratio of ∆V1 to ∆V2 causes all terms on the right side of both
equations except for N1 and N2 to cancel. This result is the transformer
equation.

Transformer Equation

∆V2 = _​NN  21   ​∆V1

induced emf in secondary =

( )​ _​ nnuummbbeerroo_fftut u rrnnssini n s_perciomn  adrayry ​  ​applied emf in primary

Another way to express this equation is to equate the ratio of the potential
differences to the ratio of the number of turns.

_​ ∆∆VV21   ​= _​NN  21   ​
When N2 is greater than N1, the secondary emf is greater than that of the
primary, and the transformer is called a step-up transformer. When N2 is
less than N1, the secondary emf is less than that of the primary, and the
transformer is called a step-down transformer.

Electromagnetic Induction 711

It may seem that a transformer provides something for nothing. For
example, a step-up transformer can change an applied emf from 10 V to
100 V. However, the power output at the secondary is, at best, equal to the
power input at the primary. In reality, energy is lost to heating and
radiation, so the output power will be less than the input power. Thus, an
increase in induced emf at the secondary means that there must be a
proportional decrease in current.

Transformers Premium Content

Sample Problem C  A step-up transformer is used on a 120 V Interactive Demo
line to provide a potential difference of 2400 V. If the primary has
75 turns, how many turns must the secondary have? HMDScience.com

Analyze Given: ∆V1 = 120 V    ∆V2 = 2400 V    N1 = 75 turns
Unknown:
Diagram: N2 = ?

N1 = N2 = ?
75 turns

∆V1 = 120 V ∆V2 = 2400 V

PLAN Choose an equation or s_​NN  it21uP  a​H∆Ht9ioRV9nPW1:EU•-CsHe2ot2hl-te0P0thr3ay-ns0is0cf4so-rAmer equation.
solve
∆V2 =

Rearrange the equation to isolate the unknown:

N2 = _​∆∆  VV12  ​N1

Substitute the values into the equation and solve:

( )N2 = ​ _​2  142000VV ​   ​75 turns = 1500 turns

N2 = 1500 turns

check The greater number of turns in the secondary accounts for the
your work increase in the emf in the secondary. The step-up factor for the
transformer is 20:1.

Continued

712 Chapter 20

Transformers  (continued)

1.  A step-down transformer providing electricity for a residential neighborhood has
exactly 2680 turns in its primary. When the potential difference across the primary
is 5850 V, the potential difference at the secondary is 120 V. How many turns are in
the secondary?

2.  A step-up transformer used in an automobile has a potential difference across the
primary of 12 V and a potential difference across the secondary of
2.0 × 104 V. If the number of turns in the primary is 21, what is the number
of turns in the secondary?

3.  A step-up transformer for long-range transmission of electric power is used to
create a potential difference of 119 340 V across the secondary. If the potential
difference across the primary is 117 V and the number of turns in the secondary is
25 500, what is the number of turns in the primary?

4.  A potential difference of 0.750 V is needed to provide a large current for arc
welding. If the potential difference across the primary of a step-down transformer
is 117 V, what is the ratio of the number of turns of wire on the primary to the
number of turns on the secondary?

5.  A step-down transformer has 525 turns in its secondary and 12 500 turns in its
primary. If the potential difference across the primary is 3510 V, what is the
potential difference across the secondary?

Real transformers are not perfectly efficient.

The transformer equation assumes that no power is lost between the
transformer’s primary and secondary coils. Real transformers typically
have efficiencies ranging from 90 percent to 99 percent. Power is lost
because of the small currents induced by changing magnetic fields in the
transformer’s iron core and because of resistance in the wires of the
windings.

The power lost to resistive heating in transmission lines varies as
I2R. To minimize I2R loss and maximize the deliverable energy, power
companies use a high emf and a low current when transmitting power
over long distances. By reducing the current by a factor of 10, the power
loss is reduced by a factor of 100. In practice, the emf is stepped up to
around 230 000 V at the generating station, is stepped down to 20 000 V
at a regional distribution station, and is finally stepped down to 120 V at
the customer’s utility pole. The high emf in long-distance transmission
lines makes the lines especially dangerous when high winds knock
them down.

Electromagnetic Induction 713

Figure 3.6 The ignition coil in a gasoline engine is a transformer.

A Step-Up Transformer in an Auto An automobile battery provides a constant emf of 12 dc volts to
Ignition System  The transformer in an power various systems in your automobile. The ignition system
uses a transformer, called the ignition coil, to convert the car
automobile engine raises the potential difference battery’s 12 dc volts to a potential difference that is large enough to
across the gap in a spark plug so that sparking cause sparking between the gaps of the spark plugs. The diagram
occurs. in Figure 3.6 shows a type of ignition system that has been used in
automobiles since about 1990. In this arrangement, called an
Step-up transfomer electronic ignition, each cylinder has its own transformer coil.
(ignition coil)
The ignition system on your car has to work in perfect concert
Ignition with the rest of the engine. The goal is to ignite the fuel at the exact
switch moment when the expanding gases can do the maximum amount
of work. A photoelectric detector, called a crank angle sensor, uses
+– Computer the crankshaft’s position to determine when the cylinder’s con-
12 V battery tents are near maximum compression.
Crank angle
sensor The sensor then sends a signal to the automobile’s computer.
Upon receiving this signal, the computer closes the primary circuit
Spark plug to the cylinder’s coil, causing the current in the primary to rapidly
increase. As we learned earlier in this chapter, the increase in
current induces a rapid change in the magnetic field of the trans-
former. Because the change in magnetic field on the primary side
is so quick, the change induces a very large emf, from 40 000 to
100 000 V. The emf is applied across the spark plug and creates a
spark that ignites and burns the fuel that powers your automobile.

