# Electromagnetic Waves

Urban and Civil

Nov 16, 2013 (4 years and 5 months ago)

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Electromagnetic Waves
•Production of EM waves
•Maxwell’s Equations
•Antennae
•The EM Spectrum
•Speed of EM Waves
•Energy Transport
•Polarization
•Doppler Effect
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Electromagnetic Waves
…are waves composed of undulating electrical fields and
magnetic fields. The different kinds of electromagnetic
waves, such as light and radio waves, form the
electromagnetic spectrum. All electromagnetic waves
have the same speed in a vacuum, a speed expressed
by the letter c(the speed of light) and equal to about
186,000 miles (or 300,000 kilometers) per second.
…transport energy, due to oscillating electric and magnetic
fields,
…are called electromagnetic radiation, light, or
photons.
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Fundamental Question:
For two charges q and Q the strength of attraction depends on
distance between both charges (Coulombs Law). Now we grap
charge Q and jiggle it around. The jiggling causes the distance
attraction to vary.
How does charge q know that I am jiggling charge Q?
We create a disturbance which launches an electromagnetic
wave into the universe. The wave tells the Universe we
generated an electric disturbance which propagates away
from the point of the disturbance

(Predicted by Clerk Maxwell (1831-1879) in 1864)
The faster we jiggle the charge the shorter the wavelength
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Maxwell’s theoryis a mathematical formulation that
relates electric and magnetic phenomena.
His theory, among other things, predicted that electric
and magnetic fields can travel through space as
waves.
The uniting of electricity and magnetism resulted in the
Theory of Electromagnetism.
Maxwell predicted (in 1864)
:
A changing electric field produces a magnetic field.
Accelerating chargeswill radiate electromagnetic waves.
Electromagnetic waves travel at the speed of light c:
c 
3 ×
××
×108
m/s
The electric and magnetic fields in the wave are
fluctuating.
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Maxwell’s Equations
Integral form in the absence of magnetic or polarizablemedia:
I. Gauss' law for electricity
II. Gauss' law for magnetism
III. Faraday's law of induction
IV. Ampere -Maxwell’slaw
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In 1887, Heinrich Hertzgenerated and detected electromagnetic
waves in his lab.
The waves radiated from a transmitter circuit and were detected in
Hertz used the fact that electrical circuits have resonant
frequencies just like mechanical systems do.
Conceptual Schematic of Hertz's Experiment
http://people.deas.harvard
.edu/~jones/cscie129/nu_l
ectures/lecture6/hertz/Her
tz_exp.html
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In 1675 the Danish atronomerOle
Römer(1644-1710) presented a
calculation of the speed of light. He
used the time between eclipses (the
times between eclipses -particularly
Io's-got shorter as Earth approached
Jupiter, and longer as Earth moved
farther away of Jupiter’s Gallilean
Satellites to show that the speed of
light was finite and that its value was
2.25×108
m/s.
This second inequality appears to be
due to light taking some time to reach
us from the satellite; light seems to
take about ten to eleven minutes to
cross a distance equal to the half-
diameter of the terrestrial orbit.
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The frechphysicist Armand HippolyteLouis
Fizeau(September 23, 1819-1896 discovered in
1948 the Doppler effect for electromagnetic waves
and in 1849 he published the first results obtained by
his method for determining the speed of light
(Fizeau-Foucault apparatus), Fizeau’sexperiment of
1849 measured the value to be about 3×108
m/s.
(Fizeau'svalue for light's speed was about 5% too
high )
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Production of EM Waves
A stationary charge produces an electric field.
A charge moving at constant speed produces electric
and magnetic fields.
A charge that is accelerated will produce variable electric
and magnetic fields. These are electromagnetic 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 finite-
sized wave).
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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.
k
c
k
v
tkxzBB
tkxyEE
π
λ
ω
ω
ω
2
)cos(
ˆ
)cos(
ˆ
0
0
=
==
−=

=
Waveapplet
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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…but only when fields are related by the relationship
),,,(),,,(tzyxcBtzyxE
=
A EM wave carries one-half of its
energy in its electric field and one-
half in its magnetic field.
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The direction of propagation
is given by:
.BE
×
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B
E
15
.BE
×
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Antenna
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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Example A dipole radio antenna has its rod-shaped antenna
oriented vertically. At a point due south of the transmitter,
what is the orientation of the emitted wave’s B-field?
Looking down from
above the Electric
Dipole antenna
N
W
S
E
South of the transmitter, the E-field is directed into/out of
the page. The B-field is perpendicular to this direction and
also to the direction of travel (South). The B-field must be
east-west.
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Example The electric field of an EM wave is given by:
0
0
6
sin
=
=

+−=
y
x
mz
E
E
tkyEE
π
ω
(a) In what direction is this wave traveling?
The wave does not depend on the coordinates x or z; it
must travel parallel to the y-axis. The wave travels in the +y
direction.
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(b) Write expressions for the magnetic field of this wave.
B
E
×
must be in the +y-direction
(Eis in the z-direction).
Therefore,B must be along the x-axis.
c
E
B
tkyBB
BB
m
m
mx
yz
=

+−=
=
=
with
6
sin
0,0
π
ω
Example continued:
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The EM Spectrum:
Energy increases with increasing frequency.
http://www.lon-capa.org/~mmp/applist/Spectrum/s.htm
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