Lecture 34: MON 13 APR Ch.33.1

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Lecture 34 MON 13 APR Ch.33.13,57 EM Waves
James Clerk Maxwell (1831-1879)
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MT03 Avg 65/100
Q1/P3 K. Schafer Office hours MW 130-230 pm
222B Nicholson P1/Q2 J. Dowling Office hours MWF
1030-1130 am 453 Nicholson P2/Q3 M. Gaarde
Office hours TTh 230-330 pm 215B
Nicholson P3/Q2 C. Buth Office hours MF
230-330 pm 222A Nicholson
A 90-100 B 80-89 C 60-79 D
50-59
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Right Hand Rule Vector Addition!
Right Hand Rule BIgtBII Since I is Closer!
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Maxwell, Waves and Light
A solution to the Maxwell equations in empty
space is a traveling wave
electric and magnetic forces can travel!
The electric waves travel at the speed of light!
Light itself is a wave of electricity and
magnetism!
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Electromagnetic Waves
A solution to Maxwells equations in free space
Visible light, infrared, ultraviolet, radio
waves, X rays, Gamma rays are all electromagnetic
waves.
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Radio waves are reflected by the layer of the
Earths atmosphere called the ionosphere. This
allows for transmission between two points which
are far from each other on the globe, despite the
curvature of the earth. Marconis experiment
discovered the ionosphere! Experts thought he was
crazy and this would never work.
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Maxwells Rainbow
The wavelength/frequency range in which
electromagnetic (EM) waves (light) are visible is
only a tiny fraction of the entire
electromagnetic spectrum.
(33-2)
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The Traveling Electromagnetic (EM) Wave,
Qualitatively
An LC oscillator causes currents to flow
sinusoidally, which in turn produces oscillating
electric and magnetic fields, which then
propagate through space as EM waves.
(33-3)
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Mathematical Description of Traveling EM Waves
All EM waves travel a c in vacuum
Wavenumber
EM Wave Simulation
Frequency
Vacuum Permittivity
Vacuum Permeability
(33-5)
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The Poynting Vector Points in Direction of
Power Flow
Electromagnetic waves are able to transport
energy from transmitter to receiver (example
from the Sun to our skin).
The power transported by the wave and
its direction is quantified by the Poynting
vector.
John Henry Poynting (1852-1914)
For a wave, since E is perpendicular to B
In a wave, the fields change with time. Therefore
the Poynting vector changes too!! The direction
is constant, but the magnitude changes from 0 to
a maximum value.
Units Watt/m2
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EM Wave Intensity, Energy Density
A better measure of the amount of energy in an EM
wave is obtained by averaging the Poynting vector
over one wave cycle. The resulting quantity is
called intensity. Units are also Watts/m2.
The average of sin2 over one cycle is ½
or,
Both fields have the same energy density.
The total EM energy density is then
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Solar Energy
The light from the sun has an intensity of about
1kW/m2. What would be the total power incident on
a roof of dimensions 8m x 20m ?
I  1kW/m2 is power per unit area. P  IA  (103
W/m2) x 8m x 20m  0.16 MegaWatt! !
The solar panel shown (BP-275) has dimensions
47in x 29in. The incident power is then 880 W.
The actual solar panel delivers 75W (4.45A at
17V) less than 10 efficiency.
The electric meter on a solar home runs backwards
Entergy Pays YOU!
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EM Spherical Waves
The intensity of a wave is power per unit area.
If one has a source that emits isotropically
(equally in all directions) the power emitted by
the source pierces a larger and larger sphere as
the wave travels outwards 1/r2 Law!
So the power per unit area decreases as the
inverse of distance squared.
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Example
A radio station transmits a 10 kW signal at a
frequency of 100 MHz. At a distance of 1km from
the antenna, find the amplitude of the electric
and magnetic field strengths, and the energy
incident normally on a square plate of side 10cm
in 5 minutes.
Received energy
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Radiation Pressure
Waves not only carry energy but also momentum.
The effect is very small (we dont ordinarily
feel pressure from light). If light is completely
absorbed during an interval Dt, the momentum
transferred is given by
F
and twice as much if reflected.
A
Newtons law
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Now, supposing one has a wave that hits a
surface of area A (perpendicularly), the amount
of energy transferred to that surface in time Dt
will be
therefore
Radiation pressure
N/m2
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Radiation Pressure Comet Tails
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Solar Sails Photons Propel Spacecraft!
StarTrek DS9
NASA Concept
NASA Demo
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EM waves polarization
Radio transmitter
If the dipole antenna is vertical, so will be the
electric fields. The magnetic field will
be horizontal.
The radio wave generated is said to be
polarized.
In general light sources produce unpolarized
wavesemitted by atomic motions in random
directions.
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EM Waves Polarization
Completely unpolarized light will have equal
components in horizontal and vertical directions.
Therefore running the light through a polarizer
will cut the intensity in half II0/2
When polarized light hits a polarizing
sheet, only the component of the field aligned
with the sheet will get through.
And therefore
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Example
Initially unpolarized light of intensity I0 is
sent into a system of three polarizers as shown.
What fraction of the initial intensity emerges
from the system? What is the polarization of the
exiting light?

• Through the first polarizer unpolarized to
  polarized, so I1½I0.
• Into the second polarizer, the light is now
  vertically polarized. Then, I2 I1cos260o 1/4
  I1 1/8 I0.
• Now the light is again polarized, but at 60o.
  The last polarizer is horizontal, so I3
  I2cos230o 3/4 I2 3 /32 I0 0.094 I0.
• The exiting light is horizontally polarized, and
  has 9 of the original amplitude.

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