Section 3 Formative ASSESSMENT

Reviewing Main Ideas

1. T he rms current that a single coil of an electric guitar produces is
0.025 mA. The coil’s resistance is 4.3 kΩ. What is the maximum instan-
taneous current? What is the rms emf produced by the coil? What is the
maximum emf produced by the coil?

2. A step-up transformer has exactly 50 turns in its primary and exactly 7000
turns in its secondary. If the applied emf in the primary is 120 V, what emf
is induced in the secondary?

3. A television picture tube requires a high potential difference, which a
step-up transformer provides in older models. The transformer has
12 turns in its primary and 2550 turns in its secondary. If 120 V is applied
across the primary, what is the output emf?

Critical Thinking

4. W hat is the average value of current over one cycle of an ac signal? Why,
then, is a resistor heated by an ac current?

714 Chapter 20

Section 4

Electromagnetic Objectives
Waves
Describe what electromagnetic
waves are and how they are
produced.

Key Terms photon Recognize that electricity and
magnetism are two aspects of a
electromagnetic radiation single electromagnetic force.

Propagation of Electromagnetic Waves Explain how electromagnetic
waves transfer energy.

Light is a phenomenon known as an electromagnetic wave. As the name Describe various applications of
implies, oscillating electric and magnetic fields create electromagnetic electromagnetic waves.
waves. In this section, you will learn more about the nature and the
discovery of electromagnetic waves.

The wavelength and frequency of electromagnetic waves vary
widely, from radio waves with very long wavelengths to gamma rays with
extremely short wavelengths. The visible light that our eyes can detect
occupies an intermediate range of wavelengths. Familiar objects “look”
quite different at different wavelengths. Figure 4.1 shows how a person
might appear to us if we could see beyond the red end of the visible
spectrum.

In this chapter, you have learned that a changing magnetic field can

induce a current in a circuit (Faraday’s law of induction). From Coulomb’s

law, which describes the electrostatic force between two charges, you

know that electric field lines start on positive charges and end

at negative charges. On the other hand, magnetic field lines Figure 4.1

always form closed loops and have no beginning or end. Infrared Image of a Person  At normal body
Finally, you learned in the chapter on magnetism that a
magnetic field is created around a current-carrying wire, as temperature, humans radiate most strongly in the
stated by Ampere’s law.
infrared, at a wavelength of about 10 microns
(10−5 m). The wavelength of the infrared radiation

can be correlated to temperature.

©Infrared Processing and Analysis Center, California Institute of Technology Electromagnetic waves consist of changing electric and
magnetic fields.

In the mid-1800s, Scottish physicist James Clerk Maxwell
created a simple but sophisticated set of equations to describe
the relationship between electric and magnetic fields.
Maxwell’s equations summarized the known phenomena of
his time: the observations that were described by Coulomb,
Faraday, Ampere, and other scientists of his era. Maxwell
believed that nature is symmetric, and he hypothesized that a
changing electric field should produce a magnetic field in a
manner analogous to Faraday’s law of induction.

Maxwell’s equations described many of the phenomena,
such as magnetic induction, that had already been observed.
However, other phenomena that had not been observed could
be derived from the equations. For example, Maxwell’s

Electromagnetic Induction 715

Figure 4.2 equations predicted that a changing magnetic field
would create a changing electric field, which would, in
An Electromagnetic Wave  An electromagnetic wave turn, create a changing magnetic field, and so on. The
predicted result of those changing fields is a wave that
consists of electric and magnetic field waves at right angles to moves through space at the speed of light.
each other. The wave moves in the direction perpendicular to
both oscillating waves. Maxwell predicted that light was electromagnetic in
nature. The scientific community did not immediately
Oscillating magnetic field accept Maxwell’s equations. However, in 1887, a German
physicist named Heinrich Hertz generated and detected
electromagnetic waves in his laboratory. Hertz’s experi-
mental confirmation of Maxwell’s work convinced the
scientific community to accept the work.

Electromagnetic waves are simply oscillating electric

and magnetic fields. The electric and magnetic fields are

at right angles to each other and also at right angles to the

Oscillating electric field direction that the wave is moving. Figure 4.2 is a simple
illustration of an electromagnetic wave at a single point

Direction of the electromagnetic wave in time. The electric field oscillates back and forth in one
plane while the magnetic field oscillates back and forth

in a perpendicular plane. The wave travels in the direc-

tion that is perpendicular to both of the oscillating fields.

In the chapter on vibrations and waves you learned that

PHYSICtShis kind of wave is called a transverse wave.
Spec. Number PH 99 PE C14-001-002-A

Electric 6Ba1no7sd.t5om2n3aG.g1rn3a3ep3thiiccsf,oIrncce.s are aspects of a single force.

Although magnetism and electricity seem like very different things, we

know that both electric and magnetic fields can produce forces on

charged particles. These forces are aspects of one and the same force,

called the electromagnetic force. Physicists have identified four fundamen-

tal forces in the universe: the strong force, which holds together the

nucleus of an atom; the electromagnetic force, which is discussed here;

the weak force, which is involved in nuclear decay; and the gravitational

force, discussed in the chapter “Circular Motion and Gravitation.” In the

1970s, physicists came to regard the electromagnetic and the weak force

as two aspects of a single electroweak interaction.

The electromagnetic force obeys the inverse-square law. The force’s
magnitude decreases as one over the distance from the source squared.
The inverse-square law applies to phenomena—such as gravity, light, and
sound—that spread their influence equally in all directions and with an
infinite range.

