Electromagnetic
Waves
Changing Electric
Fields Produce
Magnetic Fields;
Maxwell’s Equations
Maxwell’s equations
are the basic equations
of electromagnetism.
They involve calculus;
here is a summary:
1. Gauss’s law
relates electric field
to charge: Flux of
the electric field
through the closed
surface is equal to
the sum of all
electric charges
enclosed by this
surface divided by
𝜀0 .
2. A law stating there
are no magnetic
“charges”: Flux of
the magnetic field
through the closed
surface is equal to
zero.
3. A changing electric
field produces a
magnetic field and
vice versa.
4. A magnetic field is
produced by an
electric current,
and also by a
changing electric
field.
Only one part of this is
new—that a changing
electric field produces
a magnetic field.
Ampère’s law relates
the magnetic field
around a current to the
current through a
surface.
In order for Ampère’s
law to hold, it can’t
matter which surface
we choose. But look at
a discharging
capacitor; there is a
current through
surface 1 but none
through surface 2:
Therefore, Ampère’s
law is modified to
include the creation of
a magnetic field by a
changing electric
………………………………………………………………
field—the field
………………………………
between the plates of
………………………………………………………………
the capacitor in this
………………………………
example.
………………………………………………………………
Production of
………………………………
Electromagnetic
………………………………………………………………
Waves
………………………………
………………………………………………………………
Since a changing
………………………………
electric field produces
………………………………………………………………
a magnetic field, and a ………………………………
changing magnetic
field produces an
electric field, once
sinusoidal fields are
created they can
propagate on their
own.
These propagating
fields are called
electromagnetic
waves.
Oscillating charges will
produce
electromagnetic
waves:
Far from the source,
the waves are plane
waves:
The electric and
magnetic waves are
perpendicular to each
other, and to the
direction of
propagation.
When Maxwell
calculated the speed of
propagation of
electromagnetic
waves, he found:
Using the known
values of ε0 and µ0
gives
c = 3.00 x 108 m/s.
This is the speed of
light in a vacuum
Light was known to be
a wave. The
production and
measurement of
electromagnetic waves
of other frequencies
confirmed that light
was an
electromagnetic wave
as well.
The frequency of an
electromagnetic wave
is related to its
wavelength:
Light as an
Electromagnetic Wave
and the
Electromagnetic
Spectrum
Electromagnetic waves
can have any
wavelength; we have
given different names
to different parts of the
electromagnetic
spectrum.
Example 1
Electromagnetic waves
and sound waves can
have the same
frequency. (a) What is
the wavelength of a 1
kHz electromagnetic
wave? (b) What is the
wavelength of a 1 kHz
sound wave? The
speed of sound in air is
341 m/s.
Measuring the Speed
of Light
The speed of light was
known to be very large,
although careful
studies of the orbits of
Jupiter’s moons
showed that it is finite.
One important
measurement, by
Michelson, used a
rotating mirror:
Over the years,
………………………………………………………………
measurements have
………………………………
become more and
………………………………………………………………
more precise; now the ………………………………
speed of light is
………………………………………………………………
defined to be:
………………………………
c = 2.99792458 × 108
………………………………………………………………
m/s
……………………………….
This is then used to
………………………………………………………………
define the meter.
……………………………….
………………………………………………………………
Energy in EM Waves
……………………………….
………………………………………………………………
This energy is
………………………………
transported by the
………………………………………………………………
wave.
………………………………
………………………………………………………………
………………………………
………………………………………………………………
……………………………….
Radio and Television
………………………………………………………………
……………………………….
The 1800s: Earliest
………………………………………………………………
Broadcasting
……………………………….
 Maxwell
………………………………………………………………
(Theorized the
………………………………
existence of
………………………………………………………………
electromagnetic
………………………………
waves as
………………………………………………………………
“luminous ether.”)
………………………………
 Bell (Transmitting
………………………………………………………………
sounds by
……………………………….
telegraph in 1877.)
………………………………………………………………
 Hertz (Invented the ……………………………….
“spark-gap
………………………………………………………………
detector” which
……………………………….
verified the
existence of
………………………………………………………………
electromagnetic
………………………………
waves.)
………………………………………………………………
 Marconi (Invented
………………………………
radio in 1895. First
………………………………………………………………
radio company in
………………………………
London, 1897.)
………………………………………………………………
……………………………….
Generation of Radio
………………………………………………………………
Waves
……………………………….
………………………………………………………………
- Accelerating
……………………………….
charges radiate
EM energy
- If charges
………………………………………………………………
………………………………
oscillate back and ………………………………………………………………
forth, get time-
………………………………
varying fields
………………………………………………………………
………………………………
………………………………………………………………
……………………………….
………………………………………………………………
If charges oscillate
……………………………….
back and forth, get
………………………………………………………………
time-varying magnetic
……………………………….
fields too. Note that
the magnetic fields are ………………………………………………………………
perpendicular to the
………………………………
electric field vectors
………………………………………………………………
Polarization of Radio
………………………………
Waves
………………………………………………………………
………………………………
………………………………………………………………
……………………………….
………………………………………………………………
……………………………….
………………………………………………………………
……………………………….
Radio and Television;
Wireless
Communication
This figure illustrates
the process by which a
radio station transmits
information. The audio
signal is combined with
a carrier wave.
