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ENE 325ENE 325Electromagnetic Fields Electromagnetic Fields and Wavesand Waves

Lecture 1 ElectrostaticsLecture 1 Electrostatics

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SyllabusSyllabus Dr. Ekapon Siwapornsathain, email: Dr. Ekapon Siwapornsathain, email:

sie4129@hotmail.com Course webpage: Course webpage:

http://webstaffs.kmutt.ac.th/ekapon.siw Lecture: 9:30pm-12:20pm Wednesday, Rm. Lecture: 9:30pm-12:20pm Wednesday, Rm.

CB41004CB41004 Office hours :By appointmentOffice hours :By appointment Textbook: Fundamentals of Electromagnetics Textbook: Fundamentals of Electromagnetics

with Engineering Applications by Stuart M. with Engineering Applications by Stuart M. Wentworth (Wiley, 2005)Wentworth (Wiley, 2005)

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This is the course on beginning level electrodynamics. The purpose of the course is to provide junior electrical engineering students with the fundamental methods to analyze and understand electromagnetic field problems that arise in various branches of engineering science.

Course Course OObjectivesbjectives

AgreementAgreement

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The instruction will be given mostly in English. You are not allowed to say the followings (or anything of the similar nature and meaning):

“อาจารย์� , พูดภาษาไทย์เถอะ ขอร�อง” “อาจารย์�, เอาภาษาไทย์คร�บ”

If you do, I will punish you by asking you to stepoutside the lecture room. I will make a superdifficult exams and will not tutor you or reviewthe material for you before the exams.

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Basic physics background relevant to electromagnetism: charge, force, SI system of units; basic differential and integral vector calculus Concurrent study of introductory lumped circuit analysis Ability to visualize problems in 3-D is a must! Reflection: periodically review the material, ask questions to yourself or to the instructor and discuss with your classmates.

Prerequisite knowledge and/or s Prerequisite knowledge and/or skillskills

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Introduction to course:

Review of vector operations Orthogonal coordinate systems and change of coordinates

Integrals containing vector functions Gradient of a scalar field and divergence of a vector field

Course outlineCourse outline

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Electrostatics:

Fundamental postulates of electrostatics and Coulomb's Law

Electric field due to a system of discrete charges Electric field due to a continuous distribution of charge Gauss' Law and applications Electric Potential Conductors in static electric field Dielectrics in static electric fields Electric Flux Density, dielectric constant Boundary Conditions Capacitor and Capacitance Nature of Current and Current Density

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Electrostatics:

Resistance of a Conductor Joule’s Law Boundary Conditions for the current density The Electromotive Force The Biot-Savart Law

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Magnetostatics:

Ampere’s Force Law Magnetic Torque Magnetic Flux and Gauss’s Law for Magnetic Fields Magnetic Vector Potential Magnetic Field Intensity and Ampere’s Circuital Law Magnetic Material Boundary Conditions for Magnetic Fields Energy in a Magnetic Field Magnetic Circuits Inductance

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Dynamic FieldsDynamic Fields::

Faraday's Law and induced emf Faraday's Law and induced emf Transformers Transformers Displacement Current Displacement Current - Time dependent Maxwell's equations and electromag- Time dependent Maxwell's equations and electromag

netic wave equations netic wave equations TimeTime--harmonic wave problems, uniform plane waves in harmonic wave problems, uniform plane waves in lossless media, Poynting's vector and theorem lossless media, Poynting's vector and theorem

Uniform pUniform p lane waves in lossy media lane waves in lossy media Uniform plane wave transmission and reflection on Uniform plane wave transmission and reflection on normal and oblique incidencenormal and oblique incidence

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Homework 20%Homework 20%

Midterm exam 40%Midterm exam 40%

Final exam 40%Final exam 40%

GradingGrading

Vision: Providing opportunities for intellectual growth in the context of an engineering discipline for the attainment of professional competence, and for the development of a sense of the social context of technology.

