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Chapter 35. Electromagnetic Fields and
Waves
To understand a laser beam,
we need to know how electric
and magnetic fields change
with time. Examples of timedependent electromagnetic
phenomena include highspeed circuits, transmission
lines, radar, and optical
communications.
Chapter Goal: To study the
properties of electromagnetic
fields and waves.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Chapter 35. Electromagnetic Fields and
Waves
Topics:
• E or B? It Depends on Your Perspective
• The Field Laws Thus Far
• The Displacement Current
• Maxwell’s Equations
• Electromagnetic Waves
• Properties of Electromagnetic Waves
• Polarization
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Chapter 35. Reading Quizzes
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Maxwell’s equations are a set of how
many equations?
A.
B.
C.
D.
E.
Two
Three
Four
Five
Six
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Maxwell’s equations are a set of how
many equations?
A.
B.
C.
D.
E.
Two
Three
Four
Five
Six
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Maxwell introduced the displacement
current as a correction to
A.
B.
C.
D.
E.
Coulomb’s law.
Gauss’s law.
Biot-Savart’s law.
Ampère’s law.
Faraday’s law.
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Maxwell introduced the displacement
current as a correction to
A.
B.
C.
D.
E.
Coulomb’s law.
Gauss’s law.
Biot-Savart’s law.
Ampère’s law.
Faraday’s law.
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The law that characterizes polarizers
is called
A.
B.
C.
D.
Malus’s law.
Maxwell’s law.
Poynting’s law.
Lorentz’s law.
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The law that characterizes polarizers
is called
A.
B.
C.
D.
Malus’s law.
Maxwell’s law.
Poynting’s law.
Lorentz’s law.
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Experimenter A creates a magnetic field
in the laboratory. Experimenter B moves
relative to A. Experimenter B sees
A.
B.
C.
D.
E.
just the same magnetic field.
a magnetic field of different strength.
a magnetic field pointing the opposite direction.
just an electric field.
both a magnetic and an electric field.
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Experimenter A creates a magnetic field
in the laboratory. Experimenter B moves
relative to A. Experimenter B sees
A.
B.
C.
D.
E.
just the same magnetic field.
a magnetic field of different strength.
a magnetic field pointing the opposite direction.
just an electric field.
both a magnetic and an electric field.
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Chapter 35. Basic Content and Examples
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E or B? It Depends on Your Perspective
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
E or B? It Depends on Your Perspective
Whether a field is seen as “electric” or “magnetic” depends
on the motion of the reference frame relative to the sources of
the field.
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E or B? It Depends on Your Perspective
The Galilean field transformation equations are
where V is the velocity of frame S' relative to frame S and
where the fields are measured at the same point in space by
experimenters at rest in each reference frame.
NOTE: These equations are only valid if V << c.
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Ampère’s law
Whenever total current Ithrough
passes through an area bounded
by a closed curve, the line
integral of the magnetic field
around the curve is
The figure illustrates the
geometry of Ampère’s law. In
this case, Ithrough = I1 − I2 .
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Tactics: Determining the signs of flux and
current
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The Displacement Current
The electric flux due to a constant electric field E
perpendicular to a surface area A is
The displacement current is defined as
Maxwell modified Ampère’s law to read
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EXAMPLE 35.3 The fields inside a charging
capacitor
QUESTION:
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EXAMPLE 35.3 The fields inside a charging
capacitor
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EXAMPLE 35.3 The fields inside a charging
capacitor
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EXAMPLE 35.3 The fields inside a charging
capacitor
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EXAMPLE 35.3 The fields inside a charging
capacitor
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Maxwell’s Equations
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The Fundamental Ideas of Electromagnetism
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Electromagnetic Waves
Maxwell, using his equations of the electromagnetic field,
was the first to understand that light is an oscillation of the
electromagnetic field. Maxwell was able to predict that
• Electromagnetic waves can exist at any frequency,
not just at the frequencies of visible light. This
prediction was the harbinger of radio waves.
• All electromagnetic waves travel in a vacuum with
the same speed, a speed that we now call the speed
of light.
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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Properties of Electromagnetic Waves
Any electromagnetic wave must satisfy four basic
conditions:
1. The fields E and B and are perpendicular to the direction
of propagation vem.Thus an electromagnetic wave is a
transverse wave.
2. E and B are perpendicular to each other in a manner such
that E × B is in the direction of vem.