All electromagnetic waves are produced by accelerating charges.

The simplest radiation source is an oscillating charged particle. Consider
a negatively charged particle (electron) moving back and forth beside a
fixed positive charge (proton). Recall that the changing electric field
induces a magnetic field perpendicular to the electric field. In this way,
the wave propagates itself as each changing field induces the other.

716 Chapter 20

(tr) ©Big Bear Solar Observatory/New Jersey Institute of Technology; (tc) ©National Solar Observatory/AURA/NSF; (bl), (bc) ©Courtesy of SOHO/EIT consortium. SOHO is a project of international cooperation between ESA and NASA.; (tl) ©The Nobeyama Radio The frequency of oscillation determines the frequency of the wave
Observatory; (br) ©Yohkoh Solar Observatory that is produced. In an antenna, two metal rods are connected to an
alternating voltage source that is changed from positive to negative
voltage at the desired frequency. The wavelength λ of the wave is related
to the frequency f  by the equation λ = c/f, in which c is the speed of light.

Electromagnetic waves transfer energy. electromagnetic radiation  the
transfer of energy associated with an
All types of waves, whether they are mechanical or electromagnetic or are electric and magnetic field; it varies
longitudinal or transverse, have an energy associated with their motion. periodically and travels at the speed
In the case of electromagnetic waves, that energy is stored in the oscillat- of light
ing electric and magnetic fields.
Figure 4.3
The simplest definition of energy is the capacity to do work. When
work is performed on a body, a force moves the body in the direction of The Sun at Different
the force. The force that electromagnetic fields exert on a charged particle Wavelengths of Radiation 
is proportional to the electric field strength, E, and the magnetic field
strength, B. So, we can say that energy is stored in electric and magnetic The sun radiates in all parts of the
fields in much the same way that energy is stored in gravitational fields. electromagnetic spectrum, not just in the
visible light that we are accustomed to
The energy transported by electromagnetic waves is called observing. These images show what the
electromagnetic radiation. The energy carried by electromagnetic waves sun would look like if we could “see” at
can be transferred to objects in the path of the waves or converted to different wavelengths of electromagnetic
other forms, such as heat. An everyday example is the use of the energy radiation.
from microwave radiation to warm food. Energy from the sun reaches
Earth via electromagnetic radiation across a variety of wavelengths. Some
of these wavelengths are illustrated in Figure 4.3.

Radio Infrared Visible (black and white)

Ultraviolet Extreme UV X-ray
Electromagnetic Induction
717

Radio and TV Broadcasts

Y“ ou are listening to 97.7 WKID, student-run radio Similarly, amplitude modulated (AM) radio stations are all
from Central High School.” What does the radio in the 535 to 1700 kHz band. A kilohertz (kHz) is 1000
announcer mean by this greeting? Where do cycles per second, so the AM band is broadcast at lower
those numbers and letters come from? The numbers frequencies than the FM band is. The television channels
mean that the radio station is broadcasting a frequency 2 to 6 broadcast between 54 MHz and 88 MHz. Channels
modulated (FM) radio signal of 97.7 megahertz (MHz). In 7 to 13 are in the 174 MHz to 220 MHz band, and the
other words, the electric and magnetic fields of the radio remaining channels occupy even higher frequency bands
wave are changing back and forth between their in the spectrum.
minimum and maximum values 97 700 000 times per
second. That’s a lot of oscillations in a three-minute-long How are these radio waves transmitted? To create
song! a simple radio transmitter, you need to create a rapidly
changing electric current in a wire. The easiest form of
The Federal Communications Commission (FCC) assigns a changing current is a sine wave. A sine wave can be
the call letters, such as WKID, and the frequencies that the created with a few simple circuit components, such as
various stations will use. All FM radio stations are located a capacitor and an inductor. The wave is amplified, sent
in the band of frequencies that range from 88 to 108 MHz. to an antenna, and transmitted into space.

If you have a sine wave generator and a transmitter,
you have a radio station. The only problem is that a sine
wave contains very little information! To turn sound
waves or pictures into information that your radio or
television set can interpret, you need to change, or
modulate, the signal. This modulation is done by slightly
changing the frequency based on the information that you
want to send. FM radio stations and the sound part of
your TV signal convey information using this method.

photon  a unit or quantum of light; a High-energy electromagnetic waves behave like particles. ©William B. Plowman/AP Images
particle of electromagnetic radiation
that has zero mass and carries a Sometimes an electromagnetic wave behaves like a particle. This notion
quantum of energy is called the wave-particle duality of light. It is important to understand
that there is no difference in what light is at different frequencies. The
718 Chapter 20 difference lies in how light behaves.

When thinking about electromagnetic waves as a stream of particles, it
is helpful to utilize the concept of a photon. A photon is a particle that
carries energy but has zero mass. You will learn more about photons in
the chapter on atomic physics. The relationship between frequency and
photon energy is simple: E = hf, in which h, Plank’s constant, is a fixed
number and f is the frequency of the wave.

Low-energy photons tend to behave more like waves, and higher energy
photons behave more like particles. This distinction helps scientists design
detectors and telescopes to distinguish different frequencies of radiation.

The Electromagnetic Spectrum

At first glance, radio waves seem completely different from visible light
and gamma rays. They are produced and detected in very different ways.
Though your eyes can see visible light, a large antenna is needed to detect
radio waves, and sophisticated scientific equipment must be used to
observe gamma rays. Even though they appear quite different, all the
different parts of the electromagnetic spectrum are fundamentally the
same thing. They are all electromagnetic waves.

