electromagnetic field theory_1

8/3/2019 Electromagnetic Field Theory_1

1/36

Electromagnetic Field Theory

Y. Do. Dr. Hakan P. PARTAL

Fall 2011

YTU


2/36

Electromagnetic Field Theory Electromagnetics involves the macroscopic behavior of

electric charges in vacuum and matter. This behavior can beaccurately characterized by the Lorentz force law andMaxwells equations, which were derived from experimentsshowing how forces on charges depend on the relativelocations and motions of other charges nearby.

Electromagnetic phenomena underlie most of theelectrical in electrical engineering and are basic to asound understanding of that discipline.

The theory is heavily depend on vectors and phasors

analysis Simulation software tools are available for analysis


3/36

Electromagnetic Field Theory and

Applications Electrical, Electronics, Communications , and Computer Engineering are

established based on Electromagnetics and Circuits Theory.

There are countless applications in real engineering life: Telecommunications

Wireless applications

Antennas

Radars

RF / Microwaves Space electronics

Defense Electronics

Optical fiber communications

Laser applications

Localization and positioning systems Remote sensing

Sensor networks

Electromechanical energy conversions

Acoustics

etc


4/36


5/36

Course Outline Vector analysis

Coordinate systems,

Line, surface, and volume integrals

General Theorems

Static Electric Fields Fundamental Postulates

Coulomb's Law

Gauss Law Capacitances & Dielectrics in Static Electric Field

Electrostatics Poissons and Laplace Equations

Method of mages

Boundary Value Problems

Steady Electric Currents Ohms, Kirchhoffs, Joules Laws Boundary Conditions of Current Density

Static Magnetic Fields Fundamental Postulates

Vector Potentials

Biot-Savart Law

Magnetic Dipole

Inductances

Magnetic Energy

Electromagnetism Maxwells Equations,

Amperes Law,

Faradays Law,

Potential Functions Electromagnetic Boundary Conditions


6/36

Recommended Textbooks Cheng, D.K., Field and Wave Electromagnetics, Addison-Wesley, 1991.

W.H. Hayt, JR., Engineering Electromagnetics, McGraw-Hill , BookCompany, 1981.

Kraus, D. A. Fleisch, Electromagnetics, McGraw-Hill, 1999. W.K.H. Panofsky, M. Phillips, Classical Electricity and Magnetism, Addison-

Wesley Publishing Company, Inc., Massachusetts, USA, 1962.

E. M. Purcell, Electricity and Magnetism, Berkeley Physics Course,McGraw-Hill, 1974.

A. N. Matveev, Electricity and Magnetism, Mir Publishers, Moscow, 1986. Electromagnetics, Schaums Outline Series, McGraw_Hill

Math texbooks

A. D. Myskis, Introductory Mathematics for Engineers, Mir Publishers,1975.

B. M. Budak, S. V. Famin, Multiple Integrals, Field Theory and Series, MirPublishers, 1973.

Erwin Kreyszig, Advanced Engineering Mathematics, John WileyInt. Ed.,

1972.


7/36

VECTOR ANALYSIS


8/36

VECTOR ANALYSIS Scalars and Vectors


9/36

Scalars and Vectors


10/36

VECTOR ALGEBRA


11/36

VECTOR ALGEBRA

Multiplication of a vector by a scalar also

obeys the associative and distributive laws ofalgebra:


12/36

The Coordinate Systems Cartesian Coordinate system

Cylindrical Coordinate system Spherical Coordinate system


13/36


14/36

VECTOR NOTATION

VECTOR NOTATION:

zzyyxx aAaAaAA ++=r

Rectangular or

Cartesian

Coordinate

System

x

z

y

zzyyxx BABABABA ++=rr

Dot Product

zyx

zyx

zyx

BBB

AAAaaa

BA

=rr

Cross Product

( )21

222

zyx AAAA ++=r

Magnitude of vector

(SCALAR)

(VECTOR)


15/36

Cartesian Coordinates

zyx AzAyAxA ++=r

x

y

z

Z plane

x plane

++ ++== 222 zyx AAAAAArrr

xy

z

x1

y1

z1

Ax

Ay

Az

( x, y, z)

