AB - Erwin Sitompul
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Engineering Electromagnetics
Lecture 1
Dr.-Ing. Erwin Sitompul
President University
http://zitompul.wordpress.com
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Erwin Sitompul
EEM 1/1
Engineering Electromagnetics
Textbook and Syllabus
Textbook:
“Engineering Electromagnetics”,
William H. Hayt, Jr. and John A. Buck,
McGraw-Hill, 2006.
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
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Engineering Electromagnetics
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.
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Engineering Electromagnetics
Grade Policy
• Heading of Homework Papers (Required)
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).
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Engineering Electromagnetics
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
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Engineering Electromagnetics
What is Electromagnetics?
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.
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Engineering Electromagnetics
Electromagnetic Wave Spectrum
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Engineering Electromagnetics
Why do we learn Engineering Electromagnetics
Electric and magnetic field exist nearly everywhere.
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Engineering Electromagnetics
Applications
Electromagnetic principles find application in various disciplines
such as microwaves, x-rays, antennas, electric machines,
plasmas, etc.
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Engineering Electromagnetics
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.
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Engineering Electromagnetics
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.
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Chapter 1
Vector Analysis
Scalars and Vectors
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 threedimensional 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)
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Chapter 1
Vector Analysis
Vector Algebra
AB BA
A (B + C) (A B) + C
A B A (B)
A 1
A
n n
AB 0 A B
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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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Chapter 1
Vector Analysis
Vector Components and Unit Vectors
RPQ ?
r xyz
r xax ya y zaz
ax , a y , az : unit vectors
RPQ rQ rP
(2ax 2a y az ) (1ax 2a y 3az )
ax 4a y 2a z
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Chapter 1
Vector Analysis
Vector Components and Unit Vectors
For any vector B, B Bxax Bya y + Bzaz :
B Bx2 By2 Bz2 B
aB
B
Bx2 By2 Bz2
B
B
Magnitude of B
Unit vector in the direction of B
Example
Given points M(–1,2,1) and N(3,–3,0), find RMN and aMN.
RMN (3ax 3a y 0az ) (1ax 2a y 1az ) 4a x 5a y a z
a MN
4a x 5a y 1a z
R MN
0.617a x 0.772a y 0.154a z
2
2
2
R MN
4 (5) (1)
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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:
A B A B cos AB
The dot product is a scalar, and it obeys the commutative law:
A B BA
For any vector A Axax Aya y + Azaz and B Bxax Bya y + Bzaz ,
A B Ax Bx Ay By + Az Bz
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Chapter 1
Vector Analysis
The Dot Product
One of the most important applications of the dot product is that of
finding the component of a vector in a given direction.
• 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
B a B a cosBa B cosBa
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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) RAB; (b) RAC; (c) the angle
θBAC at vertex A; (d) the vector projection of RAB on RAC.
B
R AB (2ax 3a y 4az ) (6ax a y 2az ) 8a x 4a y 6a z
R AC (3ax 1a y 5az ) (6ax a y 2az ) 9a x 2a y 3a z
BAC
R AB R AC R AB R AC cosBAC
cos BAC
R R
AB AC
R AB R AC
C
A
(8a x 4a y 6a z ) (9a x 2a y 3a z )
(8) (4) (6)
2
2
2
(9) (2) (3)
2
2
2
62
116
0.594
94
BAC cos1 (0.594) 53.56
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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) RAB; (b) RAC; (c) the angle
θBAC at vertex A; (d) the vector projection of RAB on RAC.
R AB on R AC R AB a AC a AC
(9a x 2a y 3a z )
(8a x 4a y 6a z )
(9)2 (2)2 (3)2
(9a x 2a y 3a z )
2
2
2
(9) (2) (3)
62 (9a x 2a y 3a z )
94
94
5.963a x 1.319a y 1.979a z
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Chapter 1
Vector Analysis
The Cross Product
Given 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.
A B aN A B sin AB
The cross product is a vector, and it is
not commutative:
ax a y az
a y az ax
az ax a y
(B A) (A B)
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Chapter 1
Vector Analysis
The Cross Product
Example
Given A = 2ax–3ay+az and B = –4ax–2ay+5az, find AB.
A B ( Ay Bz Az By )ax ( Az Bx Ax Bz )a y ( Ax By Ay Bx )az
(3)(5) (1)(2) ax (1)(4) (2)(5) a y (2)(2) (3)(4) az
13a x 14a y 16a z
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Chapter 1
Vector Analysis
The Cylindrical Coordinate System
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Chapter 1
Vector Analysis
The Cylindrical Coordinate System
• Differential surface units:
d dz
d dz
d d
• Relation between the
rectangular and the cylindrical
coordinate systems
x cos
y sin
• Differential volume unit :
d d dz
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zz
Erwin Sitompul
x2 y 2
1 y
tan
x
zz
EEM 1/24
Chapter 1
Vector Analysis
The Cylindrical Coordinate System
?
az
az
A Ax a x Ay a y + Az a z A A a A a + Az a z
ay
A A a
( Axax Aya y + Azaz ) a
Axax a Aya y a + Azaz a
Ax cos Ay sin
• Dot products of unit vectors in
cylindrical and rectangular
coordinate systems
A A a
( Axax Aya y + Azaz ) a
Axax a Aya y a + Azaz a
Ax sin Ay cos
a
a
ax
Az A a z
( Axax Aya y + Azaz ) az
Axax az Aya y az + Azaz az
Az
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Chapter 1
Vector Analysis
The Spherical Coordinate System
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Chapter 1
Vector Analysis
The Spherical Coordinate System
• Differential surface units:
dr rd
dr r sin d
rd r sin d
• Differential volume unit :
dr rd r sin d
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Chapter 1
Vector Analysis
The Spherical Coordinate System
• Relation between the rectangular and
the spherical coordinate systems
x r sin cos
r x2 y2 z 2 , r 0
y r sin sin
cos
1
z r cos
tan
1
z
x y z
2
2
2
, 0 180
y
x
• Dot products of unit vectors in spherical and
rectangular coordinate systems
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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.
r x 2 y 2 z 2 (3) 2 (2) 2 (1) 2 3.742
cos1
tan
1
z
x2 y 2 z 2
cos 1
1
74.50
3.742
y
1 2
tan
33.69 180 146.31
x
3
C (r 3.742, 74.50, 146.31)
D( x 0.585, y 1.607, z 4.698)
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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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