SCS 139
II.5 Electromagnetic Waves
Dr. Prapun Suksompong
[email protected]
Office Hours:
1
Library (Rangsit) Mon
BKD 3601-7
Wed
16:20-16:50
9:20-11:20
Reference
 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
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Wave, Qualitatively
Integrals are taken over a closed Gaussian surface
Gauss’s Law
 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.
E 
0
 GLB: Gauss’s Law for Magnetic Fields:
Net magnetic flux through any closed
Gaussian surface is zero.
B 
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 E  dA 
qenc
 B  dA  0
Implication of GLB
 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.
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Laws of Induction
 Faraday’s law of induction: A changing magnetic flux
induces an electric field.
dB
E

ds



dt

dB
dt
Electric field induced along a closed loop by the changing magnetic
flux encircled by that loop.
 Maxwell’s law of induction: A changing electric flux
induces a magnetic field.
 B ds  0 0
dE
dt
Magnetic field induced along a closed loop by the changing electric
flux in the region encircled by that loop.
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Ampere–Maxwell Law
Magnetic field is produced by a current and/or by a
changing electric field:
dE
 B ds  0 0 dt  0ienc  0id,enc  0ienc
Displacement current (id)
dE
 B ds  0 0 dt
Maxwell’s Law of Induction
(Maxwell’s Extension of Ampere’s Law)
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 B ds   i
0 enc
Ampere’s Law
Maxwell’s Equations
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.
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Einstein described Maxwell’s accomplishments as “the most profound
and the most fruitful that physics has experienced since the time of Newton.”
7 Equations
that changed the world
… and still rule everyday
life
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Traveling Electromagnetic Wave
 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.
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Characteristics of EM Waves (1)
 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
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Characteristics of EM Waves (2)
 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 𝐵
oscillating parallel to the z axis,
amplitudes of the fields
Electric wave component
E  Em cos( kx  t )
Magnetic wave component
B  Bm cos( kx  t )
angular wave number
Wave speed
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c

k

1
0 0

amplitude ratio
Em E

Bm B
angular frequency
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,
magnitude ratio
EM spectrum (Maxwell’s Rainbow)
 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.
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[http://www.nature.com/scitable/blog/the-artful-brain/alternate_realities]
Ultraviolet Vision
 Many insects and birds can see ultraviolet wavelengths that
humans cannot.
Human vision
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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 (redblind) 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]
Ultraviolet Vision
Gazania flower shot using white light
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Gazania flower shot using ultraviolet light to make
otherwise invisible patterns visible.
Ultraviolet Vision
 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!
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Electromagnetic Spectrum
[Gosling , 1999, Fig 1.1 and 1.2]
c f
3  108 m/s
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Wavelength
Frequency
[http://www.britannica.com/EBchecked/topic-art/585825/3697/Commercially-exploited-bands-of-the-radio-frequency-spectrum]
Radio-frequency spectrum
 Commercially exploited bands
c f
3  108 m/s
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Wavelength
Frequency
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
 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; คณะกรรมการกิจการกระจายเสียง กิจการโทรทัศน์และกิจการ
โทรคมนาคมแห่งชาติ ; กสทช.)
 Blocks of spectrum are now commonly assigned through spectral
auctions to the highest bidder.
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Thailand Freq. Allocations Chart
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http://www.ntc.or.th/uploadfiles/freq_chart_thai.htm
News: Thailand 2.1GHz Auction
  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
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Application: GPS
 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.
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GPS Satellites
 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.
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How GPS Works?
 A GPS receiver measuring its distance from a group of




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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
 Intersection of three sphere narrows down the location to
just two points.
[Lathi ,1998, Fig. 9.6 ]
 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.
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