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Transcript of 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
http://zitompul.wordpress.com
President University Erwin Sitompul EEM 1/2
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
Engineering Electromagnetics
President University Erwin Sitompul EEM 1/3
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.
Engineering Electromagnetics
President University Erwin Sitompul EEM 1/4
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).
Engineering Electromagnetics
Grade Policy
• Heading of Homework Papers (Required)
President University Erwin Sitompul EEM 1/5
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.
http://zitompul.wordpress.com
Engineering Electromagnetics
President University Erwin Sitompul EEM 1/6
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.
Engineering Electromagnetics
What is Electromagnetics?
President University Erwin Sitompul EEM 1/7
Engineering Electromagnetics
Electromagnetic Wave Spectrum
President University Erwin Sitompul EEM 1/8
Engineering Electromagnetics
Electric and magnetic field exist nearly everywhere.
Why do we learn Engineering Electromagnetics
President University Erwin Sitompul EEM 1/9
Engineering Electromagnetics
Electromagnetic principles find application in various disciplines such as microwaves, x-rays, antennas, electric machines, plasmas, etc.
Applications
President University Erwin Sitompul EEM 1/10
Engineering Electromagnetics
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
President University Erwin Sitompul EEM 1/11
Engineering Electromagnetics
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
President University Erwin Sitompul EEM 1/12
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
→
President University Erwin Sitompul EEM 1/13
Chapter 1 Vector Analysis
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
President University Erwin Sitompul EEM 1/14
Chapter 1 Vector Analysis
Rectangular Coordinate System• Differential surface units:
dx dydy dzdx dz
• Differential volume unit :dx dy dz
President University Erwin Sitompul EEM 1/15
Chapter 1 Vector Analysis
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
President University Erwin Sitompul EEM 1/16
For any vector B, :
Chapter 1 Vector Analysis
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
President University Erwin Sitompul EEM 1/17
Chapter 1 Vector Analysis
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 +
President University Erwin Sitompul EEM 1/18
One of the most important applications of the dot product is that of finding the component of a vector in a given direction.
Chapter 1 Vector Analysis
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
President University Erwin Sitompul EEM 1/19
Chapter 1 Vector Analysis
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
President University Erwin Sitompul EEM 1/20
Chapter 1 Vector Analysis
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.
President University Erwin Sitompul EEM 1/21
sinN AB A B a A B
Chapter 1 Vector Analysis
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
President University Erwin Sitompul EEM 1/22
Chapter 1 Vector Analysis
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
President University Erwin Sitompul EEM 1/23
Chapter 1 Vector Analysis
The Cylindrical Coordinate System
President University Erwin Sitompul EEM 1/24
Chapter 1 Vector Analysis
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
President University Erwin Sitompul EEM 1/25
a
za
a
Chapter 1 Vector Analysis
The Cylindrical Coordinate System
• 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
President University Erwin Sitompul EEM 1/26
Chapter 1 Vector Analysis
The Spherical Coordinate System
President University Erwin Sitompul EEM 1/27
Chapter 1 Vector Analysis
The Spherical Coordinate System
• Differential surface units:dr rd
sindr r d sinrd r d
• Differential volume unit :sindr rd r d
President University Erwin Sitompul EEM 1/28
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
Chapter 1 Vector Analysis
The Spherical Coordinate System
• Dot products of unit vectors in spherical and rectangular coordinate systems
President University Erwin Sitompul EEM 1/29
Chapter 1 Vector Analysis
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
President University Erwin Sitompul EEM 1/30
Chapter 1 Vector Analysis
Homework 1D1.4. (p.14)D1.6. (p.19)D1.8. (p.22)
Due: Next week 18 January 2011, at 07:30.