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Transcript of magnetism
CHAPTER REVIEW, ASSESSMENT, AND STANDARDIZED TEST PREPARATION
Online and Technology Resources
Visit go.hrw.com to find a variety of online resources. To access this chapter’s exten-sions, enter the keyword HF6MAGXT and click the “go” button. Click Holt Online Learning for an online edition of this textbook, and other interactive resources.
Planning Guide
Chapter Openerpp. 676 – 677 CD Visual Concepts, Chapter 19 bANC Discovery Lab Magnetism*◆ b
Section 1 Magnets and Magnetic Fields• For given situations, predict whether magnets will repel or
attract each other.• Describe the magnetic field around a permanent magnet.• Describe the orientation of Earth’s magnetic field.
OSP Lesson PlansEXT Integrating Chemistry Molecular Magnetism
b
EXT Integrating Technology Magnetic Resonance Imaging b
TR 98 Magnetic Field of a Bar Magnet TR 99 Earth’s Magnetic Field
SE Quick Lab Magnetic Field of a File Cabinet, p. 681 g
TE Demonstration Magnetic Poles, p. 678 b TE Demonstration Magnetic Domains, p. 679 g TE Demonstration Magnetic Fields, p. 680 g
OSP Lesson Plans TR 100 Magnetic Field of a Current-Carrying
Wire TR 101 The Right-Hand Rule TR 102 Magnetic Field of a Current Loop and of
a Solenoid
SE Quick Lab Electromagnetism, p. 685 g SE Skills Practice Lab Magnetic Field of a Conducting
Wire, pp. 702 – 703◆ g
ANC Datasheet Magnetic Field of a Conducting Wire* g
SE CBLTM Lab Magnetic Field of a Conducting Wire, pp. 940 – 941◆ g
ANC CBLTM Experiments Magnetic Field of a Conducting Wire*◆ g
TE Demonstration Current-Carrying Wire, p. 684 b
676A Chapter 19 Magnetism
Magnetism To shorten instruction because of time limitations, omit the opener and abbrevi-ate the review.
Compression Guide
CHAPTER 19
pp. 684 – 686 PACING • 90 min
PACING • 45 min
SE Chapter Highlights, p. 694 SE Chapter Review, pp. 695 – 699 SE Graphing Calculator Practice, p. 698 g SE Alternative Assessment, p. 699 a SE Standardized Test Prep, pp. 700 – 701 g SE Appendix D: Equations, p. 863 SE Appendix I: Additional Problems, pp. 894 – 895ANC Study Guide Worksheet Mixed Review* gANC Chapter Test A* gANC Chapter Test B* a OSP Test Generator
PACING • 90 min
Section 2 Magnetism from Electricity• Describe the magnetic field produced by current in a straight
conductor and in a solenoid.• Use the right-hand rule to determine the direction of the mag-
netic field in a current-carrying wire.
OSP Lesson Plans TR 103 Force on a Moving Charge TR 104 Charge Moving in a Magnetic Field TR 105 Force on a Current-Carrying Wire TR 106 Force Between Parallel Wires TR 62A Cathode Ray Tube TR 63A Loudspeaker
TE Demonstration Electromagnetic Force, p. 687 g TE Demonstration Force Between Parallel Conductors,
p. 691 aANC Invention Lab Designing a Magnetic Spring*◆ aANC CBLTM Experiments Magnetic Field Strength*◆ a
pp. 687 – 693
Section 3 Magnetic Force• Given the force on a charge in a magnetic field, determine the
strength of the magnetic field.• Use the right-hand rule to find the direction of the force on a
charge moving through a magnetic field.• Determine the magnitude and direction of the force on a wire
carrying current in a magnetic field.
PACING • 90 min
OBJECTIVES LABS, DEMONSTRATIONS, AND ACTIVITIES TECHNOLOGY RESOURCES
pp. 678 – 682PACING • 45 min
• Holt Calendar Planner• Customizable Lesson Plans• Editable Worksheets• ExamView® Version 6
Assessment Suite
• Interactive Teacher’s Edition• Holt PuzzlePro®
• Holt PowerPoint® Resources
• MindPoint® Quiz Show
This DVD package includes:
www.scilinks.orgMaintained by the National Science Teachers Association.
Topic: MagnetsSciLinks Code: HF60901Topic: ElectromagnetsSciLinks Code: HF60484
Topic: Magnetic FieldsSciLinks Code: HF60898
SE Section Review, p. 682 gANC Study Guide Worksheet Section 1* gANC Quiz Section 1* b
SE Section Review, p. 686 gANC Study Guide Worksheet Section 2* gANC Quiz Section 2* b
Chapter 19 Planning Guide 676B
SE Sample Set A Particle in a Magnetic Field, p. 689 b TE Classroom Practice, p. 688 bANC Problem Workbook Sample Set A* bOSP Problem Bank Sample Set A b SE Sample Set B Force on a Current-Carrying conductor, p. 692
b
TE Classroom Practice, p. 692 bANC Problem Workbook Sample Set B* bOSP Problem Bank Sample Set B b
SE Section Review, p. 693 gANC Study Guide Worksheet Section 3* gANC Quiz Section 3* b
SKILLS DEVELOPMENT RESOURCES REVIEW AND ASSESSMENT CORRELATIONS
KEY SE Student Edition TE Teacher Edition ANC Ancillary Worksheet
OSP One-Stop Planner CD CD or CD-ROM TR Teaching Transparencies
EXT Online Extension * Also on One-Stop Planner ◆ Requires advance prep
• Guided Reading Audio Program• Student One Stop• Virtual Investigations• Visual Concepts
Search for any lab by topic, standard, difficulty level, or time. Edit any lab to fit your needs, or create your own labs. Use the Lab Materials QuickList software to customize your lab materials list.
ClassroomCD-ROMs
National ScienceEducation Standards
UCP 1, 2, 3, 4, 5SAI 1, 2SPSP 3, 5PS 5b
UCP 1, 2, 3, 5SAI 1, 2ST 1, 2SPSP 1, 2, 4, 5PS 2d, 4e, 5b
UCP 1, 2, 3, 5SAI 1, 2ST 1, 2HNS 1SPSP 5PS 4a, 4c, 5b
CHAPTER XCHAPTER 19Overview
676
Section 1 introduces magnetsand magnetic fields and discussesmagnetization.
Section 2 applies the right-handrule for magnetism, exploreselectromagnetism and solenoids,and introduces magneticdomains.
Section 3 concentrates on calcu-lations of magnetic fields andmagnetic forces.
About the IllustrationAstronauts Dale A. Gardner andJoseph P. Allen IV work togetherto bring the Westar VI telecom-munications satellite into theDiscovery space shuttle’s payloadbay. Allen is on a mobile footrestraint, which is attached to theDiscovery’s Remote ManipulatorSystem. The satellite had to berecovered because a propulsionsystems defect prevented it fromreaching a sufficient orbitalradius (altitude) for telecommu-nications purposes.
677677
CHAPTER 19
Magnetism
WHAT TO EXPECTIn this chapter, you will learn that a current-carrying coil of wire behaves like a magnet. Youwill also study the forces exerted on chargedparticles that are moving in a magnetic field.
Permanent magnets and electromagnets areused in many everyday and scientific applica-tions. Huge electromagnets are used to pick upand move heavy loads, such as scrap iron at arecycling plant.
CHAPTER PREVIEW
1 Magnets and Magnetic FieldsMagnetsMagnetic DomainsMagnetic Fields
2 Magnetism from ElectricityMagnetic Field of a Current-Carrying
WireMagnetic Field of a Current Loop
3 Magnetic ForceCharged Particles in a Magnetic FieldMagnetic Force on a Current-Carrying
ConductorGalvanometers
Knowledge to Review✔ A net force causes a change
in the motion of an object.
✔ Torque is the cause ofchanges in rotation. Themagnitude of a torqueequals the product of theforce and the lever arm.
✔ Electric fields surroundcharged objects and exertforces on other chargedobjects.
✔ Electric current is the rate at which electric chargesmove through a cross-sectional area.
Items to Probe✔ Electric fields: Have students
relate electric-field strengthto the force exerted on acharged particle in the field.
Tapping PriorKnowledge
Satellites sometimes contain loops of wire called magnetictorque coils that a satellite operator on Earth can activate.When current is in the coil, the magnetic field of Earthexerts a torque on the loop of wire. Torque coils are usedto align a satellite in the orientation needed for its instru-ments to work.
F
F
I
I
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B
Why it Matters
MAGNETS
Most people have had experience with different kinds of magnets, such as
those shown in Figure 1. You have probably seen a variety of magnet shapes,
such as horseshoe magnets, bar magnets, and the flat magnets frequently used
to attach items to a refrigerator. All types of magnets attract iron-containing
objects such as paper clips and nails. In the following discussion, we will
assume that the magnet has the shape of a bar. Iron objects are most strongly
attracted to the ends of such a magnet. These ends are called poles; one is
called the north pole, and the other is called the south pole. The names derive
from the behavior of a magnet on Earth. If a bar magnet is suspended from its
midpoint so that it can swing freely in a horizontal plane, it will rotate until its
north pole points north and its south pole points south. In fact, a compass is
just a magnetized needle that swings freely on a pivot.
The list of important technological applications of magnetism is very long.
For instance, large electromagnets are used to pick up heavy loads. Magnets
are also used in meters, motors, generators, and loudspeakers. Magnetic tapes
are routinely used in sound- and video-recording equipment, and magnetic
recording material is used on computer disks. Superconducting magnets are
currently being used to contain extremely high-temperature
plasmas that are used in controlled nuclear fusion research.
Superconducting magnets are also used to levitate modern
trains. These maglev trains are faster and provide a smoother
ride than the ordinary track system because of the absence of
friction between the train and the track.
Like poles repel each other, and unlike poles attracteach other
The magnetic force between two magnets can be likened to
the electric force between charged objects in that unlike poles
of two magnets attract one another and like poles repel one
another. Thus, the north pole of a magnet is attracted to the
south pole of another magnet, and two north poles (or two
south poles) brought close together repel each other. Electric
charges differ from magnetic poles in that they can be isolated,
whereas magnetic poles cannot. In fact, no matter how many
times a permanent magnet is cut, each piece always has a
north pole and a south pole. Thus, magnetic poles always
occur in pairs.
Figure 1Magnets come in a variety of shapes and sizes, but likepoles of two magnets always repel one another.
Magnets and Magnetic FieldsSECTION 1
Chapter 19678
SECTION OBJECTIVES
■ For given situations, predictwhether magnets will repelor attract each other.
■ Describe the magnetic fieldaround a permanent magnet.
■ Describe the orientation ofEarth’s magnetic field.
678
SECTION 1General Level
Demonstration
Magnetic PolesPurpose Show that all magnetshave north and south poles andthat there are attractive and repul-sive forces between two magnets.Materials two bar magnets,ring stand, string, various typesof magnets, such as those shownin Figure 1Procedure Use the string to sus-pend one bar magnet horizon-tally from the ring stand. Havestudents note that the magnetpoints north.
