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SCS 139II.5 Electromagnetic Waves

Dr. Prapun Suksompongprapun@siit.tu.ac.th

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

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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

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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

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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

7

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.”

7 Equations

8

that changed the world

… and still rule everyday

life

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Traveling Electromagnetic Wave

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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)

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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

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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!

Electromagnetic Spectrum

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[Gosling , 1999, Fig 1.1 and 1.2]

c f

Wavelength

Frequency

83 10 m/s

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.

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Thailand Freq. Allocations Chart

21http://www.ntc.or.th/uploadfiles/freq_chart_thai.htm

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 ]