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Lesson 1: Introduction toApplied Electromagnetics
Applied Electromagnetics B EE 361
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Before we get started.
Read the Course Introduction
Make sure that you have achieved the proper course prerequisites
Purchase the textbook and begin reading Chapter 1
Fundamentals of Applied Electromagnetics by Ulaby, Michielssen, and Ravaioli, 6thEdition
Bring the following supplies to class
Paper and pen Textbook
Smith Charts (some available in class, or at www.microwaves101.com/downloads/smith.PDF)
Pocket Calculator
For now all other electronics (laptops, ipods, cellphones, etc.), out-of-sight
Review Course Schedule and note when HWs are due and Exam dates Get a jump start on HW #1
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Applications of Electromagnetics
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Electromagnetics in Telecommunications
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Electromagnetics in Computer Technology
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Known Forces in Our Present Universe
1. Gravitational Forces
Force that attracts masses to one another Very, Very Weak
2. Strong Forces
Holds Protons, and Neutrons, (Nucleons) together Extremely Short Range
3. Weak Forces
Accounts for certain kinds of radioactive decay Short Range, Very Weak
4. Electromagnetic Forces
Predominant Force in everyday life Very, Very Strong over Large Range
FG
FEM
Proton
Quarks
FG
Electromagnetic Forces responsible for keeping the soccer ball from going through
the earth, friction, chemical forces that bind molecules, colliding billiard balls, etc. etc.
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Gravitational Force
Force exerted on mass 2 by mass 1
Gravitational field induced by mass 1
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What Electric Force do Charges Exert?
Coulombs Law
The E lect r i c Fo r ce F21 exerted by Charge q1 on Charge q2 :
where
and constant k is:
2
12
211221
R
qqRke
F =
2112
2112
tofromDistance:
tofromctorUnit ve:
qqR
qqR
1=k
04
1
=k41=k
Gaussian (cgs)International System of Units
SI (mks)Heavyside - Lorentz
F/m10x8.85 -12=o
Electrical Permittivity of free space
1q
2q
21eF
12R
12R
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What are the Rules and Properties of Charge?
1. Charge comes in two varieties: plus +q (positive) and minus q (negative)
Opposite charges cancel one another and come in almost exactly equal amounts to agreat degree of precision in bulk matter. Due to the large forces created by charge, if
matter were unbalanced, matter would explode!
2. Charge is conserved: it can be neither created nor destroyed
This is a conservation law of our present known universe in that before or after any
action, the net amount of charge remains the same. Whew, lucky for us. Imagine if
charge could spontaneously appear in your circuit, or perhaps disappear in your
circuit, and appear half way across the universe!
3. Charge is quantized: it comes in only integral (n=0,1,2,3) packets of
where e=1.609 x 10-19Coulombs
This is because the charge of fundamental particles (protons, nuetrons, electrons,
pions, etc.) is only +e, -e, or zero. This did not have to be so. Quarks which form
nucleons have a property similar to charge, however they come in one or two
multiples of 1 3 .
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What is the Electric Field?
Definition of Electric Field Due to Charge q1
:
The E l ec t r i c F i e l d Eoriginatingfrom charge q1 is definedas:
where
and constant k is: k = 4in SI (mks) Units
where 0 =8.854 x 1012Farrad per meter (F/m) is the
permittivity of free space
2
12
112
2 R
qRk
q
21e F
EE ==
2112
2112
tofromDistance:
tofromctorUnit ve:
qqR
qqR
Note that q
2
acts as a test charge that can be placed anywhere to
determine the Electric Field that originates from q
1
.
Volts per meter (V/m)
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Properties of the Electric Field
1. The Electric Field lines originate from charge itself; they begin on positive
charge (source) and terminate on negative charge (sink)
Even though this designation is by convention, charge being the origin of the electric
field has major implications that we will discuss in terms of the divergence of this field.
2. The Electric Field obeys the P r i n c i p a l o f L i n e a r Sup er p o si t i o n
The total vec t o r Electric Field at a point in space die to a system of point charges is
equal to the v ect o r sum of the Electric Fields at that point due to the individual
charges. We will discuss this during the 2ndhalf of the lecture.
3. The Electric Field applied to matter creates a counter field that diminishesthe Total Electric Field in the matter
We will discuss this in the next slide and during the 2ndhalf of the lecture.
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Electric Field in a Material
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What is the Magnetic Field?
Electric charges can be isolated, but magnetic poles always exist in pairs.
Magnetic field induced by a
current in a long wire
Magnetic permeability of free space
Hans Christian Oersted
(1820)
Biot-Savart Law
(1820)
Measures magnetic
field with a compassMagnetic Flux Density
B
Tesla (T)
orWeber/meter2(Wb/m2)
Right Hand Rule
N
S
N
N
S
S
Cut
inHalf
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Force on Charge in a Magnetic Field
+
+q
I2
Current defined as flow of positive (+q) charge
Second wire with current
flowing added to measure
Force.
Fm12
Fm21
Andr-Marie Ampre(1820)
where again by definition,
Further discussion in class
during 2ndhalf of lecture
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This magnetic force is equivalent to the
electrical force that would be exerted on
the particle by the electric field Em given
by
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Maxwells Equations for EM Fields Wow ! !
How did we get from there to here? Well, a lot of discoveries and experiments in the
18thAnd 19thcenturies by Ampere, Gauss, and Farraday (among others); unification
of all of these laws by Maxwell; and restating Maxwells Equations into compact
vector calculus form by Heavyside.
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EE361 Course Flow
The Three Branches of Electromagnetics
1) Transmission Line Theory
2) Vector Algebra and Vector Calculus
3)
4)
Electrostatics
=
= 0
Magnetostatics
= 0
=
Dynamics
Time varying fields and their implications for Circuit Theory
including Kirchoffs Voltage and Current Laws (KVL&KCL).
When they hold! and When they break down!
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Prior to Starting Transmission Lines Review
Complex Numbers = + = , =
Phasor Analysis
= =
Waves
(, ) = cos
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