Bring the north pole of theother bar magnet near the northpole of the suspended magnet.Have students observe the reac-tion. Ask students to predict whatwill happen when you bring thesouth pole of the unattachedmagnet near the north pole ofthe suspended magnet. Then askthem what will happen when youbring the south pole of the unat-tached magnet near the southpole of the suspended magnet.Demonstrate both cases.
Perform similar demonstra-tions with the other types ofmagnets.
www.scilinks.orgTopic: MagnetsCode: HF60901
679
SECTION 1MAGNETIC DOMAINS
The magnetic properties of many materials are explained in terms of a model
in which an electron is said to spin on its axis much like a top does. (This clas-
sical description should not be taken literally. The property of electron spin
can be understood only with the methods of quantum mechanics.) The spin-
ning electron represents a charge that is in motion. As you will learn in the
next section of this chapter, moving charges create magnetic fields.
In atoms containing many electrons, the electrons usually pair up with
their spins opposite each other causing their fields to cancel each other. For
this reason, most substances, such as wood and plastic, are not magnetic.
However, in materials such as iron, cobalt, and nickel, the magnetic fields pro-
duced by the electron spins do not cancel completely. Such materials are said
to be ferromagnetic.
In ferromagnetic materials, strong coupling occurs between neighboring
atoms to form large groups of atoms whose net spins are aligned; these groups
are called Domains typically range in size from about
10−4 cm to 10−1 cm. In an unmagnetized substance, the domains are random-
ly oriented, as shown in Figure 2. When an external magnetic field is applied,
the orientation of the magnetic fields of each domain may change slightly to
more closely align with the external magnetic field, or the domains that are
already aligned with the external field may grow at the expense of the other
domains. This alignment enhances the applied magnetic field.
Some materials can be made into permanent magnets
Just as two materials, such as rubber and wool, can become charged after they
are rubbed together, an unmagnetized piece of iron can become a permanent
magnet by being stroked with a permanent magnet. Magnetism can be
induced by other means as well. For example, if a piece of unmagnetized iron
is placed near a strong permanent magnet, the piece of iron will eventually
become magnetized. The process can be reversed either by heating and cool-
ing the iron or by hammering the iron, because these actions cause the mag-
netic domains to jiggle and lose their alignment.
A magnetic piece of material is classified as magnetically hard or soft,
depending on the extent to which it retains its magnetism. Soft magnetic
materials, such as iron, are easily magnetized but also tend to lose their mag-
netism easily. In hard magnetic materials, domain alignment persists after the
external magnetic field is removed; the result is a permanent magnet. In con-
trast, hard magnetic materials, such as cobalt and nickel, are difficult to mag-
netize, but once they are magnetized, they tend to retain their magnetism. In
soft magnetic materials, once the external field is removed, the random
motion of the particles in the material changes the orientation of the domains
and the material returns to an unmagnetized state.
magnetic domains.
679Magnetism
Figure 2When a substance is unmagnetized,its domains are randomly oriented.
magnetic domain
a region composed of a group ofatoms whose magnetic fields arealigned in the same direction
Demonstration
Magnetic DomainsPurpose Show the effects ofimpact on a magnetized ferro-magnetic material.Materials two small paper clips,bar magnetProcedure Pick up one paper clipwith the magnet. Touch the sec-ond paper clip to the bottom ofthe first paper clip so that bothare suspended from the magnet.Remove the first paper clip fromthe bar magnet, and have stu-dents note that the second paperclip remains suspended from thefirst. Have students conclude thatthe second paper clip has alsobecome magnetized. Drop bothpaper clips onto the table top. Tryto pick up one paper clip with theother, and have students note thatthe clips are no longer magnetic.Ask students to explain. (Theimpact of the clips hitting the tablecaused the domains to once againreturn to random orientations.)
Integrating ChemistryVisit go.hrw.com for the activity“Molecular Magnetism.”
Keyword HF6MAGX
680
SECTION 1MAGNETIC FIELDS
You know that the interaction between charged objects can be described using
the concept of an electric field. A similar approach can be used to describe the
that surrounds any magnetized material. As with an electric
field, a magnetic field, B, is a vector quantity that has both magnitude and
direction.
Magnetic field lines can be drawn with the aid of a compass
The magnetic field of a bar magnet can be explored using a compass, as illus-
trated in Figure 3. If a small, freely suspended bar magnet, such as the needle
of a compass, is brought near a magnetic field, the compass needle will align
with the magnetic field lines. The direction of the magnetic field, B, at any
location is defined as the direction that the north pole of a compass needle
points to at that location.
Magnetic field lines appear to begin at the north pole of a magnet and to
end at the south pole of a magnet. However, magnetic field lines have no
beginning or end. Rather, they always form a closed loop. In a permanent
magnet, the field lines actually continue within the magnet itself to form a
closed loop. (These lines are not shown in the illustration.)
This text will follow a simple convention to indicate the direction of B. An
arrow will be used to show a magnetic field that is in the same plane as the page, as
shown in Table 1. When the field is directed into the page, we will use a series of
blue crosses to represent the tails of arrows. If the field is directed out of the page,
we will use a series of blue dots to represent the tips of arrows.
Magnetic flux relates to the strength of a magnetic field
One useful way to model magnetic field strength is to define a
quantity called magnetic flux, ΦM. It is defined as the number of
field lines that cross a certain area at right angles to that area.
Magnetic flux can be calculated by the following equation.
Now look again at Figure 3. Imagine two circles of the same
size that are perpendicular to the axis of the magnet. One circle
is located near one pole of the magnet, and the other circle is
alongside the magnet. More magnetic field lines cross the circle
that is near the pole of the magnet. This greater flux indicates
that the magnetic field is strongest at the magnet’s poles.
MAGNETIC FLUX
ΦM = ABcosq
magnetic flux = (surface area) × (magnetic field component normal to the plane of surface)
magnetic field
Chapter 19680
N S
(a)
(b)
Figure 3The magnetic field (a) of a bar magnet can be tracedwith a compass (b). Note that the north poles of thecompasses point in the direction of the field lines fromthe magnet’s north pole to its south pole.
magnetic field
a region in which a magneticforce can be detected
Table 1Conventions forRepresenting theDirection of a Magnetic Field
In the plane of the page
Into the page
Out of the page
Demonstration
Magnetic FieldsPurpose Show the interaction ofmagnets and magnetic fields.Materials two bar magnets, onehorseshoe magnet, one blanktransparency, iron filings, over-head projectorProcedure Set one of the barmagnets on the overhead projec-tor, and lay the blank transparencyover the magnet. Sprinkle the ironfilings onto the transparency, andhave students observe the behaviorof the filings. Repeat the demon-stration using the following:
a. two bar magnets about 4 cmapart, aligned with oppositepoles facing each other
b. two bar magnets about 4 cmapart, aligned with like polesfacing each other
c. horseshoe magnet
Teaching Physics 5f toMastery Students know magneticmaterials and electric currents(moving electric charges) are sourcesof magnetic fields and are subject to forces arising from the magneticfields of other sources. Activity Todemonstrate the force betweenoppositely charged magnets, placefive circular magnets on a pencilso that all repel. Pass the pencilaround so students can feel thestrength of the repulsion. Todemonstrate the magnetic field ofan electric current, place a wireconnected to a battery and a 5 Ωresistor over a compass and pointout the deflection of the needle.
Focus on the Standards
681
SECTION 1Earth has a magnetic field similar to that of a bar magnet
The north and south poles of a small bar magnet are correctly
described as the “north-seeking” and “south-seeking” poles. This
description means that if a magnet is used as a compass, the
north pole of the magnet will seek, or point to, a location near
the geographic North Pole of Earth. Because unlike poles attract,
we can deduce that the geographic North Pole of Earth corre-
sponds to the magnetic south pole and the geographic South
Pole of Earth corresponds to the magnetic north pole. Note that
the configuration of Earth’s magnetic field, pictured in Figure 4,resembles the field that would be produced if a bar magnet were
buried within Earth.
If a compass needle is allowed to rotate both perpendicular to
and parallel to the surface of Earth, the needle will be exactly par-
allel with respect to Earth’s surface only near the equator. As the compass is
moved northward, the needle will rotate so that it points more toward the sur-
face of Earth. Finally, at a point just north of Hudson Bay, in Canada, the north
pole of the needle will point perpendicular to Earth’s surface. This site is consid-
ered to be the location of the magnetic south pole of Earth. It is approximately
1500 km from Earth’s geographic North Pole. Similarly, the magnetic north
pole of Earth is roughly the same distance from the geographic South Pole.
The difference between true north, which is defined by the axis of rotation
of Earth, and north indicated by a compass, varies from point to point on
Earth. This difference is referred to as magnetic declination. An imaginary line
running roughly north-south near the center of North America currently has
zero declination. Along the line a compass will indicate true north. However,
in the state of Washington, a compass aligns about 20° east of true north. To
further complicate matters, geological evidence indicates that Earth’s magnetic
field has changed—and even reversed—throughout Earth’s history.
Although Earth has large deposits of iron ore deep beneath its surface, the
high temperatures in Earth’s liquid core prevent the iron from retaining any
permanent magnetization. It is considered more likely that the source of
Earth’s magnetic field is the movement of charges in convection currents in
Teaching TipPoint out that the direction ofEarth’s magnetic field hasreversed several times during thelast million years. Evidence forthis is provided by basalt (aniron-containing rock) that issometimes spewed forth by vol-canic activity on the ocean floor.When the lava is molten, thedomains of the ferromagneticmaterial align with Earth’s mag-netic field. As the lava cools, itsolidifies and retains a picture ofEarth’s magnetic field direction.Dated basalt deposits provide evi-dence that Earth’s magnetic fieldhas reversed periodically overtime.
GENERAL
681Magnetism
N
S
Magnetic south pole
Magnetic north poleGeographic South Pole
Geographic North Pole
Figure 4Earth’s magnetic field has a configu-ration similar to a bar magnet’s. Notethat the magnetic south pole is nearthe geographic North Pole and thatthe magnetic north pole is near thegeographic South Pole.
By convention, the north pole of amagnet is frequently painted red.This practice comes from the long-standing use of magnets, in the formof compasses, as navigational aids.Long before Global Positioning Sys-tem (GPS) satellites, the compassgave humans an easy way to orientthemselves.
Did you know?
TEACHER’S NOTESIf performing this lab in class,test the file cabinet before the lab.
Possible substitutes includeiron flagpoles and iron fenceposts, such as those around tennis courts.
Magnetic Field of a File Cabinet
MATERIALS LIST
• compass
• metal file cabinet
Stand in front of the file cabinet, andhold the compass face up and parallel tothe ground. Now move the compass fromthe top of the file cabinet to the bottom.Making sure that the compass is parallel tothe ground, check to see if the direction ofthe compass needle changes as it movesfrom the top of the cabinet to the bottom.If the compass needle changes direction,the file cabinet is magnetized. Can you
explain what might have caused the filecabinet to become magnetized? Remem-ber that Earth’s magnetic field has a verti-cal component as well as a horizontalcomponent.
