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Chapter 2 1
Outline
Reading: L ivingston, Chapter 2.1-2.4, 2.6
Electromagnetic Spectrum
Anatomy of an Electromagnetic Wave Wave Equation and Solutions in Vacuum Dispersion Relation Wave Equation and Solutions in a Conductor Skin Depth Plasma Frequency Complex Conductivity
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Chapter 2 2
Electromagnetic Spectrum
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Chapter 2 3
Electromagnetic Spectrum (cont.)
Visible:
Ultraviolet:
UVA: and UVB:
VioletIndigoBlueGreenYellowOrange
Red
Infrared (IR) or heat radiation :
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Chapter 2 4
x
y z
Anatomy of an Electromagnetic Wave
wave:
transverse wave:wavelength
periodfrequency
angular frequency wave number
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Chapter 2 5
Wave Equation in Vacuum: Background Information
t B
E
=
t E
J B ooo
+=
(4) Faradays Law:
(5) Amperes Law:
curl = cross productof del and a vector z
k y
j x
i
+
+
=(1) (2) (3)
oo
c
12 =
Read a more thorough derivation in Livingston Chapter 2.1-2.2.
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Chapter 2 6
Wave Equation in Vacuum: Derivation
(1) ( ) ( )t
B E E
== 2
2
22
t E
E oo
=
t B
E
=
t E
J B ooo
+=
(2)
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Chapter 2 7
Solutions to Wave Equation
2
22
t E
E oo
=
x
y z
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Chapter 2 8
Practice Writing Solutions to Wave Equation
1. Write an equation for an electric field traveling in the -z directionwith wave number 9.666 x 10 6 m -1 and angular frequency of 2.900x 10 15 s -1
2. Write an equation for an electric field traveling in vacuum in the +zdirection with a wavelength of 500 nm.
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Chapter 2 9
Dispersion Relationship
vacuummaterial
dielectric
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Chapter 2 10
Wave Equation in Metal (unbound e -): Derivation
(1) ( ) ( )t
B E E
== 2
t B
E
=
t E
J B ooo
+=
(2)
Faradays Law Amperes Law
Take the curl of Faradays Law
Substitute Amperes Lawand Ohms Law t E
t E E
+
= 2
2
2
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Chapter 2 12
Skin Depth versus Frequency
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Chapter 2 13
Plasma FrequencyX em
dt d m D D =+
vv
Newtons Law:
==
2
2
22
22 1
peme N
k
2/12
=
me N e
p
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Chapter 2 14
Plasma Frequency (cont.)
=
2
2
22 1
pk
vacuum metal (thick)
Case 1: >> 1 and > p
vacuum metal (thick)
Case 2: >> 1 and < pvacuum
metal (thin)
Case 3: >> 1 and < pvacuum
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Chapter 2 15
Example: Typical Plasma Frequency
What is the plasma frequency (f p or p) of silver? Silver hasa density of 10.5 g/cm 3, an atomic mass of 107.9 amu, andone valence electron that contributes to conduction. Forsimplicity, assume = o
R e
f l e c
t i v i t y
Frequency
opaquetransparent
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Chapter 2 16
Complex Conductivity
1
How do we treat intermediate frequencies?
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Chapter 2 17
Chapter #2: Review Questions
1. Name 3 regions of the electromagnetic spectrum. Whatspeed do these waves travel in vacuum?
2. What are the relationships between the followingparameters: wavelength, period, frequency, angularfrequency, and wave number?
3. Write two general forms of an equation for a wave.
4. What happens to the speed of light when it enters amaterial?
5. Define skin depth in words.
6. Define plasma frequency in words.
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Chapter 2 18
Important Equations
Important ConstantsSpeed of light in vacuum: c = 3.0 x 10 8 m/s
Avogadros Number: N A = 6.022 x 10 23 /mole
Permeability in vacuum: 1.257 x 10-6
H/mPermittivity in vacuum: 8.85 x 10 -12 F/m
=
2
2
22 1 pk
ook 22 =
ik += 22ooc
12 =
=v
k =v
2=
2=k
2/1
2
=
2/12
2
==
me N e
p
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