ee138 chapter 2_slides - annotated 10-13

7/21/2019 EE138 Chapter 2_Slides - Annotated 10-13

1/18

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


2/18

Chapter 2 2

Electromagnetic Spectrum


3/18

Chapter 2 3

Electromagnetic Spectrum (cont.)

Visible:

Ultraviolet:

UVA: and UVB:

VioletIndigoBlueGreenYellowOrange

Red

Infrared (IR) or heat radiation :


4/18

Chapter 2 4

x

y z

Anatomy of an Electromagnetic Wave

wave:

transverse wave:wavelength

periodfrequency

angular frequency wave number


5/18

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.


6/18

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)


7/18

Chapter 2 7

Solutions to Wave Equation

2

22

t E

E oo

=

x

y z


8/18

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.


9/18

Chapter 2 9

Dispersion Relationship

vacuummaterial

dielectric


10/18

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


11/18


12/18

Chapter 2 12

Skin Depth versus Frequency


13/18

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


14/18

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


15/18

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


16/18

Chapter 2 16

Complex Conductivity

1

How do we treat intermediate frequencies?


17/18

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.


18/18

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

ee138 chapter 2_slides - annotated 10-13

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