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


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


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

I

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.


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


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?


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.


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

Science • Technology • SocietyScience • Technology • SocietyScience•Technology•Society

Science•Technology•Society

C A NC E L L P H O N E SC A U S E C A N C E R ?

Science • Technology • Society 705 705

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.

magnetism

Documents

Transcript of magnetism