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Knight/Jones/Field Instructor Guide
25
Chapter 25
Electromagnetic Induction and
Electromagnetic Waves
Recommended class days: 3
Background Information
Our study of electromagnetic induction and electromagnetic waves completes the basic development
of electricity and magnetism. This chapter is also a culmination of the development of the field
model. The electric field, in particular, was introduced in a rather ad hoc fashion. Students were
simply told that they would see experimental evidence that fields are real at a later time.
That time is here. The final proof of the reality of electric magnetic fields is the existence of
electromagnetic waves, self-sustaining oscillations of the electric and magnetic field that can carry
energy. All students in high school are taught the basics of the electromagnetic spectrum; they know
that it spans a range of phenomena from radio waves to gamma rays. But after a full development of
their understanding of fields and their interactions with matter, students are poised to understand the
similarities and differences between the different classes of waves, to settle questions they may have
long wondered about. Is radiation from a microwave different from the radiation one gets in an x
ray? Many students aren’t sure.
Electromagnetic waves are something students have heard of, but the same cannot be said of
electromagnetic induction. Induction can seem fairly magical, and the mathematical description
involves aspects that we already know cause students great difficulty. Students have trouble
distinguishing between the velocity and the change in velocity. Similarly, as most instructors are
aware, many students think that the induced field opposes the applied field itself rather than
opposing the change in the applied field. We know that students have difficulty with vectors, and
the fully three-dimensional reasoning required for solving some of the problems in the chapter will
stretch even the most capable students in your class. The good news is that these student difficulties
arise from lack of sufficient opportunities for qualitative reasoning, with appropriate feedback,
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rather than from any fundamental misconceptions about the nature of electromagnetic induction—
they simply don’t know enough to have misconceptions.
In this book we are moving gently toward an early introduction of modern physics. We suggest
teaching relativity earlier in the course than it appears in the book. There are frequent references to
modern physics topics throughout each chapter. The “One Step Beyond” sections in the part
summaries go into some depth on some more modern topics; we hope these will be read and used by
the students. Without such efforts, we are in danger, in the introductory course, of teaching a subject
that seems to have discovered nothing new in the last 200 years. It is important to convey to students
at least some of the exciting ideas of twentieth-century physics. There is a natural way to do this in
this chapter—by introducing the idea of a photon. Students will have heard the word, and most will
have had a chance to use the concept to explain atomic spectra in a chemistry class. The photon
picture is required for a full understanding of the electromagnetic spectrum, but, more importantly,
its introduction is a taste of the modern physics topics that lie just ahead.
Student Learning Objectives
In covering the material of this chapter, students will learn to
• Understand the circumstances under which changing magnetic fields lead to induced currents.
• Understand how the movement of a conductor through a magnetic field leads to a motional emf.
• Use Lenz’s law and Faraday’s law to determine the direction and size of induced currents.
• Understand how induced electric and magnetic fields lead to electromagnetic waves.
• Apply wave and photon models to the electromagnetic spectrum.
• Understand the properties of different types of electromagnetic waves.
Pedagogical Approach
The chapter forms a continuous whole, but there is a change in focus as it shifts from induction to
electromagnetic waves. The chapter moves from the topic that, arguably, causes students the most
difficulty of any topic commonly taught in the college physics course, to one for which students
already have a broad understanding. Rather than rush the first part of the chapter, it is important for
instructors to take the time for students to develop a solid conceptual understanding. It is important
to give students many chances to reason about flux, flux change, and induced emfs and currents.
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Without such a conceptual background, your students will certainly be able to solve quantitative
problems, but they will be doing plug-and-chug in its purest form, with no idea what the equations
or numbers actually represent. In the daily outlines presented below, we stress the concepts and
phenomena; most of the questions require students to reason, not to calculate. This conceptual
grounding is very important.
If you rely on graduate students to teach your lab and recitation sections, you might want to give
them a refresher on these concepts as well. At Colorado State University, we have found that our
graduate students often harbor certain misconceptions that they pass on to undergraduate students.
We do a laboratory exercise on determining the direction of an AM radio station from the
orientation of a loop antenna; if we don’t properly prepare the laboratory instructors, it is common
for them to explain that the loop needs to “point at” the antenna, so that the electromagnetic waves
can “go through” the loop—making no reference to the magnetic field or flux change.
