president universityerwin sitompuleem 1/1 dr.-ing. erwin sitompul president university lecture 1...

President University Erwin Sitompul EEM 1/1

Dr.-Ing. Erwin SitompulPresident University

Lecture 1

Engineering Electromagnetics

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Textbook:“Engineering Electromagnetics”, William H. Hayt, Jr. and John A. Buck, McGraw-Hill, 2006.

Textbook and Syllabus

Syllabus: Chapter 1: Vector AnalysisChapter 2: Coulomb’s Law and Electric Field IntensityChapter 3: Electric Flux Density, Gauss’ Law, and

DivergenceChapter 4: Energy and Potential Chapter 5: Current and ConductorsChapter 6: Dielectrics and CapacitanceChapter 8: The Steady Magnetic FieldChapter 9: Magnetic Forces, Materials, and Inductance



Grade Policy Grade Policy:Final Grade = 10% Homework + 20% Quizzes +

30% Midterm Exam + 40% Final Exam + Extra Points

Homeworks will be given in fairly regular basis. The average of homework grades contributes 10% of final grade.

Homeworks are to be written on A4 papers, otherwise they will not be graded.

Homeworks must be submitted on time. If you submit late,< 10 min. No penalty10 – 60 min. –20 points> 60 min. –40 points

There will be 3 quizzes. Only the best 2 will be counted. The average of quiz grades contributes 20% of final grade.



Grade Policy: Midterm and final exam schedule will be announced in time. Make up of quizzes and exams will be held one week after

the schedule of the respective quizzes and exams. The score of a make up quiz or exam can be multiplied by 0.9

(the maximum score for a make up is 90).


Grade Policy

• Heading of Homework Papers (Required)


Grade Policy Grade Policy:Extra points will be given every time you solve a problem in front of the class. You will earn 1 or 2 points.Lecture slides can be copied during class session. It also will be available on internet around 3 days after class. Please check the course homepage regularly.

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Electric field Produced by the presence of electrically charged particles, and gives rise to the electric force.

Magnetic fieldProduced by the motion of electric charges, or electric

current, and gives rise to the magnetic force associated

with magnets.


What is Electromagnetics?



Electromagnetic Wave Spectrum



Electric and magnetic field exist nearly everywhere.

Why do we learn Engineering Electromagnetics



Electromagnetic principles find application in various disciplines such as microwaves, x-rays, antennas, electric machines, plasmas, etc.

Applications



Electromagnetic fields are used in induction heaters for melting, forging, annealing, surface hardening, and soldering operation.

Electromagnetic devices include transformers, radio, television, mobile phones, radars, lasers, etc.

Applications



Transrapid Train

• A magnetic traveling field moves the vehicle without contact.

• The speed can be continuously regulated by varying the frequency of the alternating current.

Applications


Chapter 1 Vector Analysis

Scalar refers to a quantity whose value may be represented by a single (positive or negative) real number.

Some examples include distance, temperature, mass, density, pressure, volume, and time.

A vector quantity has both a magnitude and a direction in space. We especially concerned with two- and three-dimensional spaces only.

Displacement, velocity, acceleration, and force are examples of vectors.

• Scalar notation: A or A (italic or plain)• Vector notation: A or A (bold or plain with arrow)

Scalars and Vectors

→



A B B A

( ) ( ) A B+C A B +C

( ) A B A B

1

n n

AA

0 A B A B

Vector Algebra



Rectangular Coordinate System• Differential surface units:

dx dydy dzdx dz

• Differential volume unit :dx dy dz



Vector Components and Unit Vectors

r x y z

x y zx y z r a a a

, , : x y za a a unit vectors

?PQR

PQ Q P R r r

(2 2 ) (1 2 3 )x y z x y z a a a a a a

4 2x y z a a a


For any vector B, :


Vector Components and Unit Vectorsx x y y z zB B B B a a + a

2 2 2x y zB B B B Magnitude of BB

2 2 2B

x y zB B B

Ba

B

B Unit vector in the direction of B

ExampleGiven points M(–1,2,1) and N(3,–3,0), find RMN and aMN.

(3 3 0 ) ( 1 2 1 )MN x y z x y z R a a a a a a 4 5x y z a a a

MNMN

MN

R

aR 2 2 2

4 5 1

4 ( 5) ( 1)

x y z

a a a0.617 0.772 0.154x y z a a a



The Dot ProductGiven two vectors A and B, the dot product, or scalar product,

is defines as the product of the magnitude of A, the magnitude of B, and the cosine of the smaller angle between them:

cos AB A B A B

The dot product is a scalar, and it obeys the commutative law:

A B B A

For any vector and ,x x y y z zA A A A a a + a x x y y z zB B B B a a + a

x x y y z zA B A B A B A B +


One of the most important applications of the dot product is that of finding the component of a vector in a given direction.