The electromagnetic spectrum can be expressed in terms of wave-
length, frequency, or energy. The electromagnetic spectrum is shown in
Figure 4.4. Longer wavelengths, like radio waves, are usually described in
terms of frequency. If your favorite FM radio station is 90.5, the frequency
is 90.5 MHz (9.05 × 107 Hz). Infrared, visible, and ultraviolet light are
usually described in terms of wavelength. We see the wavelength 670 nm
(6.70 × 10−7 m) as red light. The shortest wavelength radiation is gener-
ally described in terms of the energy of one photon. For example, the
element cesium-137 emits gamma rays with energy of 662 keV (10−13 J).
(A keV is a kilo-electron volt, equal to 1000 eV or 1.60 × 10−16 J.)

Radio waves. Figure 4.4

Radio waves have the longest wavelengths in the spectrum. The wave- The Electromagnetic Spectrum 
lengths range in size from the diameter of a soccer ball to the length of a
soccer field and beyond. Because long wavelengths easily travel around The electromagnetic spectrum ranges
objects, they work well for transmitting information long distances. In the from very long radio waves, with
United States, the FCC regulates the radio spectrum by assigning the wavelengths equal to the height of a tall
bands that certain stations can use for radio and television broadcasting. building, to very short-wavelength gamma
rays, with wavelengths as short as the
Objects that are far away in deep space also emit radio waves. Because diameter of the nucleus of an atom.
these waves can pass through Earth’s atmosphere, scientists can use huge
antennas on land to collect the waves, which can help them understand
the nature of the universe.

Wavelength 103 102 101 1 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-10 10-11 10-12
(m)
longer shorter
Common
name of infrared ultraviolet gamma rays
wave
radio waves visible X rays

microwaves

One wavelength football human soccer needle red blood microchip DNA atomic
about the same eld being ball cell transistor molecule nucleus
size as a...
10 6 10 7 10 8 10 9 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020
Frequency
(Hz)

lower higher

Electromagnetic Induction 719

Figure 4.5 Microwaves. ©Beat Glanzmann/Corbis

The Visible Light The wavelengths of microwaves range from 30 cm to 1 mm in length.
Spectrum  When white light These waves are considered to be part of the radio spectrum and are also
regulated by the FCC. Microwaves are used to study the stars, to talk with
shines through a prism or through satellites in orbit, and to heat up your after-school snack.
water, such as in this rainbow, you
can see the colors of the visible light Microwave ovens use the longer-wavelength microwaves to cook your
spectrum. popcorn quickly. Microwaves are also useful for transmitting information
because they can penetrate mist, clouds, smoke, and haze. Microwave
720 Chapter 20 towers throughout the world convey telephone calls and computer data
from city to city. Shorter-wavelength microwaves are used for radar.
Radar works by sending out bursts of microwaves and detecting the
reflections off of objects the waves hit.

Infrared.

Infrared light lies between the microwave and the visible parts of the
electromagnetic spectrum. The far-infrared wavelengths, which are close
to the microwave end of the spectrum, are about the size of the head of a
pin. Short, near-infrared wavelengths are microscopic. They are about the
size of a cell.

You experience far-infrared radiation every day as heat given off by
anything warm: sunlight, a warm sidewalk, a flame, and even your own
body! Television remote controls and some burglar alarm systems use
near-infrared radiation. Night-vision goggles show the world as it looks in
the infrared, which helps police officers and rescue workers to locate people,
animals, and other warm objects in the dark. Mosquitoes can also “see” in
the infrared, which is one of the tools in their arsenal for finding dinner.

Visible light.

The wavelengths that the human eye can see range from about 700 nm
(red light) to 400 nm (violet light). This range is a very small part of the
electromagnetic spectrum! We see the visible spectrum as a rainbow, as
shown in Figure 4.5.

Visible light is produced in many ways. An incandescent light bulb
gives off light—and heat—from a glowing filament. In neon lights and in
lasers, atoms emit light directly. Televisions and fluorescent lights make
use of phosphors, which are materials that emit light when they are
exposed to high-energy electrons or ultraviolet radiation. Fireflies create
light through a chemical reaction.

Ultraviolet.

Ultraviolet (UV) light has wavelengths that are shorter than visible light,
just beyond the violet. Our sun emits light throughout the spectrum, but
the ultraviolet waves are the ones responsible for causing sunburns. Even
though you cannot see ultraviolet light with your eyes, this light will also
damage your retina. Only a small portion of the ultraviolet waves that the
sun emits actually penetrates Earth’s atmosphere. Various atmospheric
gases, such as ozone, block most of the UV waves.

Ultraviolet light is often used as a disinfectant to kill bacteria in city Figure 4.6
water supplies or to sterilize equipment in hospitals. Scientists use
ultraviolet light to determine the chemical makeup of atoms and mol- X-ray Image of a Hand 
ecules and also the nature of stars and other celestial bodies. Ultraviolet
light is also used to harden some kinds of dental fillings. Wilhelm Roentgen took this X-ray
image of Bertha Roentgen’s hand one
X rays. week after his discovery of this new
type of electromagnetic radiation.
As the wavelengths of electromagnetic waves decrease, the associated
photons increase in energy. X rays have very short wavelengths, about the
size of atoms, and are usually thought of in terms of their energy instead
of their wavelength.

While the German scientist Wilhelm Conrad Roentgen was experi-
menting with vacuum tubes, he accidentally discovered X rays. A week
later, he took an X-ray photograph of his wife’s hand, which clearly
revealed her wedding ring and her bones. This first X ray is shown in
Figure 4.6. Roentgen called the phenomenon X ray to indicate that it was
an unknown type of radiation, and the name remains in use today.

