Engineering Electromagnetics
Lecture 1
Dr.-Ing. Erwin Sitompul
President University
http://zitompul.wordpress.com
2 0 1 3
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Engineering Electromagnetics
Textbook and Syllabus
Textbook:
“Engineering Electromagnetics”,
William H. Hayt, Jr. and John A. Buck,
McGraw-Hill, 2006.
Syllabus:
Chapter 1:
Chapter 2:
Chapter 3:
Chapter 4:
Chapter 5:
Chapter 6:
Chapter 8:
Chapter 9:
Vector Analysis
Coulomb’s Law and Electric Field Intensity
Electric Flux Density, Gauss’ Law, and Divergence
Energy and Potential
Current and Conductors
Dielectrics and Capacitance
The Steady Magnetic Field
Magnetic Forces, Materials, and Inductance
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Engineering Electromagnetics
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, one day before the
schedule of the lecture. Late submission will be penalized by
point deduction of –10·n, where n is the total number of
lateness made.
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
Engineering Electromagnetics
Homework 7
Rudi Bravo
009201700008
21 March 2021
D6.2. Answer: . . . . . . . .
• Heading of Homework Papers (Required)
 Midterm and final exams follow the schedule released by AAB
(Academic Administration Bureau)
 Make up for quizzes must be requested within one week after
the date of the respective quizzes.
 Make up for mid exam and final exam must be requested
directly to AAB.
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Engineering Electromagnetics
Grade Policy
 To maintain the integrity, the score of a make up quiz or exam,
upon discretion, can be multiplied by 0.9 (i.e., the maximum
score for a make up will be 90).
 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 1 days after class. Please
check the course homepage regularly.
http://zitompul.wordpress.com
 The use of internet for any purpose during class sessions is
strictly forbidden.
 You are expected to write a note along the lectures to record
your own conclusions or materials which are not covered by
the lecture slides.
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Engineering Electromagnetics
Chapter 0
Introduction
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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
What is Electromagnetics?
 An electromagnetic field
is generated when charged
particles, such as electrons,
are accelerated.
 All electrically charged
particles are surrounded by
electric fields.
 Charged particles in motion
produce magnetic fields.
 When the velocity of a
charged particle changes,
an electromagnetic field is
produced.
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Engineering Electromagnetics
Why do we learn Engineering Electromagnetics?
 EEM is the study of the underlying laws that govern the
manipulation of electricity and magnetism, and how we use
these laws to our advantage.
 EEM is the source of fundamental principles behind many
branches of electrical engineering, and indirectly impacts many
other branches.
 EM fields and forces are the basis of modern electrical
systems. It represents an essential and fundamental
background that underlies future advances in modern
communications, computer systems, digital electronics, signal
processing, and energy systems.
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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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Engineering Electromagnetics
Applications
AGM-88E Anti-Radiation
Guided Missile
E-bomb (Electromagnetic• Able to guide itself to destroy a
radar using the signal transmitted
pulse bomb)
by the radar.
• Designed to attack people’s
• Destroy radar and intimidate its
dependency on electricity.
operators, creates hole in enemy
