Knight/Jones/Field Instructor Guide
24
Chapter 24
Magnetic Fields and Forces
Recommended class days: 3 minimum
Background Information
Research has found that more than 50% of a typical class of students begins their study
believing that
• A positively charged rod held near the center of a pivoted bar magnet causes the magnet to
rotate, with the positive charge repelling the north pole and attracting the south pole.
• If one end of a bar magnet attracts a paper clip, the opposite end will repel the paper clip.
In addition to thinking that electric charges and magnet poles are more or less equivalent,
students tend to use electric and magnetic fields interchangeably. These beliefs are little changed
by conventional instruction.
For most students, their experience of magnetism extends little beyond the use of refrigerator
magnets. Virtually all school children have used a magnet to pick up small steel objects, but the
high percentage that expect one end of a magnet to repel the object suggests that these
experiences have been infrequent. Informal surveys find that many students have never seen or
experienced the repulsive force between two magnets. And, not surprisingly, few students are
familiar with electromagnets.
24-1
Knight/Jones/Field Instructor Guide
Chapter 24
The presentation of magnetism usually begins by reminding students that they are familiar
with refrigerator magnets and perhaps other permanent magnets, then switches immediately to
the development of a theory of electromagnetism. This is a classic case of bait-and-switch, with
few texts ever making any connection between electromagnetism and permanent magnets. Few,
if any, conventional textbooks ever answer the most obvious question that a student might have,
namely, “How does the magnet stick to the refrigerator?” This is the magnetic equivalent of
“How does a charged comb pick up pieces of paper?”
Student Learning Objectives
In covering the material of this chapter, students will learn to
• Acquire familiarity with basic magnetic phenomena.
• Develop a dipole model of magnetism, analogous to the charge model of electricity, that
allows students to understand and reason about basic magnetic phenomena.
• Understand the magnetic fields due to currents in wires, loops, and solenoids.
• Understand the magnetic forces and torques on moving charges, wires, and current loops.
• Study the motion of charged particles in magnetic fields.
• Present a simple atomic-level model of ferromagnetism.
Pedagogical Approach
Many students are unfamiliar with the most basic of magnetic phenomena. Without such
knowledge and awareness, the theory that is to be developed is not grounded in physical reality.
Consequently, this chapter emphasizes:
• The phenomena of magnetism. Although many basic characteristics are described in the
textbook, this cannot substitute for demonstrations and hands-on experience.
• The idea that both magnets and currents can create magnetic fields. In particular, we
emphasize the striking similarities between the field due to a magnet and that due to a current
loop or solenoid. This is our first hint that both phenomena may have a common origin.
• That magnetic forces and torques acting on current loops are similar to those observed acting
on magnets. This again points to a connection between the electromagnetism of currents and
permanent magnetism.
24-2
Knight/Jones/Field Instructor Guide
Chapter 24
There is a high density of information in this chapter, and essentially all of it is new to
students. This chapter can be covered in three days if more than usual reliance is placed on
student reading. If possible, four days would be better to allow adequate time for demonstrations
and for exercises about the right-hand rule, forces, torques, and so on.
A troublesome issue is how to introduce and define the magnetic field. The electric field was
introduced by starting with the electric force between two charges, and then using the electric
force to define the field. If only there were magnetic monopoles, we could follow an analogous
procedure to define B . Alas, we have to find an alternative. Unfortunately, the magnetic force
on a moving charge does not uniquely define the magnetic field.
Most textbooks start with the magnetic force on a charged particle. This is unsatisfying and
unilluminating to students because it assumes the existence of a new field about which they
know nothing in order to define a force law that, to them, makes little sense. From a pedagogical
perspective, it’s preferable to begin with the analog of a test charge—namely, a “test dipole” in
the form of a compass needle. Students generally know, and it is easily demonstrated, that a
compass needle responds to a magnet. They readily accept that the needle orientation defines the
magnetic field direction. Furthermore, students’ experience with electric dipoles allows them to
recognize that the magnetic field is exerting equal but opposite forces on the two inseparable
poles of the dipole, causing a torque until the dipole aligns with the field. Although the test
dipole gives only the shape of the field, not the strength, that is still a big step forward toward
understanding magnetism.
Oersted’s discovery that a current deflects a compass needle implies that a current is another
way to make a magnetic field. For students at this level, it’s best to take the circular magnetic
field produced by a wire as the basic element of a current-generated field. This can easily be
demonstrated with a long wire and a compass or set of compasses. Then the field due to a current
loop can be understood in terms of a wire bent into a circle, and a solenoid as a number of
current loops placed together.