Try tracing the field around some largemetal objects around your house. Can youfind an object that has been magnetized bythe horizontal component of Earth’s mag-netic field?
682
SECTION 1Earth’s core. These currents occur because the temperature in Earth’s liquid
core is not evenly distributed. Charged ions or electrons circling in the liquid
interior of Earth could produce a magnetic field. There is also evidence that
the strength of a planet’s magnetic field is related to the planet’s rate of rota-
tion. For example, Jupiter rotates at a faster rate than Earth does, and recent
space probes indicate that Jupiter’s magnetic field is stronger than Earth’s is.
Conversely, Venus rotates more slowly than Earth does and has been found to
have a weaker magnetic field than Earth does. Investigation into the cause of
Earth’s magnetism continues.
Chapter 19682
SECTION REVIEW
1. For each of the cases in the figure below, identify whether the magnets
will attract or repel one another.
a.
b.
c.
2. When you break a bar magnet in half, how many poles does each piece have?
3. Interpreting Graphics Which of the compass-needle orientations
in the figure below might correctly describe the magnet’s field at that
point?
4. Critical Thinking Satellite ground operators use the feedback from
a device called a magnetometer, which senses the direction of Earth’s
magnetic field, to decide which torque coil to activate. What direction
will the magnetometer read for Earth’s magnetic field when the satellite
passes over Earth’s equator?
5. Critical Thinking In order to protect other equipment, the body of
a satellite must remain unmagnetized, even when the torque coils have
been activated. Would hard or soft magnetic materials be best for build-
ing the rest of the satellite?
(a)
(b) (c)
(d)
(f) (e)
S N
S
N
N
S
S S NN
S SNN
1. a. repelb. attractc. attract
2. two
3. a, b
4. parallel to Earth’s surface,pointing from approximatelythe geographic South Pole(magnetic north pole) toapproximately the geo-graphic North Pole (mag-netic south pole)
5. hard magnetic material,because it is less easily magnetized
SECTION REVIEWANSWERS
Integrating TechnologyVisit go.hrw.com for the activity“Magnetic Resonance Imaging.”
Keyword HF6MAGX
683
SECTION 1
683Magnetism
Magnetic resonance imaging(MRI) evolved from nuclear mag-netic resonance (NMR) spec-troscopy, a technique that hasbeen used in physics researchsince the middle of the 20th cen-tury. The 1952 Nobel Prize inphysics was awarded to FelixBloch and Edward Purcell fortheir use of NMR spectroscopy tostudy the behavior of atomicnuclei in the presence of strongmagnetic fields.
Raymond Damadian producedthe first two-dimensional MRIimages in 1973. The first use ofMRI on a human was in 1977, andMRI became a regular part ofclinical medicine in the 1980s.The 2003 Nobel Prize in physiolo-gy or medicine was awarded toPaul C. Lauterbur and Sir PeterMansfield for their contributionsto the development of MRI tech-niques for diagnostic and researchapplications in medicine.
Magnetic resonance imaging, orMRI, is an imaging technique thathas been used in clinical medicinesince the early 1980s. MRI allowsdoctors to make two-dimensionalimages of or three-dimensionalmodels of parts of the humanbody. The use of MRI in medicinehas grown rapidly. MRI produceshigh-resolution images that can betailored to study different types oftissues, depending on the applica-tion. Also, MRI procedures aregenerally much safer than comput-erized axial tomography (CAT) scans,which flood the body with X rays.
A typical MRI machine looks likea giant cube, 2–3 meters on eachside, with a cylindrical hollow in thecenter to accommodate the patientas shown in the illustration. TheMRI machine uses electromag-nets to create magnetic fieldsranging in strength from0.5–2.0 T. These fields arestrong enough to erase creditcards and to pull pens out ofpockets, even across the MRIexam room. Because resistancewould cause normal electro-magnets to dissipate a hugeamount of heat when creatingfields this strong, the electro-magnets in most MRI machinescontain superconducting wiresthat have zero resistance.
The creation of an imagewith MRI depends on thebehavior of atomic nuclei withina magnetic field. In a strong
magnetic field, the nucleus of anatom tends to line up along thedirection of the field. This behavioris particularly true for hydrogenatoms, which are the most com-mon atoms in the body.
The primary magnet in an MRIsystem creates a strong, uniformmagnetic field centered on the partof the patient that is being exam-ined. The field causes hydrogennuclei in the body to line up in thedirection of the field. Smaller mag-nets, called gradient magnets, arethen turned on and off to createsmall variations, or pulses, in theoverall magnetic field. Each pulsecauses the hydrogen nuclei to shiftaway from their alignment. Afterthe pulse, the nuclei return toalignment, and as they do so, they
emit radio frequency electromag-netic waves. Scanners within theMRI machine detect these radiowaves, and a computer processesthe waves into images.
Different types of tissues can beseen with MRI, depending on thefrequency and duration of the puls-es. MRI is particularly good forimaging the brain and spinal tissuesand can be used to study brainfunction, brain tumors, multiplesclerosis, and other neurologicaldisorders. MRI can also be used tocreate images of blood vesselswithout the surrounding tissue,which can be very useful for study-ing the circulatory system. Themain drawbacks of MRI are thatMRI systems are very expensiveand that MRI cannot be used onsome patients, such as those withpacemakers or certain types ofmetal implants.
The imaging magnet in most MRImachines is of the superconductingtype. The magnet is the most expensive component of the MRI system.
Why it Matters
Magnetic Resonance Imaging Magnetic ResonanceImaging
Why it Matters
684
Magnetism from ElectricitySECTION 2General Level SECTION 2
MAGNETIC FIELD OF A CURRENT-CARRYING WIRE
Scientists in the late 1700s suspected that there was a relationship between
electricity and magnetism, but no theory had been developed to guide their
experiments. In 1820, Danish physicist Hans Christian Oersted devised a
method to study this relationship. Following a lecture to his advanced class,
Oersted demonstrated that when brought near a current-carrying wire, a
compass needle is deflected from its usual north-south orientation. He pub-
lished an account of this discovery in July 1820, and his work stimulated other
scientists all over Europe to repeat the experiment.
A long, straight, current-carrying wire has a cylindrical magnetic field
The experiment shown in Figure 5(a) uses iron filings to show that a
current-carrying conductor produces a magnetic field. In a similar experiment,
several compass needles are placed in a horizontal plane near a long vertical
wire, as illustrated in Figure 5(b). When no current is in the wire, all needles
point in the same direction (that of Earth’s magnetic field). However, when the
wire carries a strong, steady current, all the needles deflect in directions tangent
to concentric circles around the wire. This result points out the direction of B,the magnetic field induced by the current. When the current is reversed, the
needles reverse direction.
Chapter 19684
SECTION OBJECTIVES
■ Describe the magnetic fieldproduced by current in astraight conductor and in asolenoid.
■ Use the right-hand rule todetermine the direction ofthe magnetic field in a current-carrying wire.
(a) (b)
Figure 5(a) When the wire carries astrong current, the alignments of the iron filings show that themagnetic field induced by the current forms concentric circlesaround the wire. (b) Compassescan be used to show the directionof the magnetic field induced bythe wire.
Demonstration
Current-CarryingWirePurpose Show that a long,straight, current-carrying wirehas a magnetic field.Materials wire, dc power supply,small compasses, cardboard, ringstand, two clamps Procedure Cut a small hole inthe center of the cardboard. Usethe clamp and ring stand to holdthe cardboard parallel to thedesktop. Thread the wire throughthe hole in the cardboard, andclamp the wire to the top of thering stand so that it is perpendic-ular to the cardboard. Leave atleast 10 cm of wire above andbelow the cardboard. Connect thewire to the dc power supply. Placethe compasses on the cardboardin a circular pattern around thewire. Turn on the power supplymomentarily, and have studentsnote the deflection of the com-pass needles. Ask students todescribe the magnetic fieldaround the wire (concentric cir-cles). Ask students to predict whatwill happen if the leads of thewires are reversed (the compasseswill reverse). Demonstrate.
685
SECTION 2The right-hand rule can be used to determine thedirection of the magnetic field
These observations show that the direction of B is consis-
tent with a simple rule for conventional current, known as
the right-hand rule: If the wire is grasped in the right hand
with the thumb in the direction of the current, as shown in
Figure 6, the four fingers will curl in the direction of B.As shown in Figure 5(a), the lines of B form concentric
circles about the wire. By symmetry, the magnitude of B is
the same everywhere on a circular path centered on the wire
and lying in a plane perpendicular to the wire. Experiments
show that B is proportional to the current in the wire and
inversely proportional to the distance from the wire.
MAGNETIC FIELD OF A CURRENT LOOP
The right-hand rule can also be applied to find the direction of the magnetic
field of a current-carrying loop, such as the loop represented in Figure 7(a).Regardless of where on the loop you apply the right-hand rule, the field within
the loop points in the same direction—upward. Note that the field lines of the
current-carrying loop resemble those of a bar magnet, as shown in Figure 7(b).If a long, straight wire is bent into a coil of several closely spaced loops, as
shown on the next page in Figure 8, the resulting device is called a solenoid.
685Magnetism
B
I
B
(a) I
I
B
(b)
N
SFigure 7(a) The magnetic field of acurrent loop is similar to(b) that of a bar magnet.
Figure 6You can use the right-hand rule to find thedirection of this mag-netic field.
solenoid
a long, helically wound coil ofinsulated wire
TEACHER’S NOTESTell students that a short circuit isbeing created and that the poten-tial difference across the batterygoes to zero quickly. Be sure stu-dents disconnect the battery aftermaking their observations.
Have students compare thenumber of paper clips they canpick up with respect to the num-ber of windings around the nail.More windings result in a largerfield, so students should be ableto pick up more paper clips withmore windings.
Electromagnetism
MATERIALS LIST
• D-cell battery
• 1 m length of insulated wire
• large nail
• compass
• metal paper clips
Wind the wire around the nail, asshown below. Remove the insulation fromthe ends of the wire, and hold these endsagainst the metal terminals of the battery.
Use the compass to determinewhether the nail is magnetized. Next, flip
the battery so that the direction of thecurrent is reversed. Again, bring the com-pass toward the same part of the nail. Canyou explain why the compass needle nowpoints in a different direction?
Bring paper clips near the nail whileconnected to the battery.What happensto the paper clips? How many can you pick up?
686
SECTION 2Solenoids produce a strong magnetic field by combining several loopsA solenoid is important in many applications because it acts as a magnet when
it carries a current. The magnetic field strength inside a solenoid increases with
the current and is proportional to the number of coils per unit length. The mag-
netic field of a solenoid can be increased by inserting an iron rod through the
center of the coil; this device is often called an electromagnet. The magnetic field
that is induced in the rod adds to the magnetic field of the solenoid, often creat-
ing a powerful magnet.
