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Chapter #32 Electromagnetic Waves
•  34.1: Displacement Current and the General Form of
Ampere's Law
•  34.2: Maxwell's Equations and Hertz's Discoveries
•  34.3: Plane Electromagnetic Waves
•  34.4: Energy Carried by Electromagnetic Waves
•  34.5: Momentum and Radiation Pressure
•  34.6: Production of Electromagnetic Waves by an
Antenna
•  34.7: The Spectrum of Electromagnetic Waves
Laws of Electromagnetism

Gauss’s Law for E

Gauss’s Law for B
Qnclosed
ε0

∫ B ⋅ dA = 0
€
Ampere’s Law

∫ E ⋅ dA =


∫ B ⋅ d l = (µ I)
0
€
Faraday’s Law
€


enclosed
dΦ
dt
∫ E⋅dl =−
•  This is what we€ already get in our course
Maxwell’s Equation

Gauss’s Law for E

Gauss’s Law for B
€
Ampere’s Law

∫ E ⋅ dA =
Qnclosed
ε0

∫ B ⋅ dA = 0


&
∫ B ⋅ d l = µ (' I + ε
0
€
Faraday’s Law


∫ E⋅dl =−
0
d Φ)
+
d t * enclosed
dΦ
dt
€
•  This is Maxwell’s
Equations for Free Space!
€
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Ampere’s Law
•  The line integral:
 
∫ B ⋅ d l = µ0Ienclosed
•  around any closed
path equals µ0 times
the net current
through the area
enclosed by the path.
€


