President University
Erwin Sitompul
EEM
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Dr.
-
Ing. Erwin Sitompul
President University
Lecture
1
Engineering Electromagnetics
http://zitompul.wordpress.com
President University
Erwin Sitompul
EEM
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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 Analysis
Chapter 2:
Coulomb’s Law and Electric Field Intensity
Chapter 3:
Electric Flux Density, Gauss’ Law, and
Divergence
Chapter 4:
Energy and Potential
Chapter 5:
Current and Conductors
Chapter 6:
Dielectrics and Capacitance
Chapter 8:
The Steady Magnetic Field
Chapter 9:
Magnetic Forces, Materials, and Inductance
Engineering Electromagnetics
President University
Erwin Sitompul
EEM
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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 penalty
10
–
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
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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
(
i
.
e
., the
maximum score for a make up
will be
90).
Engineering Electromagnetics
Grade Policy
•
Heading of Homework Papers (Required)
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Erwin Sitompul
EEM
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Grade Policy
Grade Policy:
Ex
tra 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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Engineering Electromagnetics
President University
Erwin Sitompul
EEM
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Electric field
Produced by the presence of
electrically charged particles,
and gives rise to the electric
force.
Magnetic field
Produced by the motion of
electric charges, or electric
current, and gives rise to the
magnetic force associated
with magnets.
Engineering Electromagnetics
What is Electromagnetics?
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Erwin Sitompul
EEM
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Engineering Electromagnetics
Electromagnetic Wave Spectrum
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Engineering Electromagnetics
Electric and magnetic field exist nearly everywhere.
Why do we learn Engineering Electromagnetics
President University
Erwin Sitompul
EEM
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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
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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
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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
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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
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Chapter 1
Vector Analysis
A B B A
( ) ( )
A B+C A B +C
( )
A B A B
1
n n
A
A
0
A B A B
Vector Algebra
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Chapter 1
Vector Analysis
Rectangular Coordinate System
•
Differential surface units:
dx dy
dy dz
dx dz
•
Differential volume unit :
dx dy dz
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Erwin Sitompul
EEM
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Chapter 1
Vector Analysis
Vector Components and Unit Vectors
r x y z
x y z
x y z
r a a a
, , :
x y z
a a a
unit vectors
?
PQ
R
PQ Q P
R r r
(2 2 ) (1 2 3 )
x y z x y z
a a a a a a
4 2
x y z
a a a
President University
Erwin Sitompul
EEM
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For any vector
B
, :
Chapter 1
Vector Analysis
Vector Components and Unit Vectors
x x y y z z
B B B
B a a + a
2 2 2
x y z
B B B
B
Magnitude of
B
B
2 2 2
B
x y z
B B B
B
a
B
B
Unit vector in the direction of
B
Example
Given points
M
(
–
1,2,1) and
N
(3,
–
3,0), find
R
MN
and
a
MN
.
(3 3 0 ) ( 1 2 1 )
MN x y z x y z
R a a a a a a
4 5
x y z
a a a
MN
MN
MN
R
a
R
2 2 2
4 5 1
4 ( 5) ( 1)
x y z
a a a
0.617 0.772 0.154
x y z
a a a
President University
Erwin Sitompul
EEM
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Chapter 1
Vector Analysis
The Dot Product
Given 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 z
A A A
A a a + a
x x y y z z
B B B
B a a + a
x x y y z z
A B A B A B
A B +
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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
Ba
B
•
The scalar component of
B
in the direction
of the unit vector
a
is
B
a
•
The vector component of
B
in the direction
of the unit vector
a
is (
B
a
)
a
President University
Erwin Sitompul
EEM
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Chapter 1
Vector Analysis
The Dot Product
Example
The three vertices of a triangle are located at
A
(6,
–
1,2),
B
(
–
2,3,
–
4), and
C
(
–
3,1,5). Find: (
a
)
R
AB
;
(
b
)
R
AC
; (
c
) the angle
θ
BAC
at vertex
A
; (
d
) the vector projection of
R
AB
on
R
AC
.