What quantities
characterize a radio
wave?
………………………………………………………………
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………………………………………………………………
………………………………
………………………………………………………………
………………………………
………………………………………………………………
……………………………….
………………………………………………………………
……………………………….
………………………………………………………………
……………………………….
………………………………………………………………
Two common ways to
………………………………
carry analog
………………………………………………………………
information with radio
………………………………
waves
………………………………………………………………
- Amplitude
Modulation (AM)
- Frequency
………………………………
………………………………………………………………
……………………………….
Modulation (FM):
………………………………………………………………
“static free”
……………………………….
………………………………………………………………
AM Radio
……………………………….
Amplitude Modulation
………………………………………………………………
(AM) uses changes in
………………………………
the signal
………………………………………………………………
strength to convey
………………………………
information.
………………………………………………………………
………………………………
AM Radio in Practice
………………………………………………………………
……………………………….
• Uses frequency
………………………………………………………………
range from 530
……………………………….
kHz to 1700 kHz
………………………………………………………………
– each station
……………………………….
uses 9 kHz
– spacing is 10 ………………………………………………………………
kHz (a little
………………………………
breathing
………………………………………………………………
room) ® 117 ………………………………
channels
– 9 kHz of
………………………………………………………………
………………………………
bandwidth
………………………………………………………………
means 4.5
……………………………….
kHz is
………………………………………………………………
highest
……………………………….
audio
………………………………………………………………
frequency
……………………………….
that can be
encoded
• falls
………………………………………………………………
………………………………
short of ………………………………………………………………
20 kHz
………………………………
capabili ………………………………………………………………
ty of
………………………………
human
………………………………………………………………
ear
……………………………….
• Previous diagram
is exaggerated:
– audio signal
changes
………………………………………………………………
……………………………….
………………………………………………………………
……………………………….
slowly with
respect to
………………………………………………………………
radio carrier
• typical
………………………………
………………………………………………………………
speech
………………………………
sound
………………………………………………………………
of 500
………………………………
Hz
………………………………………………………………
varies
……………………………….
1000
………………………………………………………………
times
……………………………….
slower
………………………………………………………………
than
……………………………….
carrier
• thus will
see
1000
cycles
of
carrier
to every
one
cycle of
audio
FM Radio
Frequency Modulation
(FM) uses changes in
the wave’s
frequency to convey
information.
• Spans 87.8 MHz
to 108.0 MHz in
200 kHz intervals
– 101 possible
stations
– example:
91X runs
from 91.0–
91.2 MHz
(centered at
91.1)
• Nominally uses
150 kHz around
center
– 75 kHz on
each side
– 30 kHz for L
+ R (mono)
® 15 kHz
audio
capability
– 30 kHz offset
for stereo
difference
signal (L - R)
• Again: figure
exaggerated
– 75 kHz from
band center,
modulation
is > 1000
times slower
than carrier,
so many
cycles go by
before
frequency
noticeably
changes
AM vs. FM
• FM is not
inherently higher
frequency than
AM
– these are
just choices
– aviation
band is 108–
136 MHz
uses AM
technique
• Besides the
greater bandwidth
(leading to stereo
and higher audio
frequencies), FM
is superior in
immunity to
environmental
influences
– there are lots
of ways to
mess with an
EM-wave’s
amplitude
• pass
under a
bridge
• reorient
the
antenn
a
– no natural
processes
mess with
the
frequency
• FM still
works
in the
face of
amplitu
de
foolery
AM is easy: just pass
the AC signal from the
antenna into a diode
or better yet, a diode
bridge then use
capacitor to smooth
out bumps but not so
much as to smooth out
audio bumps.
Exercise 1
1. The electric field in
an EM wave
traveling north
oscillates in an
east–west plane.
Describe the
direction of the
magnetic field
vector in this wave.
2. Is sound an
electromagnetic
wave? If not, what
kind of wave is it?
3. Can EM waves
travel through a
perfect vacuum?
Can sound waves?
4. When you flip a
light switch on,
does the light go
on immediately?
Explain.
5. Are the
wavelengths of
radio and television
signals longer or
shorter than those
detectable by the
human eye?
6. When you connect
two loudspeakers to
the
output of a stereo
amplifier, should
you be sure the
lead-in wires are
equal in length so
that there will not
be a time lag
between speakers?
Explain.
7. In the
electromagnetic
spectrum, what
type of EM
wave would have a
wavelength of 1
km? 1 m? 1 cm? 1
mm?
8. Can radio waves
have the same
frequencies as
sound waves (20
Hz–20,000 Hz)?
9. Can two radio or TV
stations broadcast
on the
same carrier
frequency? Explain.
10. The carrier
frequencies of FM
broadcasts are
much higher than
for AM broadcasts.
On the basis of
what you learned
about diffraction in
Chapter 11, explain
why AM signals can
be detected more
readily than FM
signals behind low
hills or buildings.
11. Discuss how
cordless telephones
make use of EM
waves. What about
cell phones?
12. A lost person may
signal by flashing a
flashlight
on and off using
Morse code. This is
actually a
modulated EM
wave. Is it AM or
FM? What is the
frequency of the
carrier,
approximately?