Transcript Chapter 22: Electromagnetic Waves

My
Chapter 22
Lecture
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Chapter 22: Electromagnetic
Waves
•Production of EM waves
•Maxwell’s Equations
•Antennae
•The EM Spectrum
•Speed of EM Waves
•Doppler Effect
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§22.1 Maxwell’s Equations and EM
Waves
A stationary charge produces an electric field.
A charge moving at constant speed produces electric and
magnetic fields.
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A charge that is accelerated will produce variable electric
and magnetic fields. These are electromagnetic (EM)
waves.
If the charge oscillates with a frequency f, then the
resulting EM wave will have a frequency f. If the charge
ceases to oscillate, then the EM wave is a pulse (a finitesized wave).
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Faraday’s Law:
A changing magnetic field creates an
electric field.
Ampère-Maxwell Law
A current or a changing electric field creates
a magnetic field.
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When Maxwell’s equations are combined, the solutions are
electric and magnetic fields that vary with position and time.
These are EM waves.
An electric field only wave cannot exist, nor can a magnetic
field only wave.
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§22.2 Antennae
An electric field parallel to an antenna (electric dipole)
will “shake” electrons and produce an AC current.
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An EM wave also has a
magnetic component. A
magnetic dipole antenna
can be oriented so that the
B-field passes into and out
of the plane of a loop,
inducing a current in the
loop.
The B-field of an EM wave is perpendicular to its E-field
and also the direction of travel.
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§22.3 The EM Spectrum
EM waves of any frequency can exist.
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The EM Spectrum:
Energy increases with increasing frequency.
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§22.4 Speed of Light
Maxwell was able to derive the speed of EM waves in
vacuum. EM waves do not need a medium to travel
through.
c

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 0 0
8.8510
12
1


C 2 /Nm2 4  107 T m/A
 3.00  108 m/s
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In 1675 Ole Römer presented a calculation of the speed of
light. He used the time between eclipses of Jupiter’s
Gallilean Satellites to show that the speed of light was finite
and that its value was 2.25108 m/s.
Fizeau’s experiment of 1849 measured the value to be
about 3108 m/s. (done before Maxwell’s work)
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When light travels though a material medium, its speed is
reduced.
c
v
n
where v is the speed of light in the medium and n is the
refractive index of the medium.
When a wave passes from one medium to another the
frequency stays the same, but the wavelength is changed.
A dispersive medium is one in which the index of refraction
depends on the wavelength of light.
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Example (text problem 22.22): In order to study the
structure of a crystalline solid, you want to illuminate it with
EM radiation whose wavelength is the same as the spacing
of the atoms in the crystal (0.20 nm).
(a) What is the frequency of the EM radiation?
3.0 108 m/s
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f  

1
.
5

10
Hz
9
 0.2010 m
c
(b) In what part of the EM spectrum does it lie?
X-ray
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§22.5 Properties of EM Waves
All EM waves in vacuum travel at the “speed of light” c.
Both the electric and magnetic fields have the same
oscillation frequency f.
The electric and magnetic fields oscillate in phase.
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The fields are related by the relationship
E ( x, y, z, t )  cB( x, y, z, t )
EM waves are transverse. The fields oscillate in a direction
that is perpendicular to the wave’s direction of travel. The
fields are also perpendicular to each other.
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The direction of propagation is given by
E B.
The wave carries one-half of its energy in its electric field
and one-half in its magnetic field.
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§22.8 The Doppler Effect
For EM waves, the Doppler shift formula is
fo  f s
v
c
v
1
c
1
where fs is the frequency emitted by the source, fo is the
frequency received by the observer, v is the relative velocity
of the source and the observer, and c is the speed of light.
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If the source and observer are approaching each other, then
v is positive, and v is negative if they are receding.
When v/c << 1, the previous expression can be approximated
as:
 v
f o  f s 1  
 c
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Example (text problem 22.56): Light of wavelength 659.6 nm
is emitted by a star. The wavelength of this light as
measured on Earth is 661.1 nm. How fast is the star moving
with respect to the Earth? Is it moving toward Earth or away
from it?
The wavelength shift is small ( << ) so v << c.
 v
f o  f s 1  
 c
c / o
s
v fo
 1 
 1   1  0.0023
c fs
c / s
o
v  6.8 105 m/s  680 km/s
Star is receding.
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Summary
•Maxwell’s Equations
•Electric and Magnetic Dipole Antennae
•EM Spectrum
•Properties of EM Waves
•Doppler Effect
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