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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

http://www.youtube.com/watch?v=AU8PId_6xec

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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

Electromagnetic radiation

(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

a receiver circuit.

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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http://www.youtube.com/watch?v=SJ-8yFgWt-c

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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