The chapter begins, as many of the chapters in Part VI do, with a careful summary of the
experimental evidence for the phenomena. You should probably begin your series of lectures in this
fashion, presenting demonstrations that show what induction is, and how it comes about. Students
don’t know what induction is, so it’s important to give them a sense for the physical phenomena
before developing the theory. The text then begins the development of the theory of induction with a
study of motional emf, a direct and obvious extension of Chapter 24. You may be tempted to
downplay this piece, but it is important for student understanding; it’s the one piece that they will
certainly be able to get their minds around.
This textbook introduces Lenz’s law before Faraday’s law, opposite the traditional approach of
treating Lenz’s law as an adjunct to Faraday’s law. In fact, Lenz discovered his “law” for finding the
direction of an induced current before Faraday and others determined the quantitative relationship
that we today call Faraday’s law. Starting with Lenz’s law has the pedagogical advantage of getting
students to reason about induced currents before having to worry about a numerical value of
induced emf. After all, most of the demonstrations of induction are concerned only with the
direction of the induced current. An early statement of Lenz’s law also allows Faraday’s law to be
stated without the troublesome minus sign.
Many of the applications of magnetic induction, such as eddy currents or demonstrations that
shoot aluminum rings into the air, are consequences of magnetic forces on induced currents. These
applications can be understood easily in terms of attractive/repulsive forces between
parallel/antiparallel currents or between opposite/like magnetic poles. This reasoning is illustrated
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in the section on eddy currents, and it should be used as needed to explain demonstrations that you
do in class.
The final aspect of induction in Chapter 25 is the development of a model of electromagnetic
waves. As noted above, your students will certainly have some familiarity with the electromagnetic
spectrum. For example, the Colorado K–12 content standards for science require that, for all
students who graduate from high school, “What they know and are able to do includes describing
electromagnetic radiation produced by the Sun and other stars (for example, X-ray, ultraviolet,
visible light, infrared, radio.)”
Students who have had advanced science courses will have learned a good deal more than this.
But it’s not surprising that the knowledge that students possess is entirely descriptive. A typical
student will know that radio waves, light, and x rays are in some sense “the same,” and they will be
able to describe how the effects of these waves differ. But they don’t really know what electric and
magnetic fields are, and they don’t understand that the differences between the waves are due to
different wavelengths and photon energies. Conventional textbooks are often of little help. A
standard approach is to give a graph of the spectrum and then to simply describe the different waves.
Such a descriptive treatment really doesn’t build on the notions of electric and magnetic fields just
introduced, and doesn’t really advance student understanding.
We give a much more detailed introduction to electromagnetic waves. We introduce the idea of a
photon—a concept the students will have heard of—which also gives us a chance to introduce a modern
physics topic a bit earlier than usual, a plus. With the concept of a photon in hand, students can
understand the nature of the different parts of the electromagnetic spectrum in terms of photon energies
and wavelengths. With this background students are well poised to understand the interaction of these
waves with matter, to finally understand why properly shielded microwave ovens aren’t dangerous but
x rays can be. The final section of the chapter deals with just these distinctions, the difference in
behavior of electromagnetic waves that span such a wide range of photon energies and wavelengths.
Suggested Lecture Outlines
A careful treatment of this chapter will require every minute of three days of class. It might be
tempting to skimp on some of the conceptual development, but this is where students most need
help. And it might be tempting to skip the introduction of the concept of the photon—arguing it will
be seen in Chapter 28—but without this concept a full development of the ideas of the
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electromagnetic spectrum will be impossible. If you need to find some efficiencies in your coverage,
we suggest going easy on some of the more complicated Faraday’s law problems that often pop up
in this course. These are more interesting to physicists than to the students in the class. Much more
interesting and much more useful are the basic concepts of induction and a solid understanding of
the electromagnetic spectrum. Whatever students go on to do for a career, it is certain that they will
encounter the principles of electromagnetic radiation. But it is quite possible that they will never see
a Faraday’s law problem ever again.
DAY 1: Induction. The chapter begins with a description of a series of experiments that
demonstrate the basic principles of electromagnetic induction. It is worthwhile to perform such a
series of demonstrations in class, because students are totally unfamiliar with the ideas of induction.