3. The wave travels in vacuum at speed vem = c
4. E = cB at any point on the wave.
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Properties of Electromagnetic Waves
The energy flow of an electromagnetic wave is described
by the Poynting vector defined as
The magnitude of the Poynting vector is
The intensity of an electromagnetic wave whose electric
field amplitude is E0 is
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EXAMPLE 35.4 The electric field of a laser
beam
QUESTION:
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EXAMPLE 35.4 The electric field of a laser
beam
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EXAMPLE 35.4 The electric field of a laser
beam
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EXAMPLE 35.4 The electric field of a laser
beam
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Radiation Pressure
It’s interesting to consider the force of an electromagnetic
wave exerted on an object per unit area, which is called the
radiation pressure prad. The radiation pressure on an object
that absorbs all the light is
where I is the intensity of the light wave. The subscript on
prad is important in this context to distinguish the radiation
pressure from the momentum p.
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EXAMPLE 35.5 Solar sailing
QUESTION:
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EXAMPLE 35.5 Solar sailing
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EXAMPLE 35.5 Solar sailing
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EXAMPLE 35.5 Solar sailing
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Malus’s Law
Suppose a polarized light wave of intensity I0 approaches a
polarizing filter. θ is the angle between the incident plane of
polarization and the polarizer axis. The transmitted intensity
is given by Malus’s Law:
If the light incident on a polarizing filter is unpolarized, the
transmitted intensity is
In other words, a polarizing filter passes 50% of unpolarized
light and blocks 50%.
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Chapter 35. Summary Slides
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General Principles
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General Principles
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General Principles
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Important Concepts
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Important Concepts
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Applications
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Chapter 35. Clicker Questions
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Which diagram
shows the fields in
frame S´?
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Which diagram
shows the fields in
frame S´?
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The electric field in four identical capacitors is
shown as a function of time. Rank in order, from
largest to smallest, the magnetic field strength at
the outer edge of the capacitor at time T.
A.
B.
C.
D.
E.
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Ba = Bb > Bc = Bd
Bd > Bc > Ba = Bb
Ba > Bb > Bc > Bd
Ba = Ba > Bc > Bd
Bc > Ba > Bd > Bb
The electric field in four identical capacitors is
shown as a function of time. Rank in order, from
largest to smallest, the magnetic field strength at
the outer edge of the capacitor at time T.
A.
B.
C.
D.
E.
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Ba = Bb > Bc = Bd
Bd > Bc > Ba = Bb
Ba > Bb > Bc > Bd
Ba = Ba > Bc > Bd
Bc > Ba > Bd > Bb
An electromagnetic wave is
propagating in the positive
x-direction. At this instant of
time, what is the direction of
at the center of the rectangle?
A. In the positive x-direction
B. In the negative x-direction
C. In the positive z-direction
D. In the negative z-direction
E. In the positive y-direction
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An electromagnetic wave is
propagating in the positive
x-direction. At this instant of
time, what is the direction of
at the center of the rectangle?
A. In the positive x-direction
B. In the negative x-direction
C. In the positive z-direction
D. In the negative z-direction
E. In the positive y-direction
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An electromagnetic wave is
traveling in the positive
y-direction. The electric
field at one instant of time
is shown at one position.
The magnetic field at this
position points
A. In the positive y-direction.
B. In the negative y-direction.
C. In the positive x-direction.
D. In the negative x-direction.
E. Away from the origin.
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An electromagnetic wave is
traveling in the positive
y-direction. The electric
field at one instant of time
is shown at one position.
The magnetic field at this
position points
A. In the positive y-direction.
B. In the negative y-direction.
C. In the positive x-direction.
D. In the negative x-direction.
E. Away from the origin.
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The amplitude of the oscillating electric field
at your cell phone is 4.0 µV/m when you are
10 km east of the broadcast antenna. What is
the electric field amplitude when you are 20
km east of the antenna?
A. 4.0 µV/m
B. 2.0 µV/m
C. 1.0 µV/m
D. There’s not enough information to tell.
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The amplitude of the oscillating electric field
at your cell phone is 4.0 µV/m when you are
10 km east of the broadcast antenna. What is
the electric field amplitude when you are 20
km east of the antenna?
A. 4.0 µV/m
B. 2.0 µV/m
C. 1.0 µV/m
D. There’s not enough information to tell.
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Unpolarized light of equal
intensity is incident on four
pairs of polarizing filters.
Rank in order, from largest to
smallest, the intensities Ia to Id
transmitted through the
second polarizer of each pair.
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A.
B.
C.
D.
E.
Ia = Id > Ib = Ic
Ib = Ic > Ia = Id
Id > Ia > Ib = Ic
Ib = Ic > Ia > Id
Id > Ia > Ib > Ic
Unpolarized light of equal
intensity is incident on four
pairs of polarizing filters.
Rank in order, from largest to
smallest, the intensities Ia to Id
transmitted through the
second polarizer of each pair.
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A.
B.
C.
D.
E.
Ia = Id > Ib = Ic
Ib = Ic > Ia = Id
Id > Ia > Ib = Ic
Ib = Ic > Ia > Id
Id > Ia > Ib > Ic