The force exerted on a current-carrying wire in a magnetic field is the starting point toward
the link between electromagnets and permanent magnets. It is easily demonstrated that:
• A current loop orients in a magnetic field.
• One side of a current loop attracts the north pole of a bar magnet and the other side of the
loop repels the north pole.
24-3
Knight/Jones/Field Instructor Guide
Chapter 24
• Two facing current loops either repel or attract each other.
These observations can be understood by attributing north and south magnetic poles to the two
faces of the current loop. Thus current loops suggest a mechanism for macroscopic magnetic
forces in terms of the interactions between moving charged particles.
Much of this presentation is rather qualitative. It is the reasoning about force and torques,
and their relationship to charged particles, that helps students to develop an understanding of
what magnetism is all about.
The motion of charged particles in magnetic fields is difficult for two reasons: the need to
visualize the situation in three dimensions and the use of the right-hand rule for the force on a
moving charged particle. Students should be led to visualize the plane containing the vectors v
and B. The force vector is then perpendicular to that plane. The right-hand rule then need only
distinguish between two completely opposite directions.
Students need at least an introduction to ferromagnetism in order to make the connection
between electromagnets and permanent magnets. A simple model of ferromagnetism is
sufficient. If you point out that electrons have an inherent electric property—namely, their
charge—students then find it believable that electrons also have an inherent magnetic property
and act—for this presentation—like tiny bar magnets. Magnetic domains provide a qualitative
explanation of both permanent magnets and of induced magnetic moments in nonmagnetized
iron. Thus we close the loop between electromagnetism and permanent magnets, arriving at the
answer to “How does the magnet stick to the refrigerator?”
Suggested Lecture Outlines
A three-day presentation is outlined here. Four days may be needed if you provide a full array of
demonstrations. One laboratory period devoted to hands-on experience with basic magnetic
phenomena is highly recommended. The exercises in the Student Workbook are especially
important to develop student reasoning about magnetism.
DAY 1: Magnetism demonstrations are both entertaining and instructive, and the main ideas of
this chapter are best illustrated with demonstrations. The chapter can be motivated with a variety
of basic demonstrations, including:
• Attractive and repulsive forces between magnets.
24-4
Knight/Jones/Field Instructor Guide
Chapter 24
• The response of demonstration-size compasses to various magnets.
• Moving both a charged rod and a magnet toward the center of a compass to see if the
compass pivots.
• Holding a magnet near a neutral pith ball. If the ball is then charged, it will be attracted to
both ends of the magnet by the now-familiar polarization force.
• Showing that both ends of a magnet attract steel objects.
• Cutting a magnet in half (if you have a cheap one to spare).
You want students to recognize from the beginning that:
• Magnetic poles are not the same as electric charges, and magnetic forces are distinct from
electric forces.
• A compass needle is itself a small bar magnet.
• A compass’s orientation can be used to define the idea of a magnetic field. The field is
defined to point in the direction of the compass needle’s north pole.
• Using a compass as a probe reveals that a magnetic field comes out of the north pole of a bar
magnet and goes in to the south pole. For a horseshoe magnet, this creates a magnetic field
from north to south between the pole tips.
Clicker Question:
Students should get some experience drawing the magnetic field due to magnets. It’s best to
start by drawing magnetic field vectors. You can ask for the field vectors at various points near a
single bar magnet and near two magnets with opposite and like poles facing each other. Now you
can show how to draw field lines, a more abstract representation that students often find difficult.
The relationship between field lines and vectors is of course the same for magnetic fields as it
was for electric fields, and so these exercises cycle back to what they’ve already studied.
24-5
Knight/Jones/Field Instructor Guide
Chapter 24
To establish the big picture, let students know that the goal of this chapter is to understand
how and why the various magnetic phenomena you’ve just demonstrated occur. However, the
starting point will seem to have little to do with magnets. They will need to be especially
attentive to the logic that leads from currents in wires to permanent magnets.
Demonstration: The primary demonstration that begins the development of electromagnetism
is, of course, Oersted’s discovery that a current deflects a compass needle.
Although this can be demonstrated with a horizontal wire on the lecture bench, a more
convincing demonstration can be done with a copper rod cemented into a clear plastic plate.