Figure 8 shows the magnetic field lines of a solenoid. Note that the field
lines inside the solenoid point in the same direction, are nearly parallel, are
uniformly spaced, and are close together. This indicates that the field inside
the solenoid is strong and nearly uniform. The field outside the solenoid is
nonuniform and much weaker than the interior field. Solenoids are used in a
wide variety of applications, from most of the appliances in your home to
very high-precision medical equipment.
Visual Strategy
Figure 8Have students practice using theright-hand rule by confirmingthat the direction of the magne-tic field shown in Figure 8 is cor-rectly drawn at all points aroundthe solenoid. Point out to stu-dents that the fingers curl alongthe turns of the solenoid.
If the current in the solenoidis reversed, which end of the
solenoid is the north pole?
the right sideA
Q
Chapter 19686
SN
I
I
SECTION REVIEW
1. What is the shape of the magnetic field produced by a straight current-
carrying wire?
2. Why is the magnetic field inside a solenoid stronger than the magnetic
field outside?
3. If electrons behave like magnets, then why aren’t all atoms magnets?
4. Critical Thinking In some satellites, torque coils are replaced by
devices called torque rods. In torque rods, a ferromagnetic material is
inserted inside the coil. Why does a torque rod have a stronger magnetic
field than a torque coil?
1. concentric circles around the wire
2. The fields produced by thetop and bottom of everyloop all point in the samedirection and are confined toa small region of space.
3. Electrons usually pair upwith their spins oppositeeach other, and their fieldscancel each other.
4. The magnetic field that isinduced (by domain varia-tion) in the rod adds to the magnetic field ofthe solenoid.
SECTION REVIEWANSWERS
Figure 8The magnetic field inside a solenoid is strong and nearly uniform.Note that the field lines resemble those of a bar magnet, so a sole-noid effectively has north and south poles.
www.scilinks.orgTopic: ElectromagnetsCode: HF60484
SECTION OBJECTIVES
■ Given the force on a chargein a magnetic field, deter-mine the strength of themagnetic field.
■ Use the right-hand rule tofind the direction of the forceon a charge moving througha magnetic field.
■ Determine the magnitudeand direction of the force ona wire carrying current in amagnetic field.
687Magnetism 687
SECTION 3General LevelMagnetic Force SECTION 3
CHARGED PARTICLES IN A MAGNETIC FIELD
Although experiments show that a constant magnetic field does not exert a net
force on a stationary charged particle, charges moving through a magnetic
field do experience a magnetic force. This force has its maximum value when
the charge moves perpendicular to the magnetic field, decreases in value at
other angles, and becomes zero when the particle moves along the field lines.
To keep the math simple in this book, we will limit our discussion to situations
in which charges move parallel or perpendicular to the magnetic field lines.
A charge moving through a magnetic field experiences a force
Recall that the electric field at a point in space is defined as the electric force
per unit charge acting on some test charge placed at that point. In a similar
manner, we can describe the properties of the magnetic field, B, in terms of
the magnetic force exerted on a test charge at a given point. Our test object is
assumed to be a positive charge, q, moving with velocity v perpendicular to B.It has been found experimentally that the strength of the magnetic force on
the particle moving perpendicular to the field is equal to the product of the
magnitude of the charge, q, the magnitude of the velocity, v, and the strength
of the external magnetic field, B, as shown by the following relationship.
Fmagnetic = qvB
This expression can be rearranged as follows:
If the force is in newtons, the charge is in coulombs, and the speed is in
meters per second, the unit of magnetic field strength is the tesla (T). Thus, if
a 1 C charge moving at 1 m/s perpendicular to a magnetic field experiences a
magnetic force of 1 N, the magnitude of the magnetic field is equal to 1 T. Most
magnetic fields are much smaller than 1 T. We can express the units of the
magnetic field as follows:
T = ⎯C•
N
m/s⎯ = ⎯
A
N
•m⎯ = ⎯
V
m
•2s
⎯
MAGNITUDE OF A MAGNETIC FIELD
B = ⎯Fma
q
g
v
netic⎯
magnetic field =magnetic force on a charged particle⎯⎯⎯⎯(magnitude of charge)(speed of charge)
Demonstration
Electromagnetic ForcePurpose Show that movingcharges in a magnetic field expe-rience a force.Materials strong horseshoe mag-net, wire, two ring stands and sup-ports, variable dc power supplyProcedure Lay the horseshoemagnet on its side so that onepole is above the other. Connectthe wire to the power supply, andsupport the wire so that it passesthrough the center of the poles ofthe horseshoe magnet. Remindstudents that current is made upof moving charges and that theywill observe the magnetic fieldexerting a force on the charges.Turn on the power supply, andgradually increase the current inthe wire until the wire is forcedto one side or the other.
Ask students what will happenif the direction of the current isreversed. (The wire will move inthe opposite direction.) Turn offthe power supply, detach thewires, and attach them to theopposite terminals. Turn on thepower supply, and increase thecurrent to confirm the students’hypotheses.
Have students sketch the magnetic fields of the magnetand the wire.
www.scilinks.orgTopic: Magnetic FieldsCode: HF60898
688
SECTION 3Conventional laboratory magnets can produce magnetic fields up to about
1.5 T. Superconducting magnets that can generate magnetic fields as great as
30 T have been constructed. For comparison, Earth’s magnetic field near its sur-
face is about 50 μT (5 × 10−5 T).
An alternative right-hand rule can be used to find the direction of the magnetic force
Experiments show that the direction of the magnetic force is always perpen-
dicular to both the velocity, v, and the magnetic field, B. To determine the
direction of the force, use the right-hand rule. As before, place your fingers in
the direction of B with your thumb pointing in the direction of v, as illustrat-
ed in Figure 9. The magnetic force, Fmagnetic , on a positive charge is directed
out of the palm of your hand.
If the charge is negative rather than positive, the force is directed opposite
that shown in Figure 9. That is, if q is negative, simply use the right-hand rule
to find the direction of Fmagnetic for positive q, and then reverse this direction
for the negative charge.
Chapter 19688
F
B
vmagnetic
Figure 9Use this alternative right-hand ruleto find the direction of the magneticforce on a positive charge.
Control grid
HeaterCathode
Focusing coil
Deflection coil
Electron beam
Anode
Glass bulb
Fluorescent screen
The force on a moving charge due to a magnetic fieldis used to create pictures on a television screen. Themain component of a television is the cathode ray tube,which is essentially a vacuum tube in which electric
fields are used to form a beam of electrons. Phosphoron the television screen glows when it is struck by theelectrons in the beam.Without magnetism, however,only the center of the screen would be illuminated bythe beam. The direction of the beam is changed by twoelectromagnets, one deflecting the beam horizontally,the other deflecting the beam vertically. The directionof the beam can be changed by changing the directionof the current in each electromagnet. In this way, thebeam illuminates the entire screen.
In a color television, three different colors of phos-phor—red, green, and blue—make up the screen. Threeelectron beams, one for each color, scan over thescreen to produce a color picture.
In a cathode ray tube, the cathode is a heated filament insidea vacuum tube, similar to the filament in a light bulb. The rayis a stream of electrons that come off the heated filamentinto a vacuum.
The electron gun is the heart of aCRT. A small, hot filament (calledthe heater) heats up a negativelycharged cathode, which emits acloud of electrons. Two positivelycharged anodes, one for accelerat-ing the electrons and one forfocusing, form the electrons into a beam, which is then directedtoward the phosphor-coatedscreen. The phosphors glow as the electrons strike them.
Particle in a Magnetic FieldAn electron moving north at 4.5 × 104 m/s enters a 1.0 mTmagnetic field pointed upward.
a. What is the magnitude anddirection of the force exertedon the electron?
b. What would the force be if theparticle were a proton?
c. What would the force be if theparticle were a neutron?
Answersa. 7.2 × 10 −18 N westb. 7.2 × 10 −18 N eastc. 0.0 N
Why it Matters
Television ScreensTelevision Screens
Why it Matters
689
SECTION 3
689Magnetism
SAMPLE PROBLEM A
Particle in a Magnetic Field
P R O B L E MA proton moving east experiences a force of 8.8 × 10−19 N upward due to the Earth’s magnetic field. At this location, the field has a magnitude of5.5 × 10−5 T to the north. Find the speed of the particle.
S O L U T I O NGiven: q = 1.60 × 10−19 C B = 5.5 × 10−5 T
Fmagnetic = 8.8 × 10−19 N
Unknown: v = ?
Use the definition of magnetic field strength. Rearrange to solve for v.
B = ⎯Fma
qg
vnetic⎯
v = ⎯Fma
qg
Bnetic⎯
v = = 1.0 × 105 m/s8.8 × 10−19 N
⎯⎯⎯⎯(1.60 × 10−19 C)(5.5 × 10−5 T)
The directions given can be used to verify the right-hand rule. Imagine standingat this location and facing north. Turn the palm of your right hand upward (thedirection of the force) with your thumb pointing east (the direction of the veloc-ity). If your palm and thumb point in these directions, your fingers point direct-ly north in the direction of the magnetic field, as they should.
PRACTICE A
Particle in a Magnetic Field
1. A proton moves perpendicularly to a magnetic field that has a magnitude
of 4.20 × 10−2 T. What is the speed of the particle if the magnitude of the
magnetic force on it is 2.40 × 10−14 N?
2. If an electron in an electron beam experiences a downward force of
2.0 × 10−14 N while traveling in a magnetic field of 8.3 × 10−2 T west,
what is the direction and magnitude of the velocity?
3. A uniform 1.5 T magnetic field points north. If an electron moves verti-
cally downward (toward the ground) with a speed of 2.5 × 107 m/s
through this field, what force (magnitude and direction) will act on it?
v SE Sample, 1–3;Ch. Rvw.30–31
PW 6–7PB 4–6
Fmagnetic SE 4–5; Ch. Rvw.35–37, 40*
PW Sample, 1–3PB 7–10
B SE 6; Ch. Rvw.34, 39
PW 4–5PB Sample, 1–3
PROBLEM GUIDE A
Solving for:
Use this guide to assign problems.SE = Student Edition TextbookPW = Problem WorkbookPB = Problem Bank on the
One-Stop Planner (OSP)
*Challenging ProblemConsult the printed Solutions Manual or the OSP for detailed solutions.
ANSWERS
Practice A1. 3.57 × 106 m/s
2. 1.5 × 106 m/s north
3. 6.0 × 10−12 N west
690
SECTION 3A charge moving through a magnetic field follows a circular path
Consider a positively charged particle moving in a uniform magnetic field.
Suppose the direction of the particle’s initial velocity is exactly perpendicular
to the field, as in Figure 10. Application of the right-hand rule for the charge
q shows that the direction of the magnetic force, Fmagnetic , at the charge’s
location is to the left. Furthermore, application of the right-hand rule at any
point shows that the magnetic force is always directed toward the center of the
circular path. Therefore, the magnetic force is, in effect, a force that maintains
circular motion and changes only the direction of v, not its magnitude.