( 2 3 4 ) (6 2 )
AB x y z x y z
R a a a a a a
8 4 6
x 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 3
x y z
a a a
A
B
C
BAC
cos
AB AC AB AC BAC
R R R R
cos
AB AC
BAC
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
1
cos (0.594)
BAC
53.56
0.594
President University
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EEM
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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 z
x y z
a a a a a a
a a a
( 9 2 3 )
62
94 94
x y z
a a a
5.963 1.319 1.979
x y z
a a a
Example
The three vertices of a triangle are located at
A
(6,
–
1,2),
B
(
–
2,3,
–
4), and
C
(
–
3,1,5). Find: (
a
)
R
AB
;
(
b
)
R
AC
; (
c
) the angle
θ
BAC
at vertex
A
; (
d
) the vector projection of
R
AB
on
R
AC
.
President University
Erwin Sitompul
EEM
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sin
N AB
A B a A B
Chapter 1
Vector Analysis
The Cross Product
Given two vectors
A
and
B
, the magnitude of the
cross product
,
or
vector product
, written as
A
B
, 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
A
䈠
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 a
a a a
a a a
President University
Erwin Sitompul
EEM
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Chapter 1
Vector Analysis
The Cross Product
Example
Given
A
= 2
a
x
–
3
a
y
+
a
z
and
B
=
–
4
a
x
–
2
a
y
+5
a
z
, find
A
B
.
( ) ( ) ( )
y z z y x z x x z y x y y x z
A 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 16
x y z
a a a
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Erwin Sitompul
EEM
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Chapter 1
Vector Analysis
The Cylindrical Coordinate System
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EEM
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Chapter 1
Vector Analysis
The Cylindrical Coordinate System
•
Differential surface units:
d dz
d dz
d d
•
Differential volume unit :
d d dz
cos
x
sin
y
z z
2 2
x y
1
tan
y
x
z z
•
Relation between the
rectangular and the cylindrical
coordinate systems
President University
Erwin Sitompul
EEM
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a
z
a
a
Chapter 1
Vector Analysis
The Cylindrical Coordinate System
•
Dot products of unit vectors in
cylindrical and rectangular
coordinate systems
y
a
z
a
x
a
A
A a
( )
x x y y z z
A A A
a a + a a
x x y y z z
A A A
a a a a + a a
cos sin
x y
A A
A
A a
( )
x x y y z z
A A A
a a + a a
x x y y z z
A A A
a a a a + a a
sin cos
x y
A A
z z
A
A a
( )
x x y y z z z
A A A
a a + a a
x x z y y z z z z
A A A
a a a a + a a
z
A
?
x x y y z z z z
A A A A A A
A a a + a A a a + a
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Erwin Sitompul
EEM
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Chapter 1
Vector Analysis
The Spherical Coordinate System
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EEM
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Chapter 1
Vector Analysis
The Spherical Coordinate System
•
Differential surface units:
dr rd
sin
dr r d
sin
rd r d
•
Differential volume unit :
sin
dr rd r d
President University
Erwin Sitompul
EEM
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sin cos
x r
sin sin
y r
cos
z r
2 2 2
, 0
r x y z r
1
2 2 2
cos, 0 180
z
x y z
1
tan
y
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
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Erwin Sitompul
EEM
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Chapter 1
Vector Analysis
The Spherical Coordinate System
Example
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 2
r x y z
1
2 2 2
cos
z
x y z
1
tan
y
x
2 2 2
( 3) (2) (1)
3.742
1
1
cos
3.742
74.50
1
2
tan
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
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EEM
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Chapter 1
Vector Analysis
Homework 1
D1.4.
D1.6.
D1.8.
All homework problems from Hayt and Buck, 7th Edition.
Due: Next week
17 April 2012,
at
08:00.
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