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Examples of Electromagnetic Examples of Electromagnetic fieldsfields

Electromagnetic fields Electromagnetic fields – Solar radiationSolar radiation– LightningLightning– Radio communicationRadio communication– Microwave ovenMicrowave oven

Light consists of electric and magnetic fields. An Light consists of electric and magnetic fields. An electromagnetic wave can propagate in a electromagnetic wave can propagate in a

vacuum with a speed velocity vacuum with a speed velocity c=c=2.998x102.998x1088 m/sm/s

c = fc = ff = frequency (Hz)f = frequency (Hz) = wavelength (m)= wavelength (m)

Aurora Borealis (northern Aurora Borealis (northern lights)lights)

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Vectors Vectors - Magnitude and - Magnitude and direction direction

1. Cartesian coordinate system (x-, y-, 1. Cartesian coordinate system (x-, y-, z-) z-)

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Vectors Vectors - Magnitude and - Magnitude and direction direction

2. 2. Cylindrical coordinate system (Cylindrical coordinate system (, , , , z)z)

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Vectors Vectors - Magnitude and - Magnitude and direction direction

3.3. Spherical coordinate system ( Spherical coordinate system (, , , , ))

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Manipulation of vectorsManipulation of vectors To find a vector from point To find a vector from point mm to to nn

Vector addition and subtractionVector addition and subtraction

Vector multiplication Vector multiplication – vector vector vector = vector vector = vector– vector vector scalar = vector scalar = vector

( ) ( ) ( ) EEEEEEEEEEEEEE

x y zn m n m n mA x x a y y a z z a

( ) ( ) ( )

( ) ( ) ( )

EEEEEEEEEEEEEEEEEEEEEEEEEEEE

EEEEEEEEEEEEEEEEEEEEEEEEEEEEx y zx x y y z z

x y zx x y y z z

A B A B a A B a A B a

A B A B a A B a A B a

4 4 EEEEEEEEEEEEEEEEEEEEEEEEEEEE

yQ p a

4 5 20x y zQ a a a EEEEEEEEEEEEEE

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Ex1Ex1: : Point P Point P (0, 1, 0), Point R (2, 2, 0)(0, 1, 0), Point R (2, 2, 0)

The The magnitudemagnitude of the vector line from the origin of the vector line from the origin (0, 0, 0)(0, 0, 0) to point P to point P

The The unit vector unit vector pointed in the direction of vectorpointed in the direction of vector

1EEEEEEEEEEEEEE

yop a

2 2

(2, 2,0) 2 2

2 2 2 2

x y

R

R R a a

R Ra

R R

EEEEEEEEEEEEEEEEEEEEEEEEEEEE

EEEEEEEEEEEEEE

EEEEEEEEEEEEEE

REEEEEEEEEEEEEE

(2 2 )

2 2

x yR

R a aa

R

EEEEEEEEEEEEEE

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Ex2Ex2: : P P (0,-4, 0), (0,-4, 0), Q Q (0,0,5), (0,0,5), R R (1,8,0), and (1,8,0), and S S (7,0,2) (7,0,2) a) Find the vector from point a) Find the vector from point PP to point to point QQ

b) Find the vector from point b) Find the vector from point RR to point to point SS

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c) Find the direction of c) Find the direction of EEEEEEEEEEEEEEEEEEEEEEEEEEEEA B

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Coulomb’s lawCoulomb’s law Law of attraction: positive charge attracts Law of attraction: positive charge attracts

negative chargenegative charge Same polarity charges repel one anotherSame polarity charges repel one another Forces between two chargesForces between two charges

Coulomb’s Law

1 212 122

0 124

EEEEEEEEEEEEEE Q QF a

Rpe

Q = electric charge (coulomb, C)e0 = 8.854x10-12 F/m

910/

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F mp

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Electric field intensityElectric field intensity An electric field from An electric field from QQ11 is exerted by a force is exerted by a force

between between QQ11 and and QQ22 and the magnitude of and the magnitude of QQ22

or we can writeor we can write

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2V/m

FE

Q

EEEEEEEEEEEEEEEEEEEEEEEEEEEE

2

0

V/m4

RQ

E aR

EEEEEEEEEEEEEE

pe

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Electric field linesElectric field lines