Now consider a charged particle traveling with its initial velocity at some angle
to a uniform magnetic field. A component of the particle’s initial velocity is par-
allel to the magnetic field. This parallel part is not affected by the magnetic field,
and that part of the motion will remain the same. The perpendicular part results
in a circular motion, as described above. The particle will follow a helical path,
like the red stripes on a candy cane, whose axis is parallel to the magnetic field.
MAGNETIC FORCE ON A CURRENT-CARRYINGCONDUCTOR
Recall that current consists of many charged particles in motion. If a force is
exerted on a single charged particle when the particle moves through a mag-
netic field, it should be no surprise that a current-carrying wire also experi-
ences a force when it is placed in a magnetic field. The resultant force on the
wire is the sum of the individual magnetic forces on the charged particles. The
force on the particles is transmitted to the bulk of the wire through collisions
with the atoms making up the wire.
Consider a straight segment of wire of length l carrying current, I, in a
uniform external magnetic field, B, as in Figure 11. When the current and
magnetic field are perpendicular, the magnitude of the total magnetic force
on the wire is given by the following relationship.
The direction of the magnetic force on a wire can be obtained by using the
right-hand rule. However, in this case, you must place your thumb in the direc-
tion of the current rather than in the direction of the velocity, v. In Figure 11,the direction of the magnetic force on the wire is to the left. When the current
is either in the direction of the field or opposite the direction of the field, the
magnetic force on the wire is zero.
FORCE ON A CURRENT-CARRYING CONDUCTOR PERPENDICULARTO A MAGNETIC FIELD
Fmagnetic = BI l
magnitude of magnetic force = (magnitude of magnetic field)(current)(length of conductor within B)
Visual Strategy
Figure 10Students should be encouragedto apply the right-hand rule todescribe the force on the chargeat several points on the circle.
What direction would theforce on a moving charged
particle be if the particle were onthe left side of the circle?
to the right, toward the centerA
Q
GENERAL
Chapter 19690
v
B
qFmagnetic
+
Figure 10When the velocity, v, of a chargedparticle is perpendicular to a uni-form magnetic field, the particlemoves in a circle whose plane isperpendicular to B.
B
IFmagnetic
l
Figure 11A current-carrying conductor in amagnetic field experiences a forcethat is perpendicular to the direc-tion of the current.
691
SECTION 3
691Magnetism
I2I1
B1
F1 F2
B2
F1 = −F2(a)
Figure 12Two parallel wires, each carrying asteady current, exert magneticforces on each other. The force is (a) attractive if the currents have the same direction and (b) repulsive if the two currentshave opposite directions.
I2
I1
B1
F1 F2
B2
F1 = −F2(b)
N
S
S
Papercone
Voicecoil
Figure 13In a loudspeaker, when the direction and magnitude of the cur-rent in the coil of wire change, the paper cone attached to thecoil moves, producing sound waves.
Two parallel conducting wires exert a force on one another
Because a current in a conductor creates its own magnetic field, it is easy to
understand that two current-carrying wires placed close together exert magnetic
forces on each other. When the two conductors are parallel to each other, the
direction of the magnetic field created by one is perpendicular to the direction of
the current of the other, and vice versa. In this way, a force of Fmagnetic = BIl acts
on each wire, where B is the magnitude of the magnetic field created by the other
wire.
Consider the two long, straight, parallel wires shown in Figure 12. When the
current in each is in the same direction, the two wires attract one another. Con-
firm this by using the right-hand rule. Point your thumb in the direction of cur-
rent in one wire, and point your fingers in the direction of the field produced by
the other wire. By doing this, you find that the direction of the force (pointing
out from the palm of your hand) is toward the other wire. When the currents in
each wire are in opposite directions, the wires repel one another.
Loudspeakers use magnetic force to produce sound
The loudspeakers in most sound systems use a magnetic force acting on a
current-carrying wire in a magnetic field to produce sound waves. One
speaker design, shown in Figure 13, consists of a coil of wire, a flexible paper
cone attached to the coil that acts as the speaker, and a permanent
magnet. In a speaker system, a sound signal is converted to a varying electric
signal by the microphone. This electrical signal is amplified and sent to the
loudspeaker. At the loudspeaker, this varying electrical current causes a vary-
ing magnetic force on the coil. This alternating force on the coil results in
vibrations of the attached cone, which produce variations in the density of
the air in front of it. In this way, an electric signal is converted to a sound
wave that closely resembles the sound wave produced by the source.
Demonstration
Force Between ParallelConductorsPurpose Show that two current-carrying parallel wires exert aforce on each other.Materials two 10 cm × 1 cmstrips of aluminum foil, two 9.0 VNiCad batteries, clay, connectingwire with alligator clips, twoswitches, overhead projectorProcedure Arrange the strips ofaluminum foil so that they areparallel to one another, and securethe ends of the foil to the over-head projector with the clay. Makesure the two pieces of foil can beseen clearly when projected onto ascreen. Using the wire and alliga-tor clips, connect each piece of foilto a battery and a switch so thatthe direction of the current ineach piece of foil is the same.Leave the switches open until youbegin the demonstration.
Point out to students that thedirection of the current in eachstrip will be the same when theswitch is closed. Momentarilyclose the switch, and have stu-dents observe that the stripsmove together.
Ask what effect the wires willhave on each other if the direc-tion of the current in one strip isreversed. Rearrange one of thecircuits so that the direction ofthe current is reversed, and havestudents note that the two stripsof aluminum repel one another.
692
SECTION 3
Chapter 19692
SAMPLE PROBLEM B
Force on a Current-Carrying Conductor
P R O B L E MA wire 36 m long carries a current of 22 A from east to west. If the magneticforce on the wire due to Earth’s magnetic field is downward (towardEarth) and has a magnitude of 4.0 × 10−2 N, find the magnitude and direc-tion of the magnetic field at this location.
S O L U T I O NGiven: l = 36 m I = 22 A Fmagnetic = 4.0 × 10−2 N
Unknown: B = ?
Use the equation for the force on a current-carrying conductor perpendicular
to a magnetic field.
Fmagnetic = BI lRearrange to solve for B.
Using the right-hand rule to find the direction of B, face north with your
thumb pointing to the west (in the direction of the current) and the palm of
your hand down (in the direction of the force). Your fingers point north.
Thus, Earth’s magnetic field is from south to north.
B = ⎯Fma
I
g
l
netic⎯⎯ = ⎯
(
4
2
.
2
0
A
×)
1
(
0
3
−
6
2
m
N
)⎯ = 5.0 × 10−5 T
PRACTICE B
Force on a Current-Carrying Conductor
1. A 6.0 m wire carries a current of 7.0 A toward the +x direction. A mag-
netic force of 7.0 × 10−6 N acts on the wire in the −y direction. Find the
magnitude and direction of the magnetic field producing the force.
2. A wire 1.0 m long experiences a magnetic force of 0.50 N due to a per-
pendicular uniform magnetic field. If the wire carries a current of 10.0 A,
what is the magnitude of the magnetic field?
3. The magnetic force on a straight 0.15 m segment of wire carrying a cur-
rent of 4.5 A is 1.0 N. What is the magnitude of the component of the
magnetic field that is perpendicular to the wire?
4. The magnetic force acting on a wire that is perpendicular to a 1.5 T uni-
form magnetic field is 4.4 N. If the current in the wire is 5.0 A, what is
the length of the wire that is inside the magnetic field?
PROBLEM GUIDE B
Solving for:
Use this guide to assign problems.SE = Student Edition TextbookPW = Problem WorkbookPB = Problem Bank on the
One-Stop Planner (OSP)
*Challenging ProblemConsult the printed Solutions Manual or the OSP for detailed solutions.
B SE Sample, 1–3; Ch. Rvw.32–33, 41–42, 44
PW 5–6PB 3–5
F PW 9–10PB 8–10
l SE 4PW 7–8PB Sample, 1–2
I PW Sample, 1–4PB 6–7
ANSWERS
Practice B1. 1.7 × 10−7 T in +z direction
2. 0.050 T
3. 1.5 T
4. 0.59 m
Force on a Current-Carrying ConductorA 4.5 m wire carries a current of12.5 A from north to south. Ifthe magnetic force on the wiredue to a uniform magnetic fieldis 1.1 × 103 N downward, what isthe magnitude and direction ofthe magnetic field?
Answer2.0 × 101 T, to the west
693
SECTION 3GALVANOMETERS
A galvanometer is a device used in the construction of both
ammeters and voltmeters. Its operation is based on the fact
that a torque acts on a current loop in the presence of a
magnetic field. Figure 14 shows a simplified arrangement
of the main components of a galvanometer. It consists of a
coil of wire wrapped around a soft iron core mounted so
that it is free to pivot in the magnetic field provided by the
permanent magnet. The torque experienced by the coil is
proportional to the current in the coil. This means that the
larger the current, the greater the torque and the more the
coil will rotate before the spring tightens enough to stop
the movement. Hence, the amount of deflection of the
needle is proportional to the current in the coil. When
there is no current in the coil, the spring returns the needle
to zero. Once the instrument is properly calibrated, it can
be used in conjunction with other circuit elements as an
ammeter (to measure currents) or as a voltmeter (to meas-
ure potential differences).
Visual Strategy
Figure 14Encourage students to use theright-hand rule to understandhow a galvanometer works.
If charges move through thecoil from the left terminal to
the right terminal, which direc-tion will the needle rotate?
clockwiseA
Q
693Magnetism
N S
Spring
Coil
Figure 14In a galvanometer, when current enters the coil, which is in amagnetic field, the magnetic force causes the coil to twist.
SECTION REVIEW
1. A particle with a charge of 0.030 C experiences a magnetic force of 1.5 N
while moving at right angles to a uniform magnetic field. If the speed of
the charge is 620 m/s, what is the magnitude of the magnetic field the
particle passes through?
2. An electron moving north encounters a uniform magnetic field. If the
magnetic field points east, what is the direction of the magnetic force on
the electron?
3. A straight segment of wire has a length of 25 cm and carries a current of
5.0 A. If the wire is perpendicular to a magnetic field of 0.60 T, then what
is the magnitude of the magnetic force on this segment of the wire?
4. Two parallel wires have charges moving in the same direction. Is the
force between them attractive or repulsive?
5. Interpreting Graphics Find the
direction of the magnetic force on the
current-carrying wire in Figure 15.
I
N N SS
1. 0.081 T
2. upward
3. 0.75 N
4. attractive
5. out of the page
SECTION REVIEWANSWERS
Figure 15
CHAPTER 19
694
HighlightsHighlights
CHAPTER 19
KEY IDEAS
Section 1 Magnets and Magnetic Fields• Like magnetic poles repel, and unlike poles attract.
• A magnetic domain is a group of atoms whose magnetic fields are aligned.
