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General Physics 203 – Lecture Notes to Electromagnetic Waves – Bjoern Seipel
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Electromagnetic Waves
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.
Transmission of energy through a vacuum or using no medium is accomplished by electromagnetic waves , caused by the oscillation of electric and magnetic fields. They move at a constant speed of 3x10^8 m/s. Often, they are called electromagnetic radiation, light, or photons.
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 and therefore 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
Æ Electromagnetic radiation
(Predicted by Clerk Maxwell (1831-1879) in 1864)
The faster we jiggle the charge the shorter the wavelength
General Physics 203 – Lecture Notes to Electromagnetic Waves – Bjoern Seipel
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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 × 10
8
m/s
- The electric and magnetic fields in the wave are
fluctuating.
General Physics 203 – Lecture Notes to Electromagnetic Waves – Bjoern Seipel
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A traveling electromagnetic wave produced by
an ac generator attached to an antenna
At t = 0 the electric field at point P is downward.
After one quarter of a cycle, at t = 1/4 T, the electric field at P vanishes.
A short time later the electric field at P is still downward, but now with a reduced magnitude. Note that the field created at t = 0 has moved to point Q. The decreasing electric field at point P creates a magnetic field at point Q pointing into the viewgraph
General Physics 203 – Lecture Notes to Electromagnetic Waves – Bjoern Seipel
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When the oscillator has
completed half a cycle, t =
1/2 T, the field at point P is
upward and of maximum
magnitude.
At t = 3/4 T the field at P
vanishes again. The fields
produced at earlier times
continue to move away
from the antenna.
The charge on the
antenna has reversed
polarity now, and the
electric field at P points
upward.
General Physics 203 – Lecture Notes to Electromagnetic Waves – Bjoern Seipel
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Properties of EM Waves
The radiated EM waves have certain
properties:
- EM waves all travel at the speed of light c.
c
2
- The E and B fields are perpendicular to
each other.
- The E and B fields are in phase (both reach
a maximum and minimum at the same
time).
- The E and B fields are perpendicular to the
direction of travel ( transverse waves ).
General Physics 203 – Lecture Notes to Electromagnetic Waves – Bjoern Seipel
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Basic elements of a tuning circuitused to receive radio waves.First, an incoming wave sets upan alternating current in theantenna. Next, the resonancefrequency of the LC circuit isadjusted to match the frequencyof the radio wave, resulting in arelatively large current in thecircuit. This current is then fedinto an amplifier to furtherincrease the signal.
Receiving radio waves
Electromagnetic radiation is greatestwhen charges accelerate at rightangles to the line of sight. Zeroradiation is observed when thecharges accelerate along the line ofsight.
General Physics 203 – Lecture Notes to Electromagnetic Waves – Bjoern Seipel
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Light
LiL
iggh
ht
t i
iss a
an
n e
el
leec
ct
tr ro
om
ma
ag
gn
ne
et
ti icc w
wa
av
ve
e
c =^ c
=
λλ
f^ f
≈≈
33
××
101
0
88
m/m
/s s
As light waves travel through space they:
transport energy
transport momentum
The energy density,
u
, of an electromagnetic wave:
2 1 2 0
2 (^12) 2 0 12
0
0
B
E
B
E
u
μ
μ
ε^
=
=
=
cB
E
=
General Physics 203 – Lecture Notes to Electromagnetic Waves – Bjoern Seipel
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Walker Problem 42, pg. 846
What is the rms value of the electricfield in a sinusoidal electromagneticwave that has a maximum electric fieldof 75 V/m?
General Physics 203 – Lecture Notes to Electromagnetic Waves – Bjoern Seipel
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Walker Problem 26, pg. 845Find the frequency of blue light with awavelength of 470 nm.Walker Problem 38, pg. 846
As you drive by an AM radio station, you notice asign saying that its antenna is 122 m high. If thisheight represents one quarter-wavelength of itssignal, what is the frequency of the station?
General Physics 203 – Lecture Notes to Electromagnetic Waves – Bjoern Seipel
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adio (0.4 GHz) Atomic Hydrogen Radio (2.7 GHz) MolecularHydrogen Infrared Mid Infrared Near Infrared Optical X-Ray Gamma Ray Finder From http://adc.gsfc.nasa.gov
Galactice latitude is measured from the galactic plane ( (Earth latitude is measured from the equator), and galactic
longitude is measured from the direction to the galactic center (Earth longitude is measured from London's Greenwich Observatory).
General Physics 203 – Lecture Notes to Electromagnetic Waves – Bjoern Seipel
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Example:A space ship heading towards a stop light – red = 750nm – see the light to be shifted togreen = 500nm. What is the speed of the space ship?Now
f^
c
c
c
c
u
c
u
λ λ
λ
= ′^
−
So we solve for u in the lower equation.
General Physics 203 – Lecture Notes to Electromagnetic Waves – Bjoern Seipel
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A beam of light that is:•^
polarized in the vertical direction
: The
electric field points in the vertical direction.
(b)
unpolarized
: Superposition of many
beams, approximately parallel, but eachwith random polarization. Every atom inthe filament of an incandescent bulbradiates a separate wave with randomphase and random polarization.
Polarization
When light is polarized, the electricfield always points in the samedirection.
General Physics 203 – Lecture Notes to Electromagnetic Waves – Bjoern Seipel
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Polarization by Scattering or Reflection Polarization is also used in the entertainment industry to produce and show 3-D movies!