You are probably familiar with the use of X rays in medicine and
dentistry. Airport security also uses X rays to see inside luggage. Emission
of X rays from otherwise dark areas of space suggests the existence of
black holes.

Gamma rays.

The shortest-wavelength electromagnetic waves are called gamma rays.
As with X rays, gamma rays are usually described by their energy. The
highest-energy gamma rays observed by scientists come from the hottest
regions of the universe.

Radioactive atoms and nuclear explosions produce gamma rays. Gamma
rays can kill living cells and are used in medicine to destroy cancer cells. The
universe is a huge generator of gamma rays. Because gamma rays do not
fully pierce Earth’s atmosphere, astronomers frequently mount gamma-ray
detectors on satellites.

Library of Congress, Prints and Photographs Division [LC-USZ62-95345] Section 4 Formative ASSESSMENT

Reviewing Main Ideas

1. W hat concepts did Maxwell use to help create his theory of electricity and
magnetism? What phenomenon did Maxwell’s equations predict?

2. W hat do electric and magnetic forces have in common?
3. The parts of the electromagnetic spectrum are commonly described in

one of three ways. What are these ways?

Critical Thinking

4. Where is the energy of an electromagnetic wave stored? Describe how
this energy can be used.

Electromagnetic Induction 721

Chapter 20 Summary

Section 1  Electricity from Magnetism Key Term

• A change in the magnetic flux through a conducting coil induces an electric electromagnetic induction
current in the coil. This concept is called electromagnetic induction.
Key Terms
• Lenz’s law states that the magnetic field of an induced current opposes the
change that caused it. generator
alternating current
• The magnitude of the induced emf can be calculated using Faraday’s law of back emf
induction. mutual inductance

Section 2  Generators, Motors, and Mutual Key Terms
Inductance
rms current
• Generators use induction to convert mechanical energy into electrical transformer
energy.
Key Terms
• Motors use an arrangement similar to that of generators to convert
electrical energy into mechanical energy. electromagnetic radiation
photon
• Mutual inductance is the process by which an emf is induced in one circuit
as a result of a changing current in another nearby circuit.

Section 3  AC Circuits and Transformers

• The root-mean-square (rms) current and rms emf in an ac circuit are
important measures of the characteristics of an ac circuit.

• Transformers change the emf of an alternating current in an ac circuit.

Section 4  Electromagnetic Waves

• Electromagnetic waves are transverse waves that are traveling at the speed
of light and are associated with oscillating electric and magnetic fields.

• Electromagnetic waves transfer energy. The energy of electromagnetic
waves is stored in the waves’ electric and magnetic fields.

• The electromagnetic spectrum has a wide variety of applications and
characteristics that cover a broad range of wavelengths and frequencies.

Variable Symbols

Quantities Units
N number of turns (unitless)

∆Vmax maximum emf V   volt Problem Solving
∆Vrms rms emf V   volt
Imax maximum current A   ampere See Appendix D: Equations for a summary
Irms rms current A   ampere of the equations introduced in this chapter.
If you need more problem-solving practice,
M mutual inductance H   henry = V•s/A see Appendix I: Additional Problems.

722 Chapter 20

Chapter 20 Review

Electricity from Magnetism 9. A n electromagnet is placed next to a coil of wire in

Reviewing Main Ideas the arrangement shown below. According to Lenz’s

1. Suppose you have two circuits. One consists of an law, what will be the direction of the induced current
electromagnet, a dc emf source, and a variable in the resistor R in the following cases?
resistor that permits you to control the strength of the a. T he magnetic field suddenly decreases after the
magnetic field. In the second circuit, you have a coil
of wire and a galvanometer. List three ways that you switch is opened.
can induce a current in the second circuit. b. T he coil is moved closer to the electromagnet.

2. Explain how Lenz’s law allows you to determine the Electromagnet B Coil
direction of an induced current.
Switch
3. W hat four factors affect the magnitude of the induced
emf in a coil of wire? -+ R

4. I f you have a fixed magnetic field and a length of wire, emf
how can you increase the induced emf across the
ends of the wire? Practice ProblemHRsW • Holt Physics

Conceptual Questions PH99PE-C22-CHR-001-A
For problems 10–12, see Sample Problem A.
5. Rapidly inserting the north pole of a bar magnet into
a coil of wire connected to a galvanometer causes the 10. A flexible loop of conducting wire has a radius of
needle of the galvanom­ eter to deflect to the right. 0.12 m and is perpendicular to a uniform magnetic
What will happen to the needle if you do the field with a strength of 0.15 T, as in figure (a) below.
following? The loop is grasped at opposite ends and stretched
a. pull the magnet out of the coil until it closes to an area of 3 × 10−3 m2, as in figure
b. let the magnet sit at rest in the coil (b) below. If it takes 0.20 s to close the loop, find the
c. thrust the south end of the magnet into the coil magnitude of the average emf induced in the loop
during this time.
6. E xplain how Lenz’s law illustrates the principle of
energy conservation. (a) (b)

7. D oes dropping a strong magnet down a long copper 11. A rectangHuRlaWr c•oHilo0l.t0P55hymsicbsy 0.085 m is positioned so
tube induce a current in the tube? If so, what effect that itPs Hcr9o9sPs-Es-eCct2i2o-nCaHl aRr-e0a0i2s-pAerpendicular to the
will the induced current have on the motion of the direction of a magnetic field, B. If the coil has 75 turns
magnet? and a total resistance of 8.7 Ω and the field decreases
at a rate of 3.0 T/s, what is the magnitude of the
8. Two bar magnets are placed side by side so that the induced current in the coil?
north pole of one magnet is next to the south pole of
the other magnet. If these magnets are then pushed
toward a coil of wire, would you expect an emf to be
induced in the coil? Explain your answer.