Demonstration: Principles of induction. Use a large demonstration galvanometer connected
to a coil of wire to illustrate how a current may be induced by:
• moving a magnet into or out of the coil.
• moving a magnet near the coil.
• turning on (or turning off) the current in a nearby coil of wire.
• flipping the coil in the field of the earth.
Some of these demonstrations are a bit tricky to get right. You will need to be certain that the meter
is far enough from a moving magnet that there is no interference; students will be quick to note that
the meter is being affected by the magnet, and will doubt the results of your demonstrations. In this
sequence of demonstrations, the key points to illustrate are:
• The meter deflects only when something is changing. Holding a magnet inside a coil
does nothing.
• Reversing the motion reverses the meter deflection.
• Pushing a north pole into a coil has the opposite effect of pushing a south pole into the
same coil. The situation is more complicated than simply “push a magnet in” or “pull a
magnet out.”
• The effect occurs both for moving the coil toward the magnet and for moving the magnet
toward the coil. This last piece is tricky to demonstrate, but it’s an important idea.
After illustrating the concept of induction, you can explain the one case where an induced emf is a
straightforward extension of concepts already taught: motional emf. You should probably review what
is meant by “emf.” Comment that a battery is a chemical emf because it separates charge via chemical
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reactions, thus causing a potential difference. The new effect is a motional emf because charge
separation, and thus a potential difference, occurs via motion of the charge carriers in a magnetic field.
The development of this topic in the chapter shows the origin of the emf, the existence of a force that
opposes the motion, and shows that there is energy required to effect a separation of charge that leads
to a current. This energy connection is vital; it is not at all uncommon for students to think that there is
no energy cost for the induced currents because there is no “physical” connection. There is—it’s the
magnetic field—and this is a key point to make, early and often.
It’s hard to do a classroom demonstration of motional emf, though there are some good
examples you can cite, such as the magnetic navigation abilities of sharks, which are likely due to
their keen electric sense detecting a motional emf, or the use of the motional emf as a power source
for satellites. (You can note, though, that this requires an energy input. Ask the students to speculate
on the source.) But you can do a demonstration that makes some key points about energy and
induced currents as described below. If you don’t have such an apparatus, it’s a worthwhile
investment to build one.
Demonstration: Induction pendulum. A coil of wire on the end of a pendulum swings back
and forth between the poles of a magnet. A lightbulb is connected to the coil of wire; a switch
allows the circuit with the bulb and coil to be open or closed.

When the circuit is open, the coil swings freely, for a long time. The lightbulb does not light.

When the circuit is closed, the lightbulb flashes when the coil moves into or out of the field—
there are two clear flashes for each swing. More importantly, the pendulum slows down as it
swings, much more quickly than before—making the energy connection quite visible.
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This demonstration with a coil is a natural place to begin a discussion of flux—there’s a clear
loop through which there is a flux, and it changes.
Students find the concept of flux quite challenging. This is especially true because we haven’t
dealt with Gauss’s law in this book. It’s worthwhile to have a good discussion about the concept of
flux, what it means. A physical demonstration can help; there are many ways to do this. Here is one
that is a bit messy but quite effective.
Demonstration: Flux bubbles. This demonstration uses a small fan whose speed can be
adjusted, plus a loop that can be used to blow bubbles. (It helps if the loop has a bit of fabric on it to
hold more bubble solution. A loop with multiple holes that blows many mini bubbles will also
work.) Dip the loop into a tray of bubble solution. Now, place the loop in front of the fan, with the
fan speed set to low. The air from the fan will blow bubbles; the number of bubbles will be a direct
measure of the flow of air through the loop. Now, ask your students: How could you adjust the
system for greater or lesser flux? They will certainly figure out that you can adjust:
• The size of the loop.
• The rate of flow of air.
• The angle between the loop and the air flow.
You can point out that Acos is the effective area of the loop as seen by the air. The visual image of
a flow through an area is very important, and this demonstration makes this connection quite well.
After such a physical demonstration of flux, it is then straightforward to use an image of
“magnetic field arrows flowing through a loop” to define the magnetic flux and introduce the
equation   Aeff B  ABcos.
