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SCS 139II.5 Electromagnetic Waves
Dr. Prapun [email protected]
Office Hours:
Library (Rangsit) Mon 16:20-16:50
BKD 3601-7 Wed 9:20-11:20
Reference
2
Principles of Physics
Ninth Edition, International Student Version
David Halliday, Robert Resnick,
and JearlWalker
Chapter 32
32-2 Gauss’ Law for Magnetic Fields
32-3 Induced Magnetic Fields
32-5 Maxwell’s Equations
Chapter 33
33-2 Maxwell’s Rainbow
33-3 The Traveling Electromagnetic
Wave, Qualitatively
Gauss’s Law
3
GLE: Gauss’s Law for Electric Fields: The net electric
flux through a closed Gaussian surface is proportional to the
net electric charge qenc enclosed by the surface.
GLB: Gauss’s Law for Magnetic Fields:
Net magnetic flux through any closed
Gaussian surface is zero.
0B B dA
enc
0
E
qE dA
Inte
gral
s ar
e ta
ken
over
a c
lose
d G
auss
ian
surf
ace
Implication of GLB
4
Magnetic monopoles (single magnetic poles) do not exist (as far as we know).
The simplest magnetic structure that can exist is a magnetic dipole
which consists of both a source and a sink for the field lines.
Thus, there must always be as much magnetic flux into the surface as out of it, and the net magnetic flux must always be zero.
If you break a magnet, each fragment becomes a separate magnet, with its own north and south poles.
Even if we break the magnet down to its individual atoms and then to its electrons and nuclei. Each fragment still has a north pole and a south pole.
Laws of Induction
5
Faraday’s law of induction: A changing magnetic flux
induces an electric field.
Maxwell’s law of induction: A changing electric flux
induces a magnetic field.
Bd
dt
Bd
E dsdt
0 0Ed
B dsdt
Electric field induced along a closed loop by the changing magnetic
flux encircled by that loop.
Magnetic field induced along a closed loop by the changing electric
flux in the region encircled by that loop.
Ampere–Maxwell Law
6
Magnetic field is produced by a current and/or by a
changing electric field:
0 encB ds i 0 0E
dtd
dB s
0 00 d,e 0nc0enc enE
cid
d isdt
B i
Displacement current (id)
Maxwell’s Law of Induction
(Maxwell’s Extension of Ampere’s Law)
Ampere’s Law
Maxwell’s Equations
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Maxwell’s equations, displayed below summarize
electromagnetism and form its foundation, including optics.
James Clerk Maxwell (1831–1879) was the first person to truly understand
the fundamental nature of light.
Einstein described Maxwell’s accomplishments as “the most profound
and the most fruitful that physics has experienced since the time of Newton.”
Traveling Electromagnetic Wave
10
Do not require material medium. Can travel across empty space.
The magnetic field varies sinusoidally and induces (via Faraday’s
law of induction) a perpendicular electric field that also varies
sinusoidally.
Electric field is varying sinusoidally and induces (via Maxwell’s law
of induction) a perpendicular magnetic field that also varies
sinusoidally.
And so on.
The two fields continuously create each other via induction, and
the resulting sinusoidal variations in the fields travel as a
electromagnetic wave.
Characteristics of EM Waves (1)
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Transverse wave: 𝐸 and
𝐵 are always perpendicular to the direction in which the wave travels.
𝐸 is always perpendicular to
𝐵 .
The cross product, 𝐸
𝐵 gives the direction of propagation.
snapshot
Characteristics of EM Waves (2)
12
The 𝐸 and
𝐵 fields vary with the same frequency and in-phase
with each other.
For an EM wave that is assume that is traveling positive direction
of an x axis, with 𝐸 oscillating parallel to the y axis, and
𝐵oscillating parallel to the z axis,
cos( )
cos( )
m
m
E E kx t
B B kx t
amplitudes of the fields
angular frequencyangular wave number
Electric wave component
Magnetic wave component
0 0
1 m
m
E Ec
k B B
Wave speed
amplitude ratio magnitude ratio
The meter has now been defined so that the
speed of light (any EM wave) in vacuum has
the exact value c = 299 792 458 m/s,
EM spectrum (Maxwell’s Rainbow)
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We now know a wide spectrum (or range) of electromagnetic
(EM) waves.
