Lecture EMwaves

7/27/2019 Lecture EMwaves

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Electromagnetic Waves

Production of EM waves

Maxwells 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 Wavesare waves composed of undulating electrical fields and

magnetic fields. The different kinds of electromagneticwaves, such as light and radio waves, form theelectromagnetic spectrum. All electromagnetic waveshave the same speed in a vacuum, a speed expressedby the letter c (the speed of light) and equal to about186,000 miles (or 300,000 kilometers) per second.

transport energy, due to oscillating electric and magneticfields,

are called electromagnetic radiation, light, orphotons .


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Fundamental Question:

For two charges q and Q the strength of attraction depends ondistance between both charges (Coulombs Law). Now we grapcharge Q and jiggle it around. The jiggling causes the distanceattraction to vary.

How does charge q know that I am jiggling charge Q?

We create a disturbance which launches an electromagneticwave into the universe. The wave tells the Universe wegenerated an electric disturbance which propagates awayfrom 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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Maxwells theory is a mathematical formulation thatrelates electric and magnetic phenomena.His theory, among other things, predicted that electricand magnetic fields can travel through space aswaves .The uniting of electricity and magnetism resulted in theTheory of Electromagnetism .

Maxwell predicted (in 1864) :A changing electric field produces a magnetic field.Accelerating charges will radiate electromagnetic waves.Electromagnetic waves travel at the speed of light c:

c 3 10 8 m/sThe electric and magnetic fields in the wave arefluctuating.


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Maxwells EquationsIntegral form in the absence of magnetic or polarizable media:

I. Gauss' law for electricity

II. Gauss' law for magnetism

III. Faraday's law of induction

IV. Ampere -Maxwellslaw

el

M

closed surface

closed path

closed path open surface


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In 1887, Heinrich Hertz generated and detected electromagneticwaves in his lab.The waves radiated from a transmitter circuit and were detected ina receiver circuit.Hertz used the fact that electrical circuits have resonantfrequencies just like mechanical systems do.

Conceptual Schematic of Hertz's Experiment

http://people.deas.harvard.edu/~jones/cscie129/nu_lectures/lecture6/hertz/Hertz_exp.html


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In 1675 the Danish atronomer Ole

Rmer (1644-1710) presented acalculation of the speed of light. Heused the time between eclipses (thetimes between eclipses -particularly

Io's- got shorter as Earth approachedJupiter, and longer as Earth movedfarther away of Jupiters GallileanSatellites to show that the speed oflight was finite and that its value was2.25 10 8 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 frech physicist Armand Hippolyte Louis

Fizeau (September 23, 1819-1896 discovered in1948 the Doppler effect for electromagnetic wavesand in 1849 he published the first results obtained byhis method for determining the speed of light(Fizeau-Foucault apparatus), Fizeaus experiment of1849 measured the value to be about 3 10 8 m/s.(Fizeau's value for light's speed was about 5% toohigh )


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Production of EM WavesA stationary charge produces an electric field.A charge moving at constant speed produces electricand magnetic fields.

A charge that is accelerated will produce variable electricand magnetic fields. These are electromagnetic waves.

If the charge oscillates with a frequency f, then theresulting 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 Maxwells equations are combined, the solutions areelectric and magnetic fields that vary with position and time.These are EM waves.

An electric field only wave cannot exist, nor can a magneticfield only wave.

k

ck

v

t kx z B B

t kx y E E

2

)cos(

)cos(

0

0

=

==

=

=

Waveapplet

EM waves are transverse. The fields oscillate in a direction that is

perpendicular to the waves direction of travel. The fields are alsoperpendicular to each other.


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but only when fields are related by the relationship

),,,(),,,( t z y xcBt z y x E =

A EM wave carries one-half of itsenergy in its electric field and one-

half in its magnetic field.


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B

E


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.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 amagnetic component. A

magnetic dipole antennacan be oriented so that theB-field passes into and outof the plane of a loop,inducing a current in theloop.

The B-field of an EM wave is perpendicular to its E-fieldand also the direction of travel.


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Example A dipole radio antenna has its rod-shaped antennaoriented vertically. At a point due south of the transmitter,what is the orientation of the emitted waves B-field?

Looking down fromabove the ElectricDipole 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 andalso to the direction of travel (South). The B-field must beeast-west.


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Example The electric field of an EM wave is given by:

0

0

6sin

=

=

+=

y

x

m z

E

E

t ky E E

(a) In what direction is this wave traveling?

The wave does not depend on the coordinates x or z; itmust travel parallel to the y-axis. The wave travels in the +ydirection.


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(b) Write expressions for the magnetic field of this wave.

BE must be in the +y-direction(E is in the z-direction).

Therefore, B must be along the x-axis.

c E

B

t ky B B

B B

mm

m x

y z

=

+=

==

with

6sin

0,0

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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Microphone receives soundwave and converts tooscillating electrical current(20 Hz 20 kHz)

An electrical carrier signal

is produced (90.9 MHz forWILL FM) indepedently

modulator

AMFM

sound electronic

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Lecture EMwaves