Chapter Review 723

Chapter review 23. A bar magnet is attached perpendicular to a rotating
shaft. The magnet is then placed in the center of a coil
12. A 52-turn coil with an area of 5.5 × 10−3 m2 is of wire. In which of the arrangements shown below
dropped from a position where B = 0.00 T to a new could this device be used as an electric generator?
position where B = 0.55 T. If the displacement occurs Explain your choice.
in 0.25 s and the area of the coil is perpendicular to
the magnetic field lines, what is the resulting average (a)
emf induced in the coil?
N
Generators, Motors, and
Mutual Inductance S

Reviewing Main Ideas R
(b) (c)
13. L ist the essential components of an electric generator,
and explain the role of each component in generating RS N SN
an alternating emf.
R
14. A student turns the handle of a small generator
attached to a lamp socket containing a 15 W bulb. 24. W ould a transformer work with pulsating direct
The bulb barely glows. What should the student do to current? Explain your answer.
make the bulb glow more brightly?
25. T he faster the coil of loops, or armature, of an ac PHYSICS
15. What is meant by the term frequency in reference to Spec. Number PH
an alternating current? generator rotates, the harder it is to turn the arma- Boston Graphics,
ture. Use Lenz’s law to explain why this happens. 617.523.1333
16. How can an ac generator be converted to a dc
generator? Explain your answer. Practice Problems

17. W hat is meant by back emf? How is it induced in an For problems 26–29, see Sample Problem B.
electric motor?
26. T he rms applied emf across high-voltage
18. Describe how mutual induction occurs. transmission lines in Great Britain is 220 000 V.
What is the maximum emf?
19. What is the difference between a step-up transformer
and a step-down transformer? 27. The maximum applied emf across certain heavy-duty

20. Does a step-up transformer increase power? Explain appliances is 340 V. If the total resistance of an
your answer. appliance is 120 Ω, calculate the following:
a. the rms applied emf
Conceptual Questions b. the rms current

21. W hen the plane of a rotating loop of wire is parallel to 28. T he maximum current that can pass through a light
the magnetic field lines, the number of lines passing
through the loop is zero. Why is the current at a bulb filament is 0.909 A when its resistance is 182 Ω.
maximum at this point in the loop’s rotation? a. W hat is the rms current conducted by the filament

22. In many transformers, the wire around one winding of the bulb?
is thicker, and therefore has lower resistance, than the b. What is the rms emf across the bulb’s filament?
wire around the other winding. If the thicker wire is c. How much power does the light bulb use?
wrapped around the secondary winding, is the device
a step-up or a step-down transformer? Explain.

724 Chapter 20

29. A 996 W hair dryer is designed to carry a peak current Chapter review
of 11.8 A.
a. H ow large is the rms current in the hair dryer? 37. T he transformer shown in the figure below is
b. W hat is the rms emf across the hair dryer? constructed so that the coil on the left has five times
as many turns of wire as the coil on the right does.
ac Circuits and Transformers a. If the input potential difference is across the coil
on the left, what type of transformer is this?
Reviewing Main Ideas b. If the input potential difference is 24 000 V, what is
the output potential difference?
30. W hich quantities remain constant when alternating
currents are generated? 60 3
turns turns
31. H ow does the power dissipated in a resistor by an
alternating current relate to the power dissipated by Electromagnetic Waves
a direct current that has potential difference and
current values that are equal to the maximum values Reviewing Main Ideas
of the alternating current?
38. How are electric and magnetic fields oriented to each
Conceptual Questions other in an electromagnetic wave?

32. I n a ground fault interrupter, would the difference in 39. How does the behavior of low-energy electromag-
current across an outlet be measured in terms of the netic radiation differ from that of high-energy
rms value of current or the actual current at a given electromagnetic radiation?
moment? Explain your answer.
Conceptual Questions
33. V oltmeters and ammeters that measure ac quantities
are calibrated to measure the rms values of emf and 40. Why does electromagnetic radiation obey the
current, respectively. Why would this be preferred to inverse-square law?
measuring the maximum emf or current?
41. W hy is a longer antenna needed to produce a
Practice Problems low-frequency radio wave than to produce a
high-frequency radio wave?
For problems 34–37, see Sample Problem C.
Mixed Review Problems
34. A transformer is used to convert 120 V to 9.0 V for use
in a portable CD player. If the primary, which is Reviewing Main Ideas
connected to the outlet, has 640 turns, how many
turns does the secondary have? 42. A student attempts to make a simple generator by
passing a single loop of wire between the poles of a
35. S uppose a 9.00 V CD player has a transformer for horseshoe magnet with a 2.5 × 10−2 T field. The area
converting current in Great Britain. If the ratio of the of the loop is 7.54 × 10−3 m2 and is moved perpen-
turns of wire on the primary to the secondary coils is dicular to the magnetic field lines. In what time
24.6 to 1, what is the outlet potential difference? interval will the student have to move the loop out of
the magnetic field in order to induce an emf of 1.5 V?
36. A transformer is used to convert 120 V to 6.3 V in Is this a practical generator?
order to power a toy electric train. If there are 210
turns in the primary, how many turns should there be
in the secondary?