With legs or spacers to hold it up, you can place this on the overhead projector and set a
transparent compass at different points around the wire. (You’ll need a power supply that can
deliver about 10 A.) You can also sprinkle iron filings on the plastic and project the circular field
patterns onto the viewing screen.
For many students, this is their first experience with the right-hand rule and with the  and
notation for vectors and currents perpendicular to the page. Students will need many
opportunities to practice before they are comfortable with these ideas. A good starting example is
simply to draw a wire with a current and ask students to draw the magnetic field, as deduced
from the right hand rule, both in the plane of the wire and as seen with the current coming toward
them. It’s best in these initial exercises to use field vectors, not field lines.
Clicker question: Point P is 5 cm above the wire as you look straight down at it. In which
direction is the magnetic field at P?
You’ll also need to go over the quantitative result for the magnitude of the field due to a long
wire. The following can be used as either a class exercise or as a clicker question.
Clicker Question: The magnetic field at point P is zero. What is the magnitude and direction
of the current in the lower wire?
A. 10 A to the right
24-6
Knight/Jones/Field Instructor Guide
Chapter 24
B. 5 A to the right
C. 2.5 A to the right
D. 10 A to the left
E. 5 A to the left
F. 2.5 A to the left
DAY 2: The magnetic field of a current loop is an important result. The magnetic field of a
current loop has north and south poles, unlike the field of a straight wire, and thus it is a first link
between electromagnetism and permanent magnets. The most important idea to get across at this
point is the shape of the current loop’s field.
You can make the field shape plausible by starting with the field of a straight, currentcarrying wire and asking students to imagine what superposition will do to the field if they bend
a segment of that wire into a circle. A nice demonstration is to have a heavy current loop
cemented into plastic, like the straight rod shown earlier, so that it can be projected onto the
screen as an edge view. Iron filings can then be used to illustrate the field pattern and to confirm
the superposition reasoning.
Draw loops seen both face on and edge on, with current in different directions, and ask
students to use the right-hand rule (Tactics Box 24.1) to deduce which side of the loop has the
field entering and which has the field leaving. Then demonstrate the interaction between a
current loop and a compass needle, and the attractive/repulsive forces between two current loops,
to show that the current loop has north and south poles.
You want students to leave this exercise with a good sense that:
• The field of a current loop converges into one side of the loop and diverges from the other.
This field is the superposition of the fields of individual moving charges.
• The field passes through the loop in a direction given by the right-hand rule.
• A current loop has north and south magnetic poles that act just like the poles of a permanent
magnet.
24-7
Knight/Jones/Field Instructor Guide
Chapter 24
In other words, the current loop is a magnet, and the face from which the magnet field emerges is the
north pole. These are new ideas to nearly all students, so the demonstrations are especially important.
The ability to quickly assess the field of a current loop will be important for using Faraday’s law in
the next chapter, so a little extra attention spent on the topic now will pay off in a few days.
The solenoid is important because it can be used to create a uniform field. Thus it is the
magnetic analog of the parallel-plate capacitor, which is used to create a uniform electric field.
To make the uniform field of a solenoid more plausible, start by drawing two facing current
loops. Then ask students to use superposition and their knowledge of the shape of a current loop
field to predict the field at three points in the mid plane. If you have two large current loops, such
as a Helmholtz coil, you can use a compass to verify that the field vectors in the mid plane are all
parallel. Once students understand the idea for two coils, they’ll readily believe that a stack of
closely-spaced coils produces a uniform field in the interior. Thus you can introduce the solenoid
as a practical way to generate a uniform magnetic field.
Students need several opportunities to practice using the right-hand rule to associate the
current direction around a solenoid with the field direction.
Good exercises are to draw solenoids in random orientations. Either show the current and ask for
the field direction, or show the field and ask for the current direction. This reasoning will be
important in the next chapter on Faraday’s law.
Students will also need some practice in finding the magnitude of magnetic field due to
wires, loops, and solenoids. Many problems of this kind involve superposition of fields,
requiring careful attention to the directions of the fields.
Example: What is the direction and magnitude of the magnetic field at point P, at the center of
the loop?
24-8
Knight/Jones/Field Instructor Guide
Chapter 24
DAY 3: At this point, students have seen how to establish a magnetic field by currents flowing
in several simple shapes of wires. Now it’s time to switch over to the effects of magnetic fields.