Vector representation

Magnitude of A

Position vector of A

),,( 111 zyxA

r

111 zzyyxx ++

Base vector properties

0

1

===

===

xzzyyx

zzyyxx

yxz

xzyzyx

=

==


16/36

x

y

z

Ax

Ay

Az

r

r

Dot product:

zzyyxx BABABABA++=

rr

Cross product:

zyx

zyx

BBB

AAA

zyx

BA

=rr


Page 108

0

1

===

===

xzzyyx

zzyyxx


17/36

VECTOR REPRESENTATION: CYLINDRICAL COORDINATES

Cylindrical representation uses: r ,, z

zzrr aAaAaAA ++= r

zzrr BABABABA ++= rr

UNIT VECTORS:

zr aaa

Dot Product

(SCALAR)

r

z

P

x

z

y


18/36

x

z

y

VECTOR REPRESENTATION: UNIT VECTORS

yaxa

zaUnit Vector

Representation

for Rectangular

Coordinate

System

xa

The Unit Vectors imply :

ya

za

Points in the direction of increasing x

Points in the direction of increasing y

Points in the direction of increasing z

Rectangular Coordinate System


19/36

r

z

P

x

z

y


Cylindrical Coordinate System

za

a

ra


za

Points in the direction of increasing r

Points in the direction of increasing

Points in the direction of increasing z

ra

a


20/36


Spherical Coordinate System

r

P

x

z

y

a

a

ra


Points in the direction of increasing r

Points in the direction of increasing

Points in the direction of increasingr

a

a

a


21/36

zr aaa aaar zyx aaa

RECTANGULAR

Coordinate Systems

CYLINDRICAL

Coordinate Systems

SPHERICAL

Coordinate Systems

NOTE THE ORDER!

r,, z r, ,

Note: Transformations between coordinate systems are possible using geometric rules.


Summary


22/36

METRIC COEFFICIENTS

1. Rectangular Coordinates:

When you move a small amount in x-direction, the distance is dx

In a similar fashion, you generate dy and dz

Unit is in meters


23/36


Differential quantities:

Length:

Area:

Volume:

dzzdyydxxld ++=r

dxdyzsd

dxdzysd

dydzxsd

z

y

x

=

=

=

r

r

r

dxdydzdv =


24/36


25/36

3. Spherical Coordinates:

Distance = r sin d

x

y

d

r sin

Differential Distances:

( dr, rd, r sin d )

r

P

x

z

y

METRIC COEFFICIENTS


26/36

Representation of differential length dl in coordinate systems:

zyx adzadyadxld ++=r

zr adzadradrld ++= r

adrardadrld r sin ++=r

rectangular

cylindrical

spherical

METRIC COEFFICIENTS

r

P

x

z

y

r

z

P

x

z

y


27/36

AREA INTEGRALS

integration over 2 delta distances

dx

dy

Example:

x

y

2

6

3 7

AREA = 7

3

6

2

dxdy = (6-2).(7-3)= 16

Note that:z = constant

For the other coordinate systems, area & surface

integrals will be on similar types of surfaces e.g. r=constant or = constant or = constant et c.


28/36

Representation of differential surface element:

zadydxsd =r

Vector is NORMAL tosurface

SURFACE NORMAL


29/36

DIFFERENTIALS FOR INTEGRALS

Example of Line differentials

or or

Example of Surface differentials

adydxsd =r

radzrdsd = r

or

Example of Volume differentials dzdydxdv =

xadxld =

r

radrld=

r

ardld=

r


30/36


31/36

Dot product:

zzrr

BABABABA ++=

rr

Cross product:

zr

zr

BBB

AAA

zr

BA

=rr

BA

Cylindrical Coordinates


32/36

Cylindrical Coordinates

Differential quantities:

Length:

Area:

Volume:

dzzrddrrld ++= r

rdrdzsd

drdzsd

dzrdrsd

z

r

=

=

=

r

r

r

dzrdrddv =


33/36

=== ,, RRR

Spherical Coordinates

(R, , )

AAARA R ++=

r

Vector representation

++ ++== 222 AAAAAA Rrrr

Magnitude of A

Base vector properties


34/36

Dot product:

BABABABA RR ++=rr

Cross product:

BBB

AAA

R

BA

R

R

=rr

BA

Spherical Coordinates


35/36


36/36

zz

yx

yxr

cossin

sincos

=

+=

+=

zz

yx

yxr

AAAAA

AAA

=+=

+=

cossin

sincos

Cartesian to Cylindrical Transformation

zzxy

yxr

==

+=

+

)/(tan

1

22

electromagnetic field theory_1

Documents