Chapter Review 725

Chapter review 46. A bolt of lightning, such as the one shown on the left
side of the figure below, behaves like a vertical wire
43. T he same student in item 42 modifies the simple conducting electric current. As a result, it produces
generator by wrapping a much longer piece of wire a magnetic field whose strength varies with the
around a cylinder with about one-fourth the area of distance from the lightning. A 105-turn circular coil is
the original loop (1.886 × 10−3 m2). Again using a oriented perpendicular to the magnetic field, as
uniform magnetic field with a strength of 2.5 × 10−2 T, shown on the right side of the figure below. The coil
the student finds that by removing the coil perpen- has a radius of 0.833 m. If the magnetic field at the
dicular to the magnetic field lines during 0.25 s, an coil drops from 4.72 × 10–3 T to 0.00 T in 10.5 µs, what
emf of 149 mV can be induced. How many turns of is the average emf induced in the coil?
wire are wrapped around the coil?
0.833 m
44. A coil of 325 turns and an area of 19.5 × 10−4 m2 is
removed from a uniform magnetic field at an angle of
45° in 1.25 s. If the induced emf is 15 mV, what is the
magnetic field’s strength?

45. A transformer has 22 turns of wire in its primary and
88 turns in its secondary.
a. Is this a step-up or step-down transformer?
b. I f 110 V ac is applied to the primary, what is the
output potential diff­erence?

PHYSICS
Spec. Number P
Boston Graphic
617.523.1333

Alternating Current

In alternating current (ac), the emf alternates from positive to In this graphing calculator activity, the calculator will use
negative. The current responds to changes in emf by oscillat- these two equations to make graphs of instantaneous current
ing with the same frequency of the emf. This relationship is and rms current versus time. By analyzing these graphs, you
shown in the following equation for instantaneous current: will be able to determine what the values of the instanta-
neous current and the rms current are at any point in time.
i = Imax sin ωt The graphs will give you a better understanding of current in
ac circuits.
In this equation, ω is the ac frequency, and Imax is the
maximum current. The effective current of an ac circuit is the Go online to HMDScience.com to find this graphing calculator
activity.
root-mean-square current (rms current), Irms. The rms
current is related to the maximum current by the following

equation: _​I  max  ​ ​ 
​√  2  ​
Irms =

726 Chapter 20

47. T he potential difference in the lines that carry electric Chapter review
power to homes is typically 20.0 kV. What is the ratio
of the turns in the primary to the turns in the 50. A generator supplies 5.0 × 103 kW of power. The
secondary of the transformer if the output potential output emf is 4500 V before it is stepped up to 510 kV.
difference is 117 V? The electricity travels 410 mi (6.44 × 105 m) through a
transmission line that has a resistance per unit length
48. The alternating emf of a generator is represented by of 4.5 × 10−4 Ω/m.
the equation emf = (245 V) sin 560t, in which emf is a. H ow much power is lost through transmission of
in volts and t is in seconds. Use these values to find the electrical energy along the line?
the frequency of the emf and the maximum emf b. H ow much power would be lost through transmis-
output of the source. sion if the generator’s output emf were not stepped
up? What does this answer tell you about the role
49. A pair of adjacent coils has a mutual inductance of of large emfs (voltages) in power transmission?
1.06 H. Determine the average emf induced in the
secondary circuit when the current in the primary
circuit changes from 0 A to 9.50 A in a time interval of
0.0336 s.

ALTERNATIVE ASSESSMENT 3. R esearch the debate between the proponents of
alternating current and those who favored direct
1. T wo identical magnets are dropped simultaneously current in the 1880–1890s. How were Thomas Edison
from the same point. One of them passes through a and George Westinghouse involved in the contro-
coil of wire in a closed circuit. Predict whether the two versy? What advantages and disadvantages did each
magnets will hit the ground at the same time. Explain side claim? What uses of electricity were anticipated?
your reasoning. Then, plan an experiment to test What kind of current was finally generated in the
which of the following variables measurably affect Niagara Falls hydroelectric plant? Had you been in a
how long each magnet takes to fall: magnetic position to fund these projects at that time, which
strength, coil cross-sectional area, and the number of projects would you have funded? Prepare your
loops the coil has. What measurements will you arguments to reenact a meeting of businesspeople in
make? What are the limits of precision in your Buffalo in 1887.
measurements? If your teacher approves your plan,
obtain the necessary materials and perform the 4. Research the history of telecommunication. Who
experiments. Report your results to the class, invented the telegraph? Who patented it in England?
describing how you made your measurements, what Who patented it in the United States? Research the
you concluded, and what additional questions need contributions of Charles Wheatstone, Joseph Henry,
to be investigated. and Samuel Morse. How did each of these men deal
with issues of fame, wealth, and credit to other
2. W hat do adapters do to potential difference, current, people’s ideas? Write a summary of your findings,
frequency, and power? Examine the input/output and prepare a class discussion about the effect
information on several adapters to find out. Do they patents and copyrights have had on modern
contain step-up or step-down transformers? How technology.
does the output current compare to the input? What
happens to the frequency? What percentage of the Chapter Review 727
energy do they transfer? What are they used for?