Because a current exerts forces (a torque) on a compass (a magnet), does a magnet exert forces
on a current? An impressive demonstration is to run a wire through the pole tips of a strong
magnet. Closing a switch to send a few amps of current through the wire causes it to jump
completely out of the magnet!
With this as a motivation, you can then introduce the magnetic force on a moving charged
particle. The idea of a force perpendicular to the motion (and to the field) is very hard for most
students to grasp. A Crookes tube or CRT in which the electron beam can be deflected with a
magnet is an important demonstration.
To make effective use of such demonstrations, you want students to predict how the electron
beam will behave if you bring a specified end of a bar magnet in from a specified direction—for
example, if you bring the south pole in from the bottom of the tube. Directional exercises such as
those shown in the figure are also important. Students find these fairly hard to do at first and
need quite a bit of practice with the cross product and the right-hand rule.
Magnetic forces on current-carrying wires and torques on current loops are much more
important applications for most of our students than the motion of charged particles. Most
departments have many good demos of these effects, but it’s important to take your time with
each. Explain what the set-up is and where the currents are (students have not seen apparatus like
this, and without an explanation they won’t have any idea what they’re looking at), give students
24-9
Knight/Jones/Field Instructor Guide
Chapter 24
an opportunity to make predictions, and then carefully explain the outcome that is observed.
There’s no pedagogical value in racing through many demonstrations simply because they’re
“neat” or have unexpected outcomes.
The torque on a current loop in a magnetic field is a particularly important idea for
understanding compass needles. First ask students to explain the torque in terms of forces
on the currents. Then ask them to identify the north and south poles of the current loop. You
want them to realize that the rotation of the current loop can be understood in terms of the
attraction/repulsion of opposite/like poles, but that this is just a shorthand way of characterizing
the interactions of currents and fields.
Torque on a current loop leads naturally to the demonstration and discussion of a DC motor.
A motor with permanent field magnets rather than electromagnets is best. This allows you to
focus on the torque on the armature and on the split-ring commutator. Then, if you wish, you can
switch to a motor that uses solenoids to generate the magnetic field. Now you have a nice
example of using a current both to create the field and to experience a torque in the field. Only a
tiny fraction of students have any idea how a motor operates, so this is a demonstration and
explanation that most find to be especially interesting.
An especially important exercise is to have students consider two facing current loops.
The figure shows antiparallel currents. Have students identify first the field direction at the
top/bottom of each loop due to the other loop, and then the forces. They can find for themselves
that two loops with antiparallel currents repel each other, a result that agrees with the repulsive
force between antiparallel currents in straight wires. Then have them identify the north and south
poles of the loops (few will think to do this on their own). Now they see two north poles
24-10
Knight/Jones/Field Instructor Guide
Chapter 24
repelling each other. The importance of this exercise lies in discovering a mechanism—in terms
of interacting charged particles—for why like poles repel.
Finally, to close the loop and return to permanent magnetism, you want to end with a
qualitative discussion of ferromagnetism. In this case, it’s worthwhile to summarize the main
ideas in a short mini-lecture. The main points are:
• Electrons are inherent magnets, with a north and south pole.
• In some metals, the atomic-level magnets throughout a small piece of the material all align
to create a macroscopic magnetic moment. The reasons why are quantum mechanical.
We’ll just accept it as an empirical finding. These small regions are magnetic domains,
and the metals in which this occurs are called ferromagnetic. Iron is the most important
example.
• A chunk of material in which most domains are oriented in the same direction is a permanent
magnet. Thus permanent magnets trace their magnetism back to the electrons.
• An external magnetic field exerts torques on the moments of the magnetic domains (and
moves domain boundaries), thus creating an induced magnetic moment. This is analogous to
polarization in electricity. The orientation of the induced magnetic moment is such that the
piece of metal is attracted to the magnet. Thus we’ve finally answered the question of how
the magnet sticks to the refrigerator.
Other Resources
In addition to the specific suggestions made above in the daily lecture outlines, here are some
other suggestions for questions that you could weave into your class time.
Sample Reading Quiz Questions
1. What is the SI unit for the strength of the magnetic field?
2. What is the shape of the trajectory that a charged particle follows when it moves
perpendicular to a uniform magnetic field?
3. The magnetic field of a straight, current-carrying wire is
a. parallel to the wire.
b. perpendicular to the wire.
24-11
Knight/Jones/Field Instructor Guide
Chapter 24
c. around the wire.
d. inside the wire.
e. zero.
24-12