• The direction of any magnetic field is defined as the direction the north
pole of a magnet would point if placed in the field. The magnetic field of a
magnet points from the north pole of the magnet to the south pole.
• The magnetic north pole of Earth corresponds to the geographic South Pole,
and the magnetic south pole corresponds to the geographic North Pole.
Section 2 Magnetism from Electricity• A magnetic field exists around any current-carrying wire; the direction of
the magnetic field follows a circular path around the wire.
• The magnetic field created by a solenoid or coil is similar to the magnetic
field of a permanent magnet.
Section 3 Magnetic Force• The direction of the force on a positive charge moving through a magnetic
field can be found by using the alternate right-hand rule.
• A current-carrying wire in an external magnetic field undergoes a mag-
netic force. The direction of the magnetic force on the wire can be found
by using the alternate right-hand rule.
• Two parallel current-carrying wires exert on one another forces that are
equal in magnitude and opposite in direction. If the currents are in the
same direction, the two wires attract one another. If the currents are in
opposite directions, the wires repel one another.
KEY TERMS
magnetic domain (p. 679)
magnetic field (p. 680)
solenoid (p. 685)
Teaching TipHave students write an essaysummarizing the various cases ofcurrent-carrying wires discussedin this chapter. Essays shouldinclude a thorough explanation ofthe magnetic field produced by acurrent-carrying wire, the mag-netic force on a current-carryingwire that is in a magnetic field,and the force between two paral-lel current-carrying wires.Remind students to include theright-hand rule for each case.
Chapter 19694
Variable Symbols
Quantities Units Conversions
B magnetic field T tesla = ⎯C•
N
m/s⎯ = ⎯
A
N
•m⎯
Fmagnetic magnetic force N newtons = ⎯kg
s
•2
m⎯
l length of conductor in field m meters
Diagram Symbols
Magnetic field vector
Magnetic field pointinginto the page
Magnetic field pointingout of the page
PROBLEM SOLVING
See Appendix D: Equations for a summary of the equationsintroduced in this chapter. Ifyou need more problem-solvingpractice, see Appendix I: Additional Problems.
MAGNETS AND MAGNETIC FIELDS
Review Questions
1. What is the minimum number of poles for a magnet?
2. When you break a magnet in half, how many polesdoes each piece have?
3. The north pole of a magnet is attracted to the geo-graphic North Pole of Earth, yet like poles repel.Can you explain this?
4. Which way would a compass needle point if youwere at the magnetic north pole?
5. What is a magnetic domain?
6. Why are iron atoms so strongly affected by mag-netic fields?
7. When a magnetized steel needle is strongly heatedin a Bunsen burner flame, it becomes demag-netized. Explain why.
8. If an unmagnetized piece of iron is attracted to onepole of a magnet, will it be repelled by the oppositepole?
Conceptual Questions
9. In the figure below, two permanent magnets withholes bored through their centers are placed one over
the other. Because the polesof the upper magnet arethe reverse of those of thelower, the upper magnetlevitates above the lowermagnet. If the upper mag-net were displaced slightly,either up or down, whatwould be the resultingmotion? Explain. Whatwould happen if the uppermagnet were inverted?
695
CHAPTER 19
Review
ANSWERS1. two
2. two
3. The geographic North Pole isnear the magnetic south pole.
4. perpendicular to Earth’s surface
5. a group of atoms whose mag-netic fields are aligned in acommon direction
6. They have unpaired electronspins.
7. The added energy causes thedomains to become lessaligned.
8. No, unmagnetized iron isattracted to either pole of amagnet.
9. a damped periodic oscillation;Gravitational force and therepulsive force along with adisplacement from equilibri-um result in periodic motion.When inverted, the two mag-nets would attract each other.
10. Hang each of the bars by thestring. The magnetized barwill align itself with Earth’smagnetic field.
11. It realigns the domains of theweaker magnet.
12. first piece: the domains alignwith the magnetic field of themagnet; second piece: thedomains align with the mag-netic field of the first piece
13. The energy absorbed disturbsthe alignment of the domains.
14. south
15. number of coils per unitlength, amount of current
16. End A will point toward thegeographic South Pole.
ReviewCHAPTER 19
10. You have two iron bars and a ball of string in yourpossession; one iron bar is magnetized, and one ironbar is not. How can you determine which iron bar ismagnetized?
11. Why does a very strong magnet attract both poles ofa weak magnet?
12. A magnet attracts a piece of iron. The iron can thenattract another piece of iron. Explain, on the basisof alignment of domains, what happens in eachpiece of iron.
13. When a small magnet is repeatedly dropped, itbecomes demagnetized. Explain what happens tothe magnet at the atomic level.
MAGNETISM FROM ELECTRICITY
Review Questions
14. A conductor carrying a current is arranged so thatelectrons flow in one segment from east to west. If acompass is held over this segment of the wire, in whatdirection is the needle deflected? (Hint: Recall thatcurrent is defined as the motion of positive charges.)
15. What factors does the strength of the magnetic fieldof a solenoid depend on?
Conceptual Questions
16. A solenoid with ends marked A and B is suspendedby a thread so that the core can rotate in the hori-zontal plane. A current is maintained in the coil sothat the electrons move clockwise when viewedfrom end A toward end B. How will the coil alignitself in Earth’s magnetic field?
17. Is it possible to orient a current-carrying loop ofwire in a uniform magnetic field so that the loopwill not tend to rotate?
695Magnetism
696
19 REVIEW
17. yes, by aligning the plane ofthe loop perpendicular to themagnetic field
18. Yes, the north pole of the sole-noid would point to Earth’sgeographic North Pole; No,the solenoid would oscillateback and forth as its polescontinually reversed.
19. They have opposite charge.
20. The proton would go left, andthe electron would go right.
21. The magnetic field of themagnet exerts a force on themoving electrons in the elec-tron beam.
22. The proton would move up ina half circle and exit above itspoint of entry. The electronwould move down in a halfcircle and exit below its pointof entry.
23. The magnetic field from onewire is perpendicular to thesecond wire (and thus the cur-rent in it) at the second wire’slocation. The magnetic forceon the second wire is awayfrom the first wire.
24. no; Magnetic fields only exerta net force on moving charges.
25. positive y direction; no; Itmoves in circles in the x-yplane.
26. a. into the pageb. to the rightc. down the page
27. a. The stream moves awayfrom the wire.
b. The stream moves towardthe wire.
28. The stream moves toward theobserver.
29. Because the wires are twistedtogether, the region where themagnetic field is non-zero isvery small.
30. 15 m/s
18. If a solenoid were suspended by a string so that itcould rotate freely, could it be used as a compasswhen it carried a direct current? Could it also beused if the current were alternating in direction?
MAGNETIC FORCE
Review Questions
19. Two charged particles are projected into a regionwhere there is a magnetic field perpendicular totheir velocities. If the particles are deflected inopposite directions, what can you say about them?
20. Suppose an electron is chasing a proton up this page when suddenly a magnetic field pointing intothe page is applied. What would happen to the particles?
21. Why does the picture on a television screenbecome distorted when a magnet is brought nearthe screen?
22. A proton moving horizontally enters a region wherethere is a uniform magnetic field perpendicular to theproton’s velocity, as shown below. Describe the pro-ton’s subsequent motion. How would an electronbehave under the same circumstances?
23. Explain why two parallel wires carrying currents inopposite directions repel each other.
24. Can a stationary magnetic field set a resting elec-tron in motion? Explain.
25. At a given instant, a proton moves in the positive x direction in a region where there is a magneticfield in the negative z direction. What is the direc-tion of the magnetic force? Does the proton con-tinue to move along the x-axis? Explain.
+ v
Bin
26. For each situation below, use the movement of thepositively charged particle and the direction of themagnetic force acting on it to find the direction ofthe magnetic field.
Conceptual Questions
27. A stream of electrons is projected horizontally tothe right. A straight conductor carrying a current issupported parallel to and above the electron stream.
a. What is the effect on the electron stream if thecurrent in the conductor is left to right?
b. What is the effect if the current is reversed?
28. If the conductor in item 27 is replaced by a magnetwith a downward magnetic field, what is the effecton the electron stream?
29. Two wires carrying equal but opposite currents aretwisted together in the construction of a circuit. Whydoes this technique reduce stray magnetic fields?
Practice Problems
For problems 30–31, see Sample Problem A.
30. A duck flying due east passes over Atlanta, where themagnetic field of Earth is 5.0 × 10−5 T directed north.The duck has a positive charge of 4.0 × 10−8 C. If themagnetic force acting on the duck is 3.0 × 10−11 N upward, what is the duck’s velocity?
31. A proton moves eastward in the plane of Earth’s mag-netic equator, where Earth’s magnetic field pointsnorth and has a magnitude of 5.0 × 10–5 T. Whatvelocity must the proton have for the magnetic forceto 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° fromthe direction of a magnetic field. If the magnitude of the magnetic force on a 5.00 m length of the wireis 15.0 N, what is the strength of the magnetic field?
F F
vvin
vout
F
Chapter 19696
(a) (b) (c)
697
19 REVIEW
31. 2.1 × 10−3 m/s
32. 0.300 T
33. 2.00 T
34. a. 4.10 × 10−14 T
b. horizontal
35. a. to the leftb. into the pagec. out of the paged. up the page
36. a. to the rightb. out of the pagec. into the paged. down the page
37. a. to the leftb. into the pagec. out of the paged. up the page
38. 1.9 × 1014 m/s2
39. 2.1 × 10−2 T, in the negative y direction
40. a. 8.7 × 10−14 Nb. downwardc. 5.2 × 1013 m/s2
41. 2.0 T, out of the page
42. 8.0 × 10−3 T, in the positive z direction
43. a. 8.0 m/s
b. 5.4 × 10−26 J
33. A thin 1.00 m long copper rod in a uniform magne-tic field has a mass of 50.0 g. When the rod carries acurrent of 0.245 A, it floats in the magnetic field.What is the field strength of the magnetic field?
MIXED REVIEW
34. A proton moves at 2.50 × 106 m/s horizontally at aright angle to a magnetic field.
a. What is the strength of the magnetic fieldrequired to exactly balance the weight of theproton and keep it moving horizontally?
b. Should the direction of the magnetic field bein a horizontal or a vertical plane?
35. Find the direction of the force on a proton movingthrough each magnetic field in the four figures below.
36. Find the direction of the force on an electron mov-ing through each magnetic field in the four figuresin item 35 above.
37. In the four figures in item 35, assume that in each casethe velocity vector shown is replaced with a wire car-rying a current in the direction of the velocity vector.Find the direction of the magnetic force acting oneach wire.
38. A proton moves at a speed of 2.0 × 107 m/s at right angles to a magnetic field with a magnitude of0.10 T. Find the magnitude of the acceleration ofthe proton.