Standards-Based Assessment

mulTiple choice 4. B y what factor do you multiply the maximum emf to
calculate the rms emf for an alternating current?
1. Which of the following equations correctly F. 2
describes Faraday’s law of induction? G. ​ √2  ​
A. emf = −N  _​∆  (AB∆_tta n θ​)   H. ​_  1    ​
B. emf = N ​_∆  (AB∆_cto s θ​)   ​√  2  ​
C. emf = −N ​_∆  (AB∆_cto s θ​)   J. ​ _21  ​
D. emf = M ​_∆  (AB∆_cto s θ​)  
5. Which of the following correctly describes the
2. F or the coil shown in the figure below, what must be composition of an electromagnetic wave?
done to induce a clockwise current? A. a transverse electric wave and a magnetic
F. Either move the north pole of a magnet down transverse wave that are parallel and are moving
into the coil, or move the south pole of the in the same direction
magnet up and out of the coil. B. a transverse electric wave and a magnetic
G. Either move the south pole of a magnet down transverse wave that are perpendicular and are
into the coil, or move the north pole of the moving in the same direction
magnet up and out of the coil. C. a transverse electric wave and a magnetic
H. Move either pole of the magnet down into the coil. transverse wave that are parallel and are moving
J. Move either pole of the magnet up and out of at right angles to each other
the coil. D. a transverse electric wave and a magnetic
transverse wave that are perpendicular and are
moving at right angles to each other

I 6. A coil is moved out of a magnetic field in order to
induce an emf. The wire of the coil is then rewound
magnet so that the area of the coil is increased by 1.5 times.
Extra wire is used in the coil so that the number of
3. W hich of the following would not increase the turns is doubled. If the time in which the coil is
emf produced by a generator? removed from the field is reduced by half and the
magnetic field strength remains unchanged, how
A. rotating the generator coil faster many times greater is the new induced emf than the
B. increasing the strength of the generator magnets original induced emf?
C. increasing the number of turns of wire in the coil F. 1.5 times
D. reducing the cross-sectional area of the coil G. 2 times
H. 3 times
J. 6 times

728 Chapter 20

Test Prep

Use the passage below to answer questions 7–8. SHORT RESPONSE

A pair of transformers is connected in series, as shown 11. T he alternating current through an electric toaster
in the figure below. has a maximum value of 12.0 A. What is the rms
value of this current?
1000 50
turns turns 12. W hat is the purpose of a commutator in an
ac generator?
240,000 V ΔV
13. How does the energy of one photon of an
600 20 electromagnetic wave relate to the
turns turns wave’s frequency?

7. From left to right, what are the types of the 14. A transformer has 150 turns of wire on the primary
two transformers? coil and 75 000 turns on the secondary coil. If the
A. Both are step-down transformers. input potential difference across the primary is
B. Both are step-up transformers. 120 V, what is the output potential difference across
C. One is a step-down transformer and one is a the secondary?
step-up transformer.
D. One is a step-up transformer and one is a EXTENDED RESPONSE
step-down transformer.
15. Why is alternating current used for power
8. W hat is the output potential difference from the transmission instead of direct current? Be sure to
secondary coil of the transformer on the right? include power dissipation and electrical safety
F. 400 V considerations in your answer.
G. 12 000 V
H. 160 000 V Base your answers to questions 16–18 on the information below.
J. 360 000 V
A device at a carnival’s haunted house involves a metal
9. W hat are the particles that can be used to describe ring that flies upward from a table when a patron passes
electromagnetic radiation called? near the table’s edge. The device consists of a photoelec-
A. electrons tric switch that activates the circuit when anyone walks
B. magnetons in front of the switch and of a coil of wire into which a
C. photons current is suddenly introduced when the switch
D. protons is triggered.

10. The maximum values for the current and potential 16. Why must the current enter the coil just as someone
difference in an ac circuit are 3.5 A and 340 V, comes up to the table?
respectively. How much power is dissipated in
this circuit? 17. Using Lenz’s law, explain why the ring flies upward
F. 300 W when there is an increasing current in the coil?
G. 600 W
H. 1200 W 18. Suppose the change in the magnetic field is 0.10 T/s.
J. 2400 W If the radius of the ring is 2.4 cm and the ring is
assumed to consist of one turn of wire, what is the
emf induced in the ring?

11 12 1 Test Tip
10 2 Be sure to convert all units of given
93 quantities to proper SI units.

84
76 5

Standards-Based Assessment 729

Physics and its world

1831 1837 1843 1850

Charles Darwin sets sail on Queen Victoria ascends the Richard Wagner’s first major operatic Rudolph Clausius
the H.M.S. Beagle to begin British throne at the age of success, The Flying Dutchman, premieres formulates the second law
studies of lifeforms in South 18. Her reign continues for 64 in Dresden, Germany. of thermodynamics, the first
America, New Zealand, and years, setting the tone for the step in the transformation
Australia. His discoveries form Victorian era. of thermodynamics into an
the foundation for the theory of exact science.
evolution by natural selection. (tl), (bcr) ©Bettmann/Corbis; (bl) Michael Faraday (1841-42), Thomas Phillips. Oil on canvas. National Portrait Gallery, London, UK. Photo ©Bridgeman Art Library/Getty Images; (tcl) ©Franz Xavier Winterhalter/
W = Qh - Qc The Bridgeman Art Library/Getty Images; (tr) ©Kean Collection/Getty Images; (tcr) © Kean Collection/Getty Images;(br) Library of Congress, Prints and Photographs Division [LC-USZ62-7816]

1830 1840 1850

1831 1843 1844 1850

Michael Faraday begins James Prescott Joule Samuel Morse sends the first Harriet Tubman, an
experiments demonstrating determines that mechanical telegraph message from Washington, ex-slave from Maryland,
electromagnetic induction. Similar energy is equivalent to energy D. C. to Baltimore. becomes a “conductor”
experiments are conducted around transferred as heat, laying the on the Underground
the same time by Joseph Henry foundation for the principle of Railroad. Over the next
in the United States, but he doesn’t energy conservation. decade, she helps more
publish the results of his work at than 300 slaves escape
this time. ∆U = Q - W to northern “free” states.

emf = -N∆ _​[ A_B_(_∆c_ot _sθ_)_] ​ 

••

730