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Spherical coordinate systemSpherical coordinate system orthogonal point (orthogonal point (rr,,, , )) r =r = a radial distance from the origin to the point (m) a radial distance from the origin to the point (m) = the angle measured from the positive z-axis (0 = the angle measured from the positive z-axis (0

pp)) = an azimuthal angle, measured from x-axis (0 = an azimuthal angle, measured from x-axis (0

2 2pp))

A vector representation in the spherical coordinate A vector representation in the spherical coordinate system:system:

rrA A a A a A a EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

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Point conversion between cartesian Point conversion between cartesian and spherical coordinate systemsand spherical coordinate systems

2 2 2

1

1

cos

tan

r x y z

zr

yx

sin cos

sin sin

cos

x r

y r

z r

A conversion A conversion from P(x,y,z) to from P(x,y,z) to

P(P(rr,,, , ))

A conversion from A conversion from P(P(rr,,, , ) to P(x,y,z) ) to P(x,y,z)

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Unit vector conversion Unit vector conversion (Spherical coordinates)(Spherical coordinates)

ra a

a

xa

ya

za

sin cos

sin sin

cos

cos cos

cos sin

sin

sin

cos

0

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differential element

volume: dv = r2sindrdd

surface vector: 2 sin

rds r d d a

Take the dot product of the vector and a unit vector in the desired direction to find any desired component of a vector.

EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

rrA A a A A a A A a

Find any desired component of a Find any desired component of a vectorvector

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Ex3Ex3 Transform the vector field Transform the vector field into spherical components into spherical components and variablesand variables

( / ) xG xz y aEEEEEEEEEEEEEE

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Ex4Ex4 Convert the Cartesian coordinate point Convert the Cartesian coordinate point P(3, 5, 9) to its equivalent point in spherical P(3, 5, 9) to its equivalent point in spherical

coordinates.coordinates.

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Line charges and the cylindrical Line charges and the cylindrical coordinate systemcoordinate system orthogonal point (orthogonal point (, , , , zz)) = a radial distance (m)= a radial distance (m) = the angle measured from x axis to the = the angle measured from x axis to the

projection of the radial line onto x-y planeprojection of the radial line onto x-y plane zz = a distance = a distance z z (m)(m)A vector representation in the cylindrical coordinate A vector representation in the cylindrical coordinate system:system:

zzA A a A a A a EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

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cos

sin

x

y

z z

2 2

1tan

x y

yx

z z

Point conversion between cartesian Point conversion between cartesian and cylindrical coordinate systemsand cylindrical coordinate systems

A conversion A conversion from P(x,y,z) to from P(x,y,z) to

P(P(rr,,, z, z))

A conversion from A conversion from P(P(rr,,, z, z) to P(x,y,z) ) to P(x,y,z)

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Unit vector conversion (Cylindrical Unit vector conversion (Cylindrical coordinates)coordinates)

a a za

xa

ya

za

cos

sin

0

sin

cos

0

0

0

1

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differential element

volume: dv = dddz

surface vector: (top)

zds d d a

ds d dza (side)

Take the dot product of the vector and a unit vector in the desired direction to find any desired component of a vector.

EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

r zr zA A a A A a A A a

Find any desired component of a Find any desired component of a vectorvector

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Ex5Ex5 Transform the vector Transform the vectorinto cylindrical coordinates into cylindrical coordinates

x y zB ya xa za

EEEEEEEEEEEEEE

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Ex6Ex6 Convert the Cartesian coordinate point Convert the Cartesian coordinate point P(3, 5, 9) to its equivalent point in cylindrical P(3, 5, 9) to its equivalent point in cylindrical

coordinates.coordinates.

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Ex7Ex7 A volume bounded by radius A volume bounded by radius from 3 to from 3 to 4 cm, the height is 0 to 6 cm, the angle is 4 cm, the height is 0 to 6 cm, the angle is 9090-135-135, determine the volume., determine the volume.