Clicker Question: A loop of wire of area A is tipped at an angle  to a uniform magnetic field B.
The maximum flux occurs for an angle   0. What angle  will give a flux that is ½ of this
maximum value?
A.   30
B.   45
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C.   60
D.   90
After introducing the concept of flux, you can redo the above induction pendulum
demonstration, reinterpreting it in terms of change in flux.
Demonstration: Induction pendulum part II. Do the induction pendulum demonstration
again, but replace the lightbulb with a pair of LEDs, one that flashes when the current is to the left,
one that flashes when the current is to the right.
Now your students can see that, for each swing of the pendulum, each of the LEDs flashes in
sequence. If you know the direction of the field and the direction of the winding of the coil, you can
note the sense of the current for given changes in flux. It’s easy to show that the induced current
opposes a change in the field through the loop—and therefore a change in the current.
The above observations lead us to Lenz’s law, which you can introduce as a new law of nature.
Students will need quite a few practice examples before they catch on to the idea that the field of the
induced current is opposing the change of flux rather than opposing the flux itself.
Clicker Question: A long conductor carrying a current runs next to a loop of wire. The current in
the wire varies as in the graph. Which segment of the graph corresponds to the largest induced
current in the loop?
Some students will still need practice using the right-hand rule to relate the field direction to the
current direction through a coil or solenoid.
Clicker Question: A magnetic field goes through a loop of wire, as at right. If the magnitude of
the magnetic field is
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1) increasing
2) decreasing
3) constant
what can we say about the current in the loop? Answer for each of the above conditions.
A. The loop has a clockwise current.
B. The loop has a counterclockwise current.
C. The loop has no current.
Clicker Question: A battery, a loop of wire, and a switch make a circuit as at right. A second
loop of wire sits directly below. At the following times:
1) just before the switch is closed
2) immediately after the switch is closed
3) long after the switch is closed
4) immediately after the switch is reopened
what can we say about the current in the lower loop? Answer for each of the above conditions.
A. The loop has a clockwise current.
B. The loop has a counterclockwise current.
C. The loop has no current.
At some point during this lecture, you will want to discuss eddy currents and eddy current damping.
The idea that you can have a current through a conductor without a well-defined loop is a key one
for understanding transcranial magnetic stimulation and other such techniques. Most schools have
a variety of interesting demonstrations of eddy current and eddy current damping. For full effect,
complement your demonstrations by having students describe the source of the force in eddy current
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damping; this will lead them through a sequence of reasoning that hits most of the key concepts of
the day.
After a discussion of Lenz’s law, you can finish the day with full treatment of Faraday’s law.
Once students have the necessary conceptual background, and once Faraday’s law is in hand, we can
solve some quantitative examples.
DAY 2: Further Development of Concepts. We suggest starting the day with a quantitative
example or two that use the full formalism of Faraday’s law.
Example: The figure shows a 10-cm-diameter loop in three different magnetic fields. The loop’s
resistance is 0.1 V. For each situation, determine the strength and direction of the induced current.
Example: A coil used to produce changing magnetic fields in a TMS (transcranial magnetic field
stimulation) device is connected to a high-current power supply. As the current ramps to hundreds
or even thousands of amps, the magnetic field increases. In a typical pulsed-field machine, the
current near the coil will go from 0 T to 2.5 T in a time of 200 µs. Suppose a technician holds his
hand near the device, and this increasing field is directed along the axis of his hand—meaning the
flux goes through his gold wedding band, which is 2.0 cm in diameter. What emf is induced in the
ring?
After some practice with Faraday’s law, you can start talking about induced fields. In the above
example, there is an emf in the ring; what is the source of the electric field that gives rise to this
emf? The TMS machine is a good example to use here, because the machine uses the induced
electric field produced by the changing magnetic field to depolarize neural tissue.
After a quick discussion of induced fields, you can discuss the concept of an electromagnetic
wave. Note that the magnetic field and the electric field that make up the electromagnetic wave must
be in a particular orientation and must have a particular ratio of field strengths, and note that the
wave will travel at a particular speed—the speed of light.
An electromagnetic wave is very difficult to visualize. It’s worthwhile to show a simulation or a
video that illustrates the time-varying fields of the electromagnetic wave.