39. A proton moves perpendicularly to a uniform mag-netic field, B, with a speed of 1.0 × 107 m/s andexperiences an acceleration of 2.0 × 1013 m/s2 in thepositive x direction when its velocity is in the posi-tive z direction. Determine the magnitude anddirection of the field.
v
Bout
v
B
vB
v
Bin
40. A proton travels with a speed of 3.0 × 106 m/s at an angle of 37° west of north. A magnetic field of0.30 T points to the north. Determine the following:
a. the magnitude of the magnetic force on theproton
b. the direction of the magnetic force on theproton
c. the proton’s acceleration as it moves throughthe magnetic field
(Hint: The magnetic force experienced by the pro-ton in the magnetic field is proportional to thecomponent of the proton’s velocity that is perpen-dicular to the magnetic field.)
41. In the figure below, a 15 cm length of conductingwire that is free to move is held in place betweentwo thin conducting wires. All the wires are in amagnetic field. When a 5.0 A current is in the wire,as shown in the figure, the wire segment movesupward at a constant velocity. Assuming the wireslides without friction on the two vertical conduc-tors and has a mass of 0.15 kg, find the magnitudeand direction of the minimum magnetic field thatis required to move the wire.
42. A current, I = 15 A, is directed along the positive x-axis and perpendicular to a uniform magneticfield. The conductor experiences a magnetic forceper unit length of 0.12 N/m in the negative y direc-tion. Calculate the magnitude and direction of themagnetic field in the region through which the current passes.
43. A proton moving perpendicular to a magnetic fieldof strength 3.5 mT experiences a force due to thefield of 4.5 × 10−21 N. Calculate the following:
a. the speed of the protonb. the kinetic energy of the proton
Recall that a proton has a charge of 1.60 × 10−19 Cand a mass of 1.67 × 10−27 kg.
5.0 A
5.0 A5.0 A
15 cm
697Magnetism
(a) (b)
(c) (d)
698
19 REVIEW
44. 1.39 × 10−2 T, toward theobserver
45. 2.82 × 107 m/s
46. a. −2.9 × 10−12 N
b. −2.6 × 10−17 N
c. 8.9 × 10−30 N
44. A singly charged positive ion that has a mass of6.68 × 10−27 kg moves clockwise with a speed of1.00 × 104 m/s. The positively charged ion moves ina circular path that has a radius of 3.00 cm. Find thedirection and strength of the uniform magneticfield through which the charge is moving. (Hint:The magnetic force exerted on the positive ion is thecentripetal force, and the speed given for the posi-tive ion is its tangential speed.)
45. What speed would a proton need to achieve inorder to circle Earth 1000.0 km above the magne-tic equator? Assume that Earth’s magnetic field iseverywhere perpendicular to the path of the pro-ton and that Earth’s magnetic field has an intensityof 4.00 × 10−8 T. (Hint: The magnetic force exertedon the proton is equal to the centripetal force, andthe speed needed by the proton is its tangentialspeed. Remember that the radius of the circularorbit should also include the radius of Earth.Ignore relativistic effects.)
46. Calculate the force on an electron in each of thefollowing situations:
a. moving at 2.0 percent the speed of light andperpendicular to a 3.0 T magnetic field
b. 3.0 × 10−6 m from a protonc. in Earth’s gravitational field at the surface of
Earth
Use the following: qe = −1.6 × 10−19 C; me = 9.1 ×10−31 kg; qp = 1.6 × 10−19 C; c = 3.0 × 108 m/s; kC =9.0 × 109 N•m2/C2
Chapter 19698
Graphing Calculator PracticeVisit go.hrw.com for answers to thisGraphing Calculator activity.
Keyword HF6MAGXT Once you determine a and b, you can predict the
magnetic field strength of a solenoid for various
currents.
The graphing calculator program that accompa-
nies this activity uses this procedure. You will be
given the magnetic field and current data for vari-
ous solenoids. You will then use this information
and the program to predict the magnetic field
strength of each solenoid.
Visit go.hrw.com and type in the keyword
HF6MAGX to find this graphing calculator activity.
Refer to Appendix B for instructions on download-
ing the program for this activity.
SolenoidsA solenoid consists of a long, helically wound coil of
insulated wire. When it carries a current, a solenoid
acts as a magnet. The magnetic field strength (B)
increases linearly with the current (I) and with the
number of coils per unit length. Because there is a
direct relation between B and I, the following equa-
tion applies to any solenoid:
B = aI + b
In this equation, the parameters a and b are differ-
ent for different solenoids. The a and b parameters
can be determined if the magnetic field strength of
the solenoid is known at two different currents.
699
19 REVIEW
699Magnetism
1. During a field investigation with your class, you
find a roundish chunk of metal that attracts iron
objects. Design a procedure to determine whether
the object is magnetic and, if so, to locate its poles.
Describe the limitations of your method. What
materials would you need? How would you draw
your conclusions? List all the possible results you
can anticipate and the conclusions you could draw
from each result.
2. Imagine you have been hired by a manufacturer
interested in making kitchen magnets. The manu-
facturer wants you to determine how to combine
several magnets to get a very strong magnet. He also
wants to know what protective material to use to
cover the magnets. Develop a method for measur-
ing the strength of different magnets by recording
the maximum number of paper clips they can hold
under various conditions. First open a paper clip to
use as a hook. Test the strength of different magnets
and combinations of magnets by holding up the
magnet, placing the open clip on the magnet, and
hooking the rest of the paper clips so that they hang
below the magnet. Examine the effect of layering
different materials between the magnet and the
clips. Organize your data in tables and graphs to
present your conclusions.
3. Research phenomena related to one of the following
topics, and prepare a report or presentation with
pictures and data.
a. How does Earth’s magnetic field vary with lat-
itude, with longitude, with the distance from
Earth, and in time?
b. How do people who rely on compasses account
for these differences in Earth’s magnetic field?
c. What is the Van Allen belt?
d. How do solar flares occur?
e. How do solar flares affect Earth?
4. Obtain old buzzers, bells, telephone receivers, speak-
ers, motors from power or kitchen tools, and so on
to take apart. Identify the mechanical and electro-
magnetic components. Examine their connections.
How do they produce magnetic fields? Work in a
cooperative group to describe and organize your
findings about several devices for a display entitled
“Anatomy of Electromagnetic Devices.”
5. Magnetic force was first described by the ancient
Greeks, who mined a magnetic mineral called mag-
netite. Magnetite was used in early experiments on
magnetic force. Research the historical develop-
ment of the concept of magnetic force. Describe the
work of Peregrinus, William Gilbert, Oersted,
Faraday, and other scientists.
Alternative Assessment
Alternative AssessmentANSWERS
1. Students’ plans should be safeand logical. A compass couldindicate the identity andlocation of the two poles.
2. Students’ plans shouldinclude safe and completeplans for testing the strengthof each magnet based onhow many paper clips themagnet can lift.
3. Earth’s magnetic field is notconstant through time orspace; People who rely oncompasses keep tables ofcorrections to apply, depend-ing on their approximatelocation; The Van Allen beltis a cloud of charged parti-cles around Earth; Solarflares are large outflows ofcharged particles that canaffect Earth’s magnetic field.
4. Students’ answers shouldclearly indicate whichdevices are likely to producea magnetic field (solenoidsand coils). Students shouldindicate how such magneticforces are converted intomechanical motions.
5. Peregrinus is credited withthe first experiments withmagnetism, using a thinpiece of iron to map themagnetic field of magnetite.William Gilbert, Oersted,and Faraday studied bothmagnetism and electricity.
Standardized Test PrepCHAPTER 19
700
ANSWERS
1. C
2. G
3. B
4. J
5. C
6. F
7. A
MULTIPLE CHOICE
1. Which of the following statements best describesthe domains in unmagnetized iron?
A. There are no domains.B. There are domains, but the domains are small-
er than in magnetized iron.C. There are domains, but the domains are ori-
ented randomly.D. There are domains, but the domains are not
magnetized.
2. Which of the following statements is most correct?
F. The north pole of a freely rotating magnetpoints north because the magnetic pole nearthe geographic North Pole is like the northpole of a magnet.
G. The north pole of a freely rotating magnetpoints north because the magnetic pole nearthe geographic North Pole is like the southpole of a magnet.
H. The north pole of a freely rotating magnetpoints south because the magnetic pole nearthe geographic South Pole is like the northpole of a magnet.
J. The north pole of a freely rotating magnetpoints south because the magnetic pole nearthe geographic South Pole is like the southpole of a magnet.
3. If you are standing at Earth’s magnetic north poleand holding a bar magnet that is free to rotate inthree dimensions, which direction will the southpole of the magnet point?
A. straight upB. straight downC. parallel to the ground, toward the northD. parallel to the ground, toward the south
4. How can you increase the strength of a magneticfield inside a solenoid?
F. increase the number of coils per unit lengthG. increase the currentH. place an iron rod inside the solenoidJ. all of the above
Use the diagram below to answer questions 5–6.
5. How will the electron move once it passes into themagnetic field?
A. It will curve to the right and then continuemoving in a straight line to the right.
B. It will curve to the left and then continue mov-ing in a straight line to the left.
C. It will move in a clockwise circle.D. It will move in a counterclockwise circle.
6. What will be the magnitude of the force on theelectron once it passes into the magnetic field?
F. qvBG. −qvB
H. ⎯q
B
v⎯
J. BI l
7. An alpha particle (q = 3.2 × 10−19 C) moves at aspeed of 2.5 × 106 m/s perpendicular to a mag-netic field of strength 2.0 × 10−4 T. What is themagnitude of the magnetic force on the particle?
A. 1.6 × 10−16 N B. −1.6 × 10−16 NC. 4.0 × 10−9 N D. zero
v
Bin
–
Chapter 19700
Standardized Test Prep
701
8. G
9. D
10. J
11. B
12. H
13. Sketches should show a barmagnet with N and S poleslabeled. Field lines should bedirected away from the northend and toward the southend. See diagram in chapterfor an example.
14. Imagine wrapping the fin-gers of your right handaround the wire and point-ing your thumb in the direc-tion of the current. Themagnetic field lines formconcentric circles that arecentered on the wire andcurve in the same directionas your fingers.
15. Diagrams should representthe magnetic field comingout of the page as an evenlyspaced area of dots. The pathof the particle is a clockwisecircle.
16. a. The field is directed out ofthe page. Using the right-hand rule, the thumbpoints in the direction ofthe tangential motion ofthe proton. The force isdirected toward the centerof the circle and comes outof the palm of the hand.For this result to be true,the fingertips must pointupward, indicating thatthe magnetic field pointsup and out of the page.
b. 1.2 × 10−2 m (See theSolutions Manual or One-Stop Planner for a fullsolution.)
Use the passage below to answer questions 8–9.
A wire 25 cm long carries a 12 A current from east towest. Earth’s magnetic field at the wire’s location has amagnitude of 4.8 × 10−5 T and is directed from southto north.
8. What is the magnitude of the magnetic force onthe wire?
F. 2.3 × 10−5 NG. 1.4 × 10−4 NH. 2.3 × 10−3 NJ. 1.4 × 10−2 N
9. What is the direction of the magnetic force on the wire?
A. northB. southC. up, away from EarthD. down, toward Earth
Use the diagram below to answer questions 10–12.