The Dot Product

cos Ba B a B a cos BaB

• The scalar component of B in the direction of the unit vector a is Ba

• The vector component of B in the direction of the unit vector a is (Ba)a



The Dot ProductExample

The three vertices of a triangle are located at A(6,–1,2), B(–2,3,–4), and C(–3,1,5). Find: (a) RAB; (b) RAC; (c) the angle θBAC at vertex A; (d) the vector projection of RAB on RAC.

( 2 3 4 ) (6 2 )AB x y z x y z R a a a a a a 8 4 6x y z a a a

( 3 1 5 ) (6 2 )AC x y z x y z R a a a a a a 9 2 3x y z a a a

A

B

CBACcosAB AC AB AC BAC R R R R

cos AB ACBAC

AB AC

R R

R R 2 2 2 2 2 2

( 8 4 6 ) ( 9 2 3 )

( 8) (4) ( 6) ( 9) (2) (3)

x y z x y z

a a a a a a 62

116 94

1cos (0.594)BAC 53.56

0.594



The Dot Product

on AB AC AB AC AC R R R a a

2 2 2 2 2 2

( 9 2 3 ) ( 9 2 3 )( 8 4 6 )

( 9) (2) (3) ( 9) (2) (3)

x y z x y zx y z

a a a a a aa a a

( 9 2 3 )62

94 94x y z

a a a

5.963 1.319 1.979x y z a a a

ExampleThe three vertices of a triangle are located at A(6,–1,2), B(–2,3,–4), and C(–3,1,5). Find: (a) RAB; (b) RAC; (c) the angle θBAC at vertex A; (d) the vector projection of RAB on RAC.


sinN AB A B a A B


The Cross ProductGiven two vectors A and B, the magnitude of the cross product,

or vector product, written as AB, is defines as the product of the magnitude of A, the magnitude of B, and the sine of the smaller angle between them.

The direction of AB is perpendicular to the plane containing A and B and is in the direction of advance of a right-handed screw as A is turned into B.

The cross product is a vector, and it is not commutative:

( ) ( ) B A A B

x y z

y z x

z x y

a a aa a aa a a



The Cross ProductExample

Given A = 2ax–3ay+az and B = –4ax–2ay+5az, find AB.

( ) ( ) ( )y z z y x z x x z y x y y x zA B A B A B A B A B A B A B a a a

( 3)(5) (1)( 2) (1)( 4) (2)(5) (2)( 2) ( 3)( 4)x y z a a a

13 14 16x y z a a a



The Cylindrical Coordinate System




• Differential surface units:d dz d dz d d

• Differential volume unit :d d dz

cosx siny

z z

2 2x y 1tany

x z z

• Relation between the rectangular and the cylindrical coordinate systems


a

za

a



• Dot products of unit vectors in cylindrical and rectangular coordinate systems

ya

za

xa

A A a( )x x y y z zA A A a a + a a

x x y y z zA A A a a a a + a acos sinx yA A

A A a( )x x y y z zA A A a a + a a

x x y y z zA A A a a a a + a asin cosx yA A

z zA A a( )x x y y z z zA A A a a + a a

x x z y y z z z zA A A a a a a + a a

zA

?x x y y z z z zA A A A A A A a a + a A a a + a



The Spherical Coordinate System




• Differential surface units:dr rd

sindr r d sinrd r d

• Differential volume unit :sindr rd r d


sin cosx r

sin siny r

cosz r

2 2 2 , 0r x y z r

1

2 2 2cos , 0 180

z

x y z

1tany

x

• Relation between the rectangular and the spherical coordinate systems



• Dot products of unit vectors in spherical and rectangular coordinate systems



The Spherical Coordinate SystemExample

Given the two points, C(–3,2,1) and D(r = 5, θ = 20°, Φ = –70°), find: (a) the spherical coordinates of C; (b) the rectangular coordinates of D.

2 2 2r x y z

1

2 2 2cos

z

x y z

1tany

x

2 2 2( 3) (2) (1) 3.742

1 1cos

3.742 74.50

1 2tan

3

33.69 180 146.31

( 3.742, 74.50 , 146.31 ) C r

( 0.585, 1.607, 4.698) D x y z



Homework 1D1.4. (p.14)D1.6. (p.19)D1.8. (p.22)

Due: Next week 18 January 2011, at 07:30.

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