Certain regions are identified by familiar labels. These labels
denote roughly defined wavelength ranges within which certain
kinds of sources and detectors
of EM waves are
in common use.
Ultraviolet Vision
14
Many insects and birds can see ultraviolet wavelengths that
humans cannot.
[http://www.nature.com/scitable/blog/the-artful-brain/alternate_realities]
UV Vision
(bright = UV).
The center target
is vastly larger than
the version we see.
Also observe a
faint UV glow in
the center
Simulated (red-
blind) bee vision
(UV+G+B)
Some species, such as
birds, along with most
reptiles, have four types
of photoreceptors
(UV+R+G+B)
[Dr.Klaus Schmitt]
Human vision
Ultraviolet Vision
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Gazania flower shot using white light Gazania flower shot using ultraviolet light to make
otherwise invisible patterns visible.
Ultraviolet Vision
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Many birds with ultraviolet vision have ultraviolet patterns on their bodies that make them even more vivid to each other than they appear to us.
Ultraviolet reflecting plumage in starlings had profound effects on observed mating preferences, while plumage in the human visible spectrum did not predict choice. Their ultraviolet feathers are part of their mating call!
Radio-frequency spectrum
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Commercially exploited bands
c f
Wavelength
Frequency
83 10 m/s
[http://www.britannica.com/EBchecked/topic-art/585825/3697/Commercially-exploited-bands-of-the-radio-frequency-spectrum]
Note that the freq. bands are
given in decades; the VHF band
has 10 times as much frequency
space as the HF band.
Spectrum Allocation
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Spectral resource is limited.
Most countries have government agencies responsible for allocating and controlling the use of the radio spectrum.
Commercial spectral allocation is governed globally by the International Telecommunications Union (ITU)
ITU Radiocommunication Sector (ITU-R) is responsible for radio communication.
in the U.S. by the Federal Communications Commission (FCC) in Europe by the European Telecommunications Standards Institute
(ETSI) in Thailand by the National Broadcasting and Telecommunications
Commission (NBTC; คณะกรรมการกจิการกระจายเสยีง กจิการโทรทศัน์และกจิการ
โทรคมนาคมแห่งชาต ิ; กสทช.)
Blocks of spectrum are now commonly assigned through spectral auctions to the highest bidder.
News: Thailand 2.1GHz Auction
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4.5bn baht per license (freq chunk)
1 license (chunk) = 5 MHz (UL) + 5 MHz (DL)
450 million baht per MHz
30 million baht per MHz per year
Application: GPS
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GPS = Global Positioning System
Original application in the (US) military
Created in the early 1990s.
Allow a person to determine the time and the person's
precise location (latitude, longitude, and altitude) anywhere
on earth.
GPS Satellites
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A minimum of 24 GPS satellites are in orbit at 20,200
kilometers (12,600 miles) above the Earth.
The satellites are spaced so that from any point on Earth, at
least four satellites will be above the horizon.
How GPS Works?
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A GPS receiver measuring its distance from a group of
satellites in space which are acting as precise reference points.
All the satellites have atomic clocks of unbelievable precision on
board and are synchronized.
The satellite are continuously transmitting the information about
their location and time.
GPS receiver on the ground is in synchronism with the satellites.
Off by an (unknown) amount .
For now, assume = 0.
By measuring the propagation time, the receiver can compute
distance d from that satellite.
GPS-Trilateration
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Intersection of three sphere narrows down the location to
just two points.
In practice, there are four unknowns, the coordinates in the
three-dimensional space of the user along with within the
user’s receiver.
Need a distance measurement from a fourth satellite.
[Lathi ,1998, Fig. 9.6 ]