Wire 1 carries current I1 and creates magnetic field B1.Wire 2 carries current I2 and creates magnetic field B2.
10. What is the direction of the magnetic field B1 atthe location of wire 2?
F. to the leftG. to the rightH. into the pageJ. out of the page
I1
I2
11. What is the direction of the force on wire 2 as aresult of B1?
A. to the leftB. to the rightC. into the pageD. out of the page
12. What is the magnitude of the magnetic force onwire 2?
F. B1I1l1G. B1I1l2H. B1I2l2J. B2I2l2
SHORT RESPONSE
13. Sketch the magnetic field lines around a bar magnet.
14. Describe how to use the right-hand rule to deter-mine the direction of a magnetic field around acurrent-carrying wire.
15. Draw a diagram showing the path of a positivelycharged particle moving in the plane of a piece ofpaper if a uniform magnetic field is coming out ofthe page.
EXTENDED RESPONSE
16. A proton (q = 1.6 × 10−19 C; m = 1.7 × 10−27 kg) isin a uniform 0.25 T magnetic field. The protonmoves in a clockwise circle with a tangential speedof 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.
701Magnetism
If you are asked to write out ananswer, to show your calculations, or to draw a dia-gram, be sure to write clearly, to show all steps of your work, and to add clear labels to your diagrams.You may receive some credit for using the rightapproach to a problem, even if you do not arrive at the correct final answer.
Chapter 19702
PROCEDURE
Preparation
1. Read the entire lab procedure, and plan the steps you will take.
2. If you are not using a datasheet provided by your teacher, prepare a data
table in your lab notebook with four columns and nine rows. In the first
row, label the columns Turns, Current (A), Current Direction, and
Compass Reading. In the first column, label the second through ninth
rows One, One, Two, Two, Three, Three, Four, and Four.
Magnetic Field of a Current-Carrying Wire
3. Wrap the wire once around the galvanometer. Place the large compass on
the stand of the galvanometer so that the compass needle is parallel to and
directly below the wire, as shown in Figure 1. (Figure 1 shows multiple
wire windings, not only one.) Turn the galvanometer until the turn of
wire is in the north-to-south plane, as indicated by the compass needle.
In this lab, you will study the magnetic field that occurs around a current-
carrying wire. You will construct a circuit with a current-carrying wire and use
a magnetic compass needle to investigate the relationship between the magnet-
ic field and the current in the wire. You will be able to determine the magnitude
and direction of the magnetic field surrounding the wire.
OBJECTIVES
•Use a compass toexplore the direction ofthe magnetic field of acurrent-carrying wire.
•Analyze the relationshipbetween the direction ofthe magnetic field of aconducting wire and thedirection of the current inthe wire.
MATERIALS LIST• 1 Ω resistor • compass• galvanometer• insulated connecting wires
and bare copper wire• multimeter or dc ammeter• power supply• switch
702
Lab PlanningBeginning on page T34 arepreparation notes and teachingtips to assist you in planning.
Blank data tables (as well as some sample data) appear on the One-Stop Planner.
No Books in the Lab?See the Datasheets for In-Text Labs workbook for areproducible master copy ofthis experiment.
CBL™ OptionA CBL™ version of this labappears in Appendix K andin the CBL™ Experimentsworkbook.
Safety CautionEmphasize the dangers of work-ing with electricity. Remind stu-dents to have you check theircircuits before turning on thepower supply or closing theswitch.
Magnetic Field of aConducting Wire
Skills Practice LabCHAPTER 19Skills Practice Lab
CHAPTER 19
• Never close a circuit until it has been approved by your teacher. Neverrewire or adjust any element of a closed circuit. Never work with elec-tricity near water; be sure the floor and all work surfaces are dry.
• If the pointer on any kind of meter moves off scale, open the circuitimmediately by opening the switch.
• Do not attempt this exercise with any batteries, electrical devices, ormagnets other than those provided by your teacher for this purpose.
• Wire coils may heat up rapidly during this experiment. If heatingoccurs, open the switch immediately and handle the equipment with ahot mitt. Allow all equipment to cool before storing it.
SAFETY
703
CHAPTER 19 LAB
703Magnetism
4. Construct a circuit that contains the power supply, a current
meter, a 1 � resistor, and a switch, all wired in series with the gal-
vanometer. Connect the galvanometer so that the direction of the
current will be from south to north through the segment of the
loop above the compass needle. Do not close the switch untilyour teacher has approved your circuit.
5. Set the power supply to its lowest output. When your teacher has
approved your circuit, close the switch briefly. Using the poten-
tiometer on the power supply, adjust the current in the circuit to
1.5 A. Use the potentiometer to maintain a current of 1.5 A
throughout the lab. Record the current, the current direction, and
the compass reading in your data table. Open the switch as soon as
you have made your measurements so that the power supply and
wires don’t overheat.
6. Reverse the direction of the current in the segment of the loop above the
needle by reversing the wires connecting to the power supply.
7. Close the switch. Adjust the power supply to 1.5 A. Record your observa-
tions in your data table, and then immediately open the switch.
8. Remove the galvanometer from the circuit. Add a second turn of wire,
and reconnect the galvanometer to the circuit so that the current direc-
tion will be south to north.
9. Close the switch. Adjust the power supply to 1.5 A. Record your observa-
tions in your data table. Open the switch immediately.
10. Repeat Steps 6 and 7 for two turns of wire.
11. Repeat the experiment for three turns and then four turns of wire. For
each, connect the circuit so that the direction of the current is from south
to north and then north to south. Record all information.
12. Clean up your work area. Put equipment away safely.
ANALYSIS
1. Organizing Data For each trial, find the tangent of the angle of the
compass needle’s deflection.
2. Constructing Graphs Use a computer, graphing calculator, or graph
paper to plot the tangents (item 1) against the number of turns in the wire.
CONCLUSIONS
3. Drawing Conclusions What is the relationship between the tangent of
the angle and the number of turns? Explain.
4. Drawing Conclusions What is the relationship between the direction
of current in the wire and the direction of the magnetic field? Explain.
Tips and Tricks• Make sure students know how
to read a compass and recordthe readings.
• See the teaching tips forinstructions on setting up mul-timeters to measure current.
• Make sure students under-stand how to wire currentmeters (in series) in a circuit.
• Show students how to set upthe wire coil on the gal-vanometer apparatus and howto determine the direction ofthe current.
CheckpointsStep 4: Make sure the powersupply, resistor, current meter, andswitch are connected correctly andare at the proper settings.
Step 6: Make sure studentsreconnect the wires properly toreverse the current.
Step 8: Make sure students havetwo loops of wire and that allconnections are correct.
ANSWERSAnalysis1. Student answers will vary. Forsample data, values for tanqrange from 0.577 to 2.747.
2. Student graphs should showthat tanq increases as the num-ber of turns increases.
Conclusions3. Because tanq increases as thenumber of turns increases, stu-dents should realize that tanq isproportional to the magneticfield strength.
4. When the current directionchanges, the direction of themagnetic field also changes.
Figure 1Step 3: Use the support pins onthe galvanometer to wrap the wireinto a loop. Adjust the apparatus sothat the needle and wire are in thenorth-to-south plane.
704 704
In 2005, lawsuits were filed against cell phone
manufacturers in Georgia, Louisiana, Maryland, New
York, and Pennsylvania. These lawsuits alleged that
there may be a link between cell phone use and brain
cancer and accused the manufacturers of failing to
adequately protect users from radiation. Is there any
truth to this claim?
Nonionizing RadiationCell phones transfer messages by sending and receiving
electromagnetic waves. The electromagnetic spectrum
includes low-energy waves, such as radio waves, and
high-energy waves, such as X rays and gamma rays.
High-energy electromagnetic waves are ionizing, which
means they have enough energy to remove an electron
from its orbit. Ionizing electromagnetic radiation can
damage living tissue and cause DNA mutations, which
is why exposure to X rays should be limited.
Cell phones use radio frequencies (RFs) ranging
from about 1800 to 2200 MHz. These nonionizing
waves do not alter the molecular structure of living
tissue. They can cause the atoms in a molecule to
vibrate but do not have enough energy to remove
electrons from their orbits. At high enough levels,
however, nonionizing radiation can cause biological
damage by heating living tissue. But the amount of heat
that a cell phone’s radiation generates is very small,
much smaller than the energy generated in a microwave
oven.
What Do the Studies Say?The effects of nonionizing radiation on the human
body are not fully known. Several studies have been
conducted to determine whether there is any possible
link between cell phone use and brain cancer. Scientists
conducting these studies have attempted to determine
whether the risk of brain cancer is greater for cell phone
users than for nonusers. Even if a link is found, it is not
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 not necessarily the cause.
Further, several issues complicate the research. In the
past, scientists had to estimate RF exposure based on
interviews with patients. (Scientists are now using RF
meters to measure the amount of exposure, so newer
studies will be more accurate in this regard.) Also, cell
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phones were not widely available until the 1990s, and
brain tumors develop over many years. Hence, the early
studies did not cover long-term cell phone use.
A study funded by the National Cancer Institute and
published in 2001 focused on 782 patients who had
brain cancer and 799 patients who did not have brain
tumors. This study did not find any increased risk of
brain cancer for the patients who had used cell phones.
Many other studies have found similar results.
However, a few studies have found a possible link,
including one Swedish study that
found an increased risk of
acoustic neuroma (a benign
tumor) in long-term cell phone
users. In 2006, the FDA
announced that it would revisit
the issue. The FDA stated that the
findings of two Swedish studies
are inconsistent with earlier
studies and acknowledged that
these studies are difficult to
interpret.
Reducing RF ExposureAlthough they have not demonstrated a link between
cell phone use and brain cancer, scientists have not
concluded that there is no risk. More research is
needed, especially on the long-term effects of RF
exposure. In the meantime, concerned cell phone users
can take measures to limit their exposure to RF.
Exposure depends on a number of factors, including
the amount of time spent using the phone, the amount
of cell phone traffic in the area, and the distance
between the antenna and the
user’s head. One way to reduce
exposure is to minimize the time
spent on cellular calls. Another
option is to use a hands-free
device that puts the antenna
farther from the head.
Researching the Issue
1. Cell phone makers are now required to report
the specific absorption rate (SAR), the amount of RF
energy absorbed by the user. The maximum allowed
SAR is 1.6 watts per kilogram. Conduct research to
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.
2. Research the effects of ionizing radiation on the
human body. What are some sources of ionizing
radiation? How does ionizing radiation affect living
tissue?
3. Use the Internet to research one of the recent
epidemiological 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.
4. As cell phones have grown in popularity,
concerns have arisen about the safety of driving
while using a cell phone. Several countries have
banned the use of cell phones while driving.
Conduct research to find out about studies
conducted on this issue. Is it hazardous? Should we
pass laws to prevent it? Choose a position on the
issue, and write a paper defending your position.