&
∫ B ⋅ d l = µ (' I + ε
0
0
d Φ)
+
d t * enclosed
•  Solve problem 34.1, page 985
€
Definition of EMW
•  Electromagnetic waves are traveling waves of
oscillating electric and magnetic field.
•  RHR: point the
fingers of your right
hand in the direction
of electric field, curl
your fingers in the
direction of magnetic
field, your thumb will
point you the
direction of
propagation.
•  Solve problem 34.2, page 991
Transverse waves versus
longitudinal waves
•  In transverse wave
the displacement is
perpendicular to the
direction of
propagation.
•  In longitudinal wave
the displacement is
in the direction of
propagation.
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The speed of light
•  Modern experiments:
•  C = 2.99792458×108 [m/s] ≈ 3.0×108 [m/s]
•  Ole Romer (1676)
observed eclipses
of Jupiter’s moon
behind the planet.
His result was
2.25×108 [m/s]
Calculate speed of light yourself
•  Radius of Sun orbit 150 million kilometers,
delay time ~ 1000 sec.
•  Later it was shown by Maxwell that we can
calculate speed of light with a help of two
constants ε0 and µ0.
c=
1
= 2.99792458 ⋅10 8 [m /s]
ε 0 µ0
€
Wavelength
•  Wavelength is
a minimum
distance over
which a wave
repeats.
•  Usual
designation is
λ [m]
•  Read all definitions in Chapter 16 in your book
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Period and Frequency
λ = cT
•  Period (T) is a time
required for one wave
to pass a given point.
•  Frequency (f) is a
number of crests/
troughs that pass a
given point per second
f = 1/T [Hz]
•  Read all definitions in Chapter 16 in your book
€
Test problems 25-11,38,39
•  An electromagnetic wave propagates along
the +y direction as shown in Figure 25-1.
If the E-field at the origin is along the +z
direction, what is the direction of the Bfield?
•  The frequency of a microwave signal is
9.76 GHz. What is its wavelength in
meters?
•  The wavelength of an electromagnetic
wave is 600 nm. What is its frequency?
Electromagnetic spectrum
•  Light spreads
out into a
rainbow of
colors from
red to violet.
•  Visible light is
a very small
part of
electromagne
tic spectrum.
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Boundaries: 106 Hz to 1022 Hz
•  E = c B
The longest part: Radio Waves
•  Frequency 106 Hz to 109 Hz (1 [km] - 1 [m])
•  Used for Radio and TV connection.
•  Produced by alternating current in metal
antennas.
Microwaves
•  Frequency 109 Hz to 1012 Hz (1 m - 1 mm)
•  Used for long-distance phone calls, for cook
food (microwave - 12.2 [cm], 2.4 [GH]).
•  The highest frequency electromagnetic
waves that can be produced by electronic
circuitry.
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Infrared Waves
•  Frequency 1012 Hz to 4.3×1014 Hz (1mm - 1µm)
•  “Heat on the skin”. Invisible.
•  Some creatures (e.g. snakes) have special infrared
receptors that allow them to “see” the infrared
waves.
•  All warm-blooded creatures produce infrared
waves.
•  Use in remote control in home electronics.
Infrared Radiation
•  If the object is at room temperature, the wavelength
of thermal radiation are mainly in the infrared region,
and hence is not visible for our eye. But if the
temperature is sufficiently high the radiation is in the
visible part of the electromagnetic spectrum like a hot
tungsten filament of a light-bulb.
Visible Light
•  Frequency 4.3×1014 Hz to 7.5×1014 Hz
(700nm - 400nm or 7000 Å - 4000 Å)
•  Produced by electrons changing their
positions within the atoms.
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Ultraviolet Light
•  Frequency 7.5×1014 Hz to 1017 Hz (400nm 3nm or 4000 Å - 30 Å)
•  Sun tam on our skin. Invisible.
•  Can be seen by some bees and butterflies.
X-Rays
1017
•  Frequency
Hz to 1020 Hz (10nm - 1 nm
or 100 Å - 1 Å)
•  Generated by the rapid deceleration of highspeed electrons (TV monitor).
•  Freely path through our bodies (X-ray or MRI
diagnostics).
•  Not safe! Damage or destroy living tissues.
Gamma Rays
•  Frequency 1020 Hz and higher (less than 1 Å
and shorter).
•  Produced in nuclear reactions.
•  They are highly penetrating and destructive
for living cell.
•  Usual component of nuclear explosion.
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Energy of Electromagnetic waves
•  Electric energy
density:
•  Magnetic energy
density:
1 2
B
2 µ0
uE =
ε0 2
E
2
u=
ε0 2
1 2
1 2
E +
B = ε0 E 2 =
B
2
2€µ0
µ0
€
uB =
•  Solve problem 34.3, page 994
E =c B
€
€
The Intensity
•  The intensity
is the amount
of energy a
wave delivers
to a unit area
in a unit time.
I=
u ( Ac Δ t )
ΔU
c
=
= uc = c ε0 E 2 = B 2
AΔ t
AΔ t
µ0
€
Momentum of Electromagnetic
wave
Energy absorbed
c
U uav Ac Δ t Iav AΔ t
Δp= =
=
c
c
c
Δ p Iav A
Fav =
=
Δt
c
•  Solve problem 34.5, page 996
Iav
pressure
=
av
• 
c
Momentum =
€
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Questions
•  Which of the following statements are true?
•  a) An electromagnetic wave is a result of
electric and magnetic fields acting together.
•  b) The speed of electromagnetic waves
through a vacuum is ten times the speed of
sound in air.
•  c) Electromagnetic waves are longitudinal.
•  d) Electromagnetic waves in a vacuum travel
with the speed of light.
•  e) Electromagnetic waves do not require a
medium to be transmitted.
Test Problem 25-2
•  The orientation of the electric and magnetic
fields in electromagnetic waves is
•  A) perpendicular to the direction of waves and
parallel to each other.
•  B) parallel to the direction of the waves and
parallel to each other.
•  C) parallel to the direction of the waves and
perpendicular to each other.
•  D) perpendicular to the direction of the waves
and perpendicular to each other.
Test problem 25-10
• 
• 
• 
• 
• 
Electromagnetic waves are
A) transverse.
B) longitudinal.
C) longitudinal and transverse.
D) None of the other answers given is
correct.
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Test problem 25-16
•  16) Which of the following expressions
is the correct representation for the
speed of light?
•  A) (ε µ )
•  B) (ε / µ )
•  C) (µ / ε )
•  D) 1/ (ε µ )
o o
o
o
o
o
o o
Test problem 25-29
•  How far does a beam of light travel in one
full year?
•  The value of the electric field for a
certain type of electromagnetic wave is
660 N/C. What is the value of the
magnetic field for that wave?
Test problem 25-35
•  35) Which one of the following is the correct order
of the electromagnetic spectrum from low to high
frequencies?
•  A) radio waves, infrared, microwaves, UV, visible,
X-rays, gamma rays
•  B) radio waves, UV, X-rays, microwaves, infrared,
visible, gamma rays
•  C) radio waves, microwaves, infrared, visible, UV,
X-rays, gamma rays
•  D) radio waves, microwaves, visible, X-rays,
infrared, UV, gamma rays
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Test problem 25-48, 53, 54
•  A 60.0 W light bulb radiates light uniformly in
all different directions. What is the average
intensity of the light bulb at a distance of
0.400 m from the bulb?
•  The electric field component of an
electromagnetic wave is 34.4 N/C. What is the
electric energy density of the wave?
•  The magnetic field component of the
electromagnetic wave is 15.0 µT. What is the
magnetic energy density of the wave?
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