Electromagnetic Waves
http://www.youtube.com/watch?v=AU8PId_6xec
•Production of EM waves
•Maxwell’s Equations
•Antennae
•The EM Spectrum
•Speed of EM Waves
•Energy Transport
•Polarization
•Doppler Effect
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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 theory is 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 charges will 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 polarizable media:
I. Gauss'law for electricity
closed surface
κel
II. Gauss'law for magnetism
III. Faraday'
s law of induction
closed path
IV. Ampere -Maxwell’slaw
closed path
κM
open surface
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In 1887, Heinrich Hertz generated 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 atronomer Ole
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 halfdiameter of the terrestrial orbit.
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The frech physicist Armand Hippolyte Louis
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’s experiment of
1849 measured the value to be about 3×108 m/s.
(Fizeau'
s value 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 finitesized 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.
Waveapplet
E = E0 yˆ cos(kx − ωt )
B = B0 zˆ cos(kx − ωt )
v=
ω
=c
k
2π
λ=
k
EM waves are transverse. The fields oscillate in a direction that is
perpendicular to the wave’s direction of travel. The fields are also10
perpendicular to each other.
…but only when fields are related by the relationship
E ( x, y, z , t ) = cB( x, y, z , t )
A EM wave carries one-half of its
energy in its electric field and onehalf in its magnetic field.
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The direction of propagation
is given by:
E× B.
http://www.youtube.com/watch?v=SJ-8yFgWt-c
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13
E
B
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E× B.
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Antenna
An electric field parallel to an antenna (electric dipole)
will “shake” electrons and produce an AC current.
16
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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The EM Spectrum:
http://www.lon-capa.org/~mmp/applist/Spectrum/s.htm
Energy increases with increasing frequency.
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electronic
sound
Microphone receives sound
wave and converts to
oscillating electrical current
(20 Hz – 20 kHz)
modulator
An electrical “carrier” signal
is produced (90.9 MHz for
WILL FM) indepedently
AM
FM
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http://www.youtube.com/watch?v=SJ-8yFgWt-c
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Computed Axial Tomography (CAT)
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Energy Transport by EM Waves
The intensity of a wave is
I =(
P
A
) avg .
This is a measure of how much energy strikes a surface of
area A every second for normal incidence.
Surface
The rays make a
90° angle with the
surface.
32
Also,
∆E uavV uav A∆x
=
=
= uav c
I=
A∆t A∆t
A∆t
where uav is the average energy density (energy per unit
volume) contained in the wave.
For EM waves:
uav = ε 0 E
2
rms
=
1
µ0
2
Brms
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What if the EM waves strike at non-normal incidence?
Replace A with Acosθ.
θ
Pav = IA cos θ
36
Radiation pressure
…. is the pressure exerted upon any surface exposed to electromagnetic
radiation. If absorbed, the pressure is the energy flux density divided by the
speed of light. If the radiation is totally reflected, the radiation pressure is
doubled. For example, the radiation of the Sun at the Earth has an energy
flux density of 1370 W/m2, so the radiation pressure is 4.6 µPa (absorbed)
If you know the total amount of energy U in a pulse of radiation, as you might for
a laser pulse, then it is most convenient to use formulas for the amount of
momentum p imparted to an object that either absorbs or reflects the pulse:
p
p
The radiation pressure formulas are
Pr
Pr
Because of the factor of c in the denominators of these pressure and momentum
formulas, these effects are usually quite small.
37
Polarization
A wave on a string is linearly polarized.
The vibrations occur in the same plane.
The orientation of this plane determines
the polarization state of a wave.
For an EM wave, the direction of
polarization is given by the direction of
the E-field.
The EM waves emitted by an
antenna are polarized; the E-field is
always in the same direction.
When light is polarized, the electric
field always points in the same
direction.
A source of EM waves is unpolarized if the E-fields are
in random directions.
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A polarizer will transmit linear polarized waves in the same
direction independent of the incoming wave.
It is only the
component of the
wave’s amplitude
parallel to the
transmission axis
that is transmitted.
39
If unpolarized light is incident on
1 polarizer, the intensity of the
light passing through is I= ½ I0.
If the incident wave is already
polarized, then the transmitted
intensity is I=I0cos2θ where θ is
the angle between the incident
wave’s direction of polarization
and the transmission axis of the
polarizer. (Law of Malus)
I1= ½ I0.
I2=I1cos260
I3=I2cos230
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Reflection and Refraction
When a light ray travels from one medium to another, part of the
incident light is reflected and part of the light is transmitted at the
boundary between the two media.
The transmitted part is said to be refracted in the second medium.
http://www.geocities.com/CapeCanaveral/Hall/6645/propagation/propagation.html
*In 1678 the great Dutch physicist Christian Huygens (1629-1695) wrote a treatise called
Traite de la Lumiere on the wave theory of light, and in this work he stated that the wavefront
of a propagating wave of light at any instant conforms to the envelope of spherical wavelets
emanating from every point on the wavefront at the prior instant. From this simple principle
Huygens was able to derive the laws of reflection and refraction
incident ray
reflected ray
refracted ray
The Law of Reflection
For specular reflection the incident angle θi
equals the reflected angle θr:
θi = θr
The angles are
measured relative
to the normal,
shown here as a
dotted line.
The Refraction of Light
The speed of light is different in different materials. We
define the index of refraction, n, of a material to be the ratio
of the speed of light in vacuum to the speed of light in the
material:
n = c/v
When light travels from one medium to another, its velocity
and wavelength change, but its frequency remains
constant. http://www.geocities.com/CapeCanaveral/Hall/6645/propagation/propagation.html
Total Internal Reflection
When light travels from a medium with n1 > n2,
there is an angle, called the critical angle θc, at
which all the light is reflected and none is
transmitted. This process is known as total
internal reflection. The critical angle occurs
when θ2= 90 degrees:
n
sin θ c = 2
n1
The incident ray is both reflected and
refracted.
Total Internal Reflection
Chromatic Dispersion
The index of refraction n encountered by light in any
medium except vacuum depends on the wavelength of the
light. The dependence of n on wavelength implies that
when a light beam consists of rays of different
wavelengths, the rays will be refracted at different angles
by a surface; that is, the light will be spread out by the
refraction. This spreading of light is called chromatic
dispersion, i
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Rainbows
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Polarization by Scattering
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Polarization by Reflection
Brewster's Law
when the light is incident at a
particular incident angle, called
the Brewster angle θB, the
reflected light has only
perpendicular components
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The Doppler Effect
For EM waves, the Doppler shift formula is
fo = f s
v
1+
c
v
1−
c
where fs is the frequency emitted by the source, fo is the
frequency received by the observer, v is the relative velocity
of the source and the observer, and c is the speed of light.
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If the source and observer are approaching each other, then
v is positive, and v is negative if they are receding.
When v/c<<1, the previous expression can be approximated
as:
v
fo ≈ f s 1 +
c
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Summary
•Maxwell’s Equations
•EM Spectrum
•Properties of EM Waves
•Energy Transport by EM Waves
•Polarization
•Doppler Effect
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