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Demonstration: Electromagnetic wave (video or simulation). There are many such videos
and simulations available. The point is to show the relative orientations of the electric field, the
magnetic field, and the direction of propagation.
You should then teach students the right-hand rule for determining these relative orientations.
Students will need some practice with this concept.
Clicker Question: A plane electromagnetic wave has electric and magnetic fields at all points in
the plane as noted at right, and B field at all points in the plane as noted. With the fields oriented as
shown, the wave is moving
A. into the plane of the paper
B. out of the plane of the paper
C. to the left
D. to the right
E. toward the top of the paper
F. toward the bottom of the paper
After introducing the concept of the electromagnetic wave, you can talk about properties of
these waves. The fields are real—they carry energy. Some energy and power calculations serve to
give a sense of the scale of these fields.
Example: Inside the cavity of a microwave oven, the 2.4 GHz electromagnetic waves have an
intensity of 5.0 kW/m2. What is the strength of the electric field? The magnetic field?
Example: A digital cell phone emits a 1.9 GHz electromagnetic wave with total power 0.60 W. At
a cell phone tower 2.0 km away, what is the intensity of the wave? (Assume that the wave spreads
out uniformly in all directions.) What are the electric and magnetic field strengths at this distance?
Field calculations clearly show that it is the electric field that does the work—the magnitude of
the magnetic field is, relatively, much smaller.
After doing energy calculations, you can discuss polarization. This is a very difficult concept
for students to understand; it is worthwhile to do a physical demonstration. There are microwave
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demonstration units commonly available with horns that emit and detect microwaves. Only one
polarization is emitted and detected, which makes for a good classroom demonstration. The easiest
way to use these devices is to have an audio signal that modulates the microwave carrier, and to
filter and amplify the output. A loud output means a large signal strength; a quiet output means a
small signal strength.
Demonstration: Microwave polarization, part I. Use a microwave emitter-detector pair, as
described above. With the emitter aimed at the detector, you will pick up a big signal. Now, rotate
the plane of polarization of the detector; the received intensity will decrease, until it vanishes when
the detector has been rotated by 90°.
This is a very physical demonstration, with the angle between the emitter and detector easily
seen. You can use the same apparatus to illustrate the operation of a polarizer, which will transmit
microwaves of one polarization only.
Demonstration: Microwave polarization, part I. Use a microwave emitter-detector pair, as
described above. Aim the emitter at the detector; give them the same polarization, so that a large
signal is detected. Now put a rack from an oven or a toaster oven between the two. This makes a
great polarizer,
because there is easy electric conduction along the lines of the grille but none perpendicular to it—
just as for optical polarizers. Show that you get large transmission if the bars of the grille are
perpendicular to the polarization but very little if the bars are parallel.
With this physical model in students’ minds, you can expand the idea to visible light. There are
many good demonstrations you can do on the overhead projector.
Demonstration: Polarization samples. Use two large sheets of polaroid on the overhead
projector. When the axes are aligned, light is transmitted freely; when perpendicular, there is no
transmission. But if certain materials (such as sugar syrup, plastics, certain minerals) are placed
between the crossed polarizers, you will get brightly colored transmission.
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After this, you can introduce Malus’s law and do a quantitative example.
Example: Light passed through a polarizing filter has an intensity of 2.0 W/m2. How should a
second polarizing filter be arranged to decrease the intensity to 1.0 W/m2?
Reflected light from shiny surfaces is strongly polarized; the scattered light of the sky is strongly
polarized as well. This polarization of skylight is used by honeybees and other insects to navigate. It
makes a great demonstration to let students observe the polarization of the light of the sky for
themselves; it’s a nice biological connection, one that is of real importance to many social insects.
This makes a good finish to the day.
Demonstration: Sky polarization. Take a sheet of polaroid and cut it into rectangles with the
long axis of the rectangles along the polarization axis. Now tape four rectangles together as noted at
right.
Unpolarized light will come through all four filters with equal intensity; polarized light will not.
Have your students look at different parts of the sky, rotating their polarizer sets, to find where the
polarization is large and where it is small. The polarization is largest at a 90° angle to the sun in the
sky.
DAY 3: Electromagnetic spectrum. This is an important topic that warrants a full day of
discussion. This discussion also allows for review and application of the concepts of the previous
two days.
