Transcript chapter34

Chapter 34
Electromagnetic Waves and light
Electromagnetic waves in our life
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Microwave oven, EM wave is used to deliver energy.
Radio/TV, cell phones, EM wave is used to carry
information.
Telephone and internet: electrical signal in copper
wires is NOT EM wave, but fiber optics is the
backbone of the network.
The wireless connection for your laptop, the bluetooth
headset for your iPod, …
Without EM wave, there would be no life on Earth.
– why?
Plane EM waves, the simplest form
A review: a wave is a disturbance
that propagates through space
and time, usually with
transference of energy
An EM wave is the oscillation
between electric and magnetic
fields.
The electric field E oscillates in
the x-y plane, along the y direction;
the magnetic field B oscillates in
the x-z plane and along the z
direction. The EM wave
propagates along the x axis, with
the speed of light c, in vacuum.
PLAY
ACTIVE FIGURE
Wave propagation
A sinusoidal EM wave moves
in the x direction with the
speed of light c, in vacuum.
The magnitudes E and B of the fields depend upon
x (the location in the wave) and t (time) only:
E  Emax cos  kx  t 
B  Bmax cos  kx  t 
Here k is the wave number.
The electric field direction (here the y axis direction) is
called the polarization direction. When this polarization
direction does not change with time, it is said that the EM
wave is linearly polarized. Another common polarization is
the circular polarization, when the electric field direction
moves in a circle
PLAY
ACTIVE FIGURE
Rays, wave front and plane wave
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A ray is a line along which the
wave travels.
In a homogeneous medium for
EM waves (vacuum being one),
rays follow straight lines.
The surface that connects
points of equal phase in a
group of rays (waves) is called
the wave front. When this
wave front is a geometric plane,
this collection of waves is called
a plane wave.
Maxwell’s equations of EM waves
Gauss’s Law of electric field:
 E   E  dA 
q
0
Gauss’s Law of magnetic field:  B   B  dA  0
d B
emf  
Faraday’s Law of induction:
dt
Here the emf is actually distributed
over the conducting ring. From the
definition of potential, V  E  ds
we know that the emf here equals:
emf 
 E  ds
So Faraday’s Law of induction now reads:
d B
 E  ds  
dt
Maxwell’s modification to Ampere’s
Law
Ampere’s Law of magnetic field:
Here the current flows in a wire.
 B  ds   I
Now let’s examine the case when there
is a capacitor in the current path:
Ampere’s Law applies to the wire part.
The current flows into the upper plate
of the capacitor, flows out from the
lower plate, creating charge
accumulation in the capacitor and build
up the electric field. Constructing a
Gaussian surface which has two parts:
S1 and S2.
0
Maxwell’s modification to Ampere’s
Law
Gauss’ Law says that:
 E  E  S2  ES 2 
So one has:
q
0
d E d  q  1 dq 1
  
 Id
dt
dt   0   0 dt  0
Here Id is called the displacement
current. With it, the Ampere’s Law is
now completed as:
d E
 B  d s  0  I  I d   0 I   0 0 dt
It is often called Ampere-Maxwell Law
Maxwell’s equations of EM waves
q
Gauss’s Law of electric field:
Gauss’s Law of magnetic field:
Faraday’s Law of induction:
Ampere-Maxwell Law:
 E  dA  
 B  dA  0
d
 E  d s   dt
 B  ds   I   
0
B
0
0
0
d E
dt
These four equations are called Maxwell’s Equations.
These are the integral forms. The differential forms are:
E 
q
0
 B  0
B
E  
t
E
  B  0 J   0  0
t
With Lorenz force Law,
F  qE  qv  B
we complete the laws of
classical electromagnetism.
James Clerk Maxwell
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1831 – 1879
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Scottish physicist
Provided a mathematical theory
that showed a close relationship
between all electric and magnetic
phenomena
His equations predict the
existence of electromagnetic
waves that propagate through
space
His equations unified the electric
and magnetic fields, and provide
foundations to many modern
scientific studies and applications.
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Energy in EM waves
From Maxwell’s equations, one can prove:
1
The speed of light is c 
 0 0
E
c
The electric field to magnetic field ratio is
B
The energy flow in an EM wave is
described by the Poynting vector
S
1
EB
0
1
B2
2
The energy density is uB  uE   0 E 
2
2 0
The wave energy intensity is
2
2
Emax Bmax Emax
cBmax
I  Sav 


2 0
2 0 c 2 0
Producing EM waves through an
antenna
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Use a half-wave antenna as an example
Two conducting rods are connected to a
source of alternating voltage
The length of each rod is one-quarter of
the wavelength of the radiation to be
emitted
The oscillator forces the charges to
accelerate between the two rods
The antenna can be approximated by an
oscillating electric dipole
The magnetic field lines form concentric
circles around the antenna and are
perpendicular to the electric field lines at
all points
The electric and magnetic fields are 90o
out of phase at all times
This dipole energy dies out quickly as
you move away from the antenna
The EM wave
Spectrum
Gamma
and X rays
Ultraviolet, UV
Infrared
Microwaves
Radio waves
Visible light
Notes on the EM wave Spectrum
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Radio Waves
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Microwaves
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Wavelengths of about 10-3 m to 7 x 10-7 m
Incorrectly called “heat waves”
Produced by hot objects and molecules
Readily absorbed by most materials
Visible light
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Wavelengths from about 0.3 m to 10-4 m
Well suited for radar systems
Microwave ovens are an application
Infrared waves
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Wavelengths of more than 104 m to about 0.1
m
Used in radio and television communication
systems
Part of the spectrum detected by the human
eye
Most sensitive at about 5.5 x 10-7 m (yellowgreen)
Ultraviolet, X-rays and Gamma rays
More About Visible Light
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Different frequencies (or wavelengths in vacuum)
correspond to different colors
The range of wavelength in vacuum is from red (λ
~ 7 x 10-7 m) to violet (λ ~4 x 10-7 m)
More notes on the EM wave Spectrum
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Ultraviolet light
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Covers about 4 x 10-7 m to 6 x 10-10 m
Sun is an important source of uv light
Most uv light from the sun is absorbed in the
stratosphere by ozone
X-rays
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Wavelengths of about 10-8 m to 10-12 m
Most common source is acceleration of highenergy electrons striking a metal target
Used as a diagnostic tool in medicine
More notes on the EM wave Spectrum
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Gamma rays
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Wavelengths of about 10-10 m to 10-14 m
Emitted by radioactive nuclei
Highly penetrating and cause serious damage
when absorbed by living tissue
Looking at objects in different portions of the
spectrum can produce different information
Wavelengths and Information
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These are images of
the Crab Nebula
They are (clockwise
from upper left) taken
with
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x-rays
visible light
radio waves
infrared waves