As noted above, students have some familiarity with the idea of the electromagnetic spectrum.
Remind them of the details of the spectrum, noting the different wavelengths—a concept they
should be familiar with from earlier chapters. After this, it’s worthwhile to present a physical
example that introduces the photon concept.
Demonstration: Radio waves / gamma rays. Show a cell phone, and note the antenna that
emits the radio waves. The antenna length is related to the emitted wavelength; longer wavelengths
require longer antennas. If you ask to borrow a few cell phones you will likely get a digital phone
(frequency 1900 MHz) and an analog phone (frequency 850 MHz) which will have different
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antenna lengths. If this fails, you can show an FM radio and pull up the telescoping antenna; the
lower frequency (100 MHz) requires a much longer antenna. Talk about how the waves are emitted
and detected. Next, use a Geiger counter and a gamma source to show the nature of gamma rays.
The wavelength is much shorter; the “antenna” is an individual nucleus, and the gamma rays arrive
as individual clicks in the counter.
The distinct arrivals of individual “rays” points out that something is different about this form
of electromagnetic radiation. This is a good jumping-off point for discussing the photon model,
supported with photos from the text or elsewhere that show individual photon events building
up a photographic image. Introduce the equation for the energy of photons, then move on to a
quantitative example.
Example: A radio wave has a frequency of 100 MHz. What is the wavelength, and what is the
energy of individual photons? Now, do the same calculations for a gamma ray of frequency
3.0 1019 Hz.
To put these values in perspective, compare them with the energies of some atomic and
molecular processes from Table 25.1. It’s clear that the energy of a radio wave is too small to do
much to an individual atom; the energy of a gamma ray is sufficient to ionize many.
Now, you are ready to look at the properties of different regions of the electromagnetic
spectrum. The text discusses three distinct regions of the spectrum. Long-wavelength waves like
radio waves and microwaves have very small photon energies; their interaction with matter is best
understood in terms of waves of the electric and magnetic field. Short-wavelength x rays and
gamma rays have correspondingly high photon energies; their interactions with matter are best
viewed from the photon perspective. The middle of the spectrum, infrared, visible light, and
ultraviolet, requires both perspectives. This dual nature of light is something that will be returned to
in Chapter 28.
In addition to the examples that you will certainly want to do, you should do a number of
physical demonstrations to help show some of the properties of these very different types of
electromagnetic waves. Begin by describing the radio wave end of the spectrum; the following
example shows the wave nature quite clearly, and allows for a nice connection with the induction
ideas of the first part of the chapter.
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Demonstration: AM radio orientation. The wavelength of AM radio is such that an antenna
with the optimal length of ¼ wavelength is over 50 m long! AM radios instead use loop antennas
that detect the changing flux of the magnetic field of the wave.
This makes AM radio antennas highly directional, which makes for a nice classroom demonstration.
In a typical radio, the loop is wrapped around a ferrite bar; this bar is horizontal in the radio. If you
pick up a station and then tip the radio by 90°, reception ceases; the bar is now perpendicular to the
magnetic field, so there is no flux change through the loop. If you pick up a station and then rotate
the radio by 90° around a vertical axis, reception will cease at one point as well—allowing you to
determine the direction of the emitting antenna.
Students are well acquainted with infrared, visible, and ultraviolet. Nonetheless, it’s worth
exploring a few facets of these regions of the spectrum. First, it’s worth illustrating the variation in
atomic radiation from hot objects.
Demonstration: Bulb color and brightness. Use a frosted incandescent bulb with a variable
transformer. As you change the current, the filament temperature varies as well, leading to
differences in the amount and the color of emitted radiation.
Demonstration: Star colors. A photograph of a typical star field shows great variation in the
colors of stars due to the varying surface temperatures.
The text discusses the different parts of the spectrum seen by other animals; bees, for instance,
have three different color sensors in their eyes that vary from ours. They don’t see red, but they do
see ultraviolet. Flowers have pigments in this part of the spectrum for just this reason.
Demonstration: An infrared view of the world. A cheap black and white camera can be
connected to your video projection system. By adding an infrared filter (exposed film works well,
or a stacked set of red and blue color filters, or the black plastic filter from the front of a remote
control) you can use the camera to give the class view of the world in the near infrared. There are
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some surprises here. For instance, most people have light skin and hair in the infrared (no matter
their hair and skin color) and it is possible to see veins under the skin.
Demonstration: An ultraviolet view of the world. If you darken the classroom and add a
source of ultraviolet (a black light works well) the above camera and filter combination also gives
an ultraviolet view of the world, allowing you to see the hidden pigments in flowers. Many flowers
have such pigments; black-eyed susans work well.
Students often confuse the near infrared, as in the above demonstration, with the far infrared, the
thermal radiation emitted by all warm objects. The near infrared seen by the black and white camera
has a wavelength of about 1 micron; the peak emission for your body is about 10 microns. You can
do a calculation to show this, and then close with a discussion of animals that can “see” this
radiation—pit vipers, a group of snakes that includes rattlesnakes. The pits have a very simple
optical system; they are really pinhole cameras with sensitive tissue at the bottom. A snake can’t
make a detailed thermal image of the world with its pits, but it can tell where significant sources of
thermal radiation are located. Good enough!
You could close the day with a brief discussion of the high-energy end of the spectrum. It’s
worthwhile to talk about x rays—something that will be very important at the start of Chapter 28,
when we begin the study of quantum mechanics.
Other Resources
In addition to the specific suggestions made above in the daily lecture outlines, here are some other
suggestions for demonstrations, examples, questions, and additional topics that you could weave
into your class time.
Suggested Demonstrations
There are many wonderful demonstrations that one could use in this chapter. Here are some
additional favorites in addition to the ones noted above.
Supercooled copper. Everyone has seen demonstrations of eddy current braking or damping.
The most dramatic demonstration of this phenomenon requires a very strong rare-earth magnet, a
block or sheet of soft copper, and a bit of liquid nitrogen. If you chill the copper with the liquid
nitrogen, its conductivity increases dramatically. A large block of chilled copper will exhibit a
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strong degree of eddy current braking; a very strong magnet dropped on the copper block will not hit
with a clang, but will simply slowly settle into place. If the magnet is dropped from some distance, it
can actually rebound without touching the copper!
Infrared transmission. If you can get your hands on a silicon wafer, you can show one of its
more remarkable properties: Silicon will transmit infrared. The IR signal from a remote control can
control a television set through a silicon wafer.
Sunset in a glass. The scattering of light by small particles (or molecules) is responsible for the
blue of the sky—and the blue of blue eyes and blue birds. The scattering is strongly dependent on
wavelength. If you take a glass of water and add a few drops of milk, white light coming from the
top will clearly separate by color. Blue light will scatter out in the top few inches, red will make it to
the bottom.
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Sample Reading Quiz Questions
1.
Which of the following will cause an induced current in a coil of wire?
A. A magnet resting near the coil
B. The constant field of the earth passing through the coil
C. A magnet being moved into or out of the coil
D. A wire carrying a constant current near the coil
2.
The speed of electromagnetic waves
A. depends upon the wavelength in a vacuum
B. depends on the photon energy
C. is the same as the speed of sound
D. is the same for all waves regardless of wavelength
3.
Comparing infrared and ultraviolet, we can say that
A. infrared has longer wavelength and higher photon energy
B. infrared has longer wavelength and lower photon energy
C. ultraviolet has longer wavelength and higher photon energy
D. ultraviolet has longer wavelength and lower photon energy
Additional Student Response System (“Clicker”) Questions
1. A bar magnet sits inside a coil of wire which is connected to a meter. For each of the following
circumstances:
1) the bar magnet is at rest in the coil
2) the bar magnet is pulled out of the coil
3) the bar magnet is completely out of the coil and at rest
4) the bar magnet is reinserted into the coil
what can we say about the current in the meter?
A. The current goes from right to left.
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B. The current goes from left to right.
C. There is no current in the meter.
2. A typical analog cell phone has a frequency of 850 MHz; a digital phone a frequency of
1950 MHz. Compared to the signal from an analog cell phone, the digital signal has
A. longer wavelength and lower photon energy.
B. longer wavelength and higher photon energy.
C. shorter wavelength and lower photon energy.
D. shorter wavelength and higher photon energy.
3. A radio tower emits two 50 W signals, one an AM signal at a frequency of 850 kHz, one an
FM signal at a frequency of 85 MHz. Which signal has more photons per second?
A. The AM signal has more photons per second.
B. The FM signal has more photons per second.
C. Both signals have the same photons per second.
Additional Examples
1. Two metal loops face each other. The upper loop is suspended by plastic springs and can move
up or down. The lower loop is fixed in place and is attached to a battery and a switch.
Immediately after the switch is closed,
a. Is there a force on the upper loop? If so, in which direction will it move? Explain your
reasoning.
b. Is there a torque on the upper loop? If so, which way will it rotate? Explain your reasoning.
2. The outer coil of wire is 10 cm long, 2 cm in diameter, wrapped tightly with one layer of 0.5mm-diameter wire, and has a total resistance of 1.0 Ω. It is attached to a battery, as shown, that
steadily decreases in voltage from 12 V to 0 V in 0.5 s, then remains at 0 V for t  0.5 s. The
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inner coil of wire is 1 cm long, 1 cm in diameter, has 10 turns of wire, and has a total
resistance of 0.01 Ω. It is connected, as shown, to a current meter.
a. As the voltage to the outer coil begins to decrease, in which direction (left-to-right or rightto-left) does current flow through the meter? Explain.
b. Draw a graph showing the current in the inner coil as a function of time for 0  t  1 s.
Include a numerical scale on the vertical axis.
One Step Beyond: Why CO2?
At the end of Part VI, there is a discussion of the greenhouse effect and global warming. The earth is
as warm as it is because the atmosphere is largely transparent to incoming visible light from the sun
but much less transparent to the outgoing infrared radiation. Much of this difference in transmission
comes from carbon dioxide. Why CO2? It only forms 0.038% of the atmosphere. Why should a gas
present in such small quantities have such a large effect?
The electromagnetic radiation emitted by the earth, peaked as it is at about 10 µm, corresponds
to photon energies that are far too low to cause electronic transitions in the gas molecules of the
atmosphere. If the radiation is to interact with the molecules, it needs to be because the electric
fields of the electromagnetic wave can rotate, vibrate, or bend the molecules.
Most of the atmosphere is made up of diatomic oxygen and nitrogen. These molecules are
completely symmetric; they have no dipole moment.
The lack of a dipole moment means that they won’t rotate in the presence of an electric field. Their
symmetry means they won’t vibrate in an oscillating electric field, as this won’t induce a dipole
moment. And there is no possible bending mode. The upshot? Diatomic nitrogen and oxygen don’t
interact with electromagnetic waves in the infrared region of the spectrum. If nitrogen and oxygen
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made up 100% of the atmosphere, it would be almost completely transparent to infrared, and the
earth would be a frosty place indeed—with an average surface temperature of around –18°C.
Fortunately, there is more to the story. Two trace gases, water vapor and carbon dioxide, do
interact—strongly—with infrared.
The water molecule is asymmetric and has a large permanent dipole moment; it will rotate,
bend, and vibrate in response to oscillating electric fields, as was discussed in the chapter.
Water vapor is a very strong absorber of infrared. Most of the atmosphere’s lack of transparency to
infrared is due to water vapor.
But water vapor isn’t found in the upper atmosphere. It’s too cold; the vapor condenses out as
liquid water and falls as precipitation. There must be some other gas present in the upper
atmosphere that absorbs infrared, or we wouldn’t see the degree of greenhouse warming that we do.
The key molecule is carbon dioxide. Carbon dioxide molecules don’t have a permanent dipole
moment, but they do develop a dipole moment when they bend. This bending mode will interact
with the oscillating field of infrared, and so CO2 has a strong absorption peak for wavelengths
around 15 µm, in the tail of the thermal radiation spectrum of the earth. At wavelengths near this
value, the atmosphere is essentially opaque to infrared. With enough outgoing radiation trapped, the
earth stays warm.
The big question before us these days is what happens when the percentage of CO2 increases
dramatically—as it is. It’s reasonable to expect changes; CO2 is such a strong absorber of infrared
near the peak of the earth’s emission that it is clear that adding CO2 will alter the earth’s energy
balance. But how much will it change? That’s an open question, but one that will be answered very
soon, unless we make significant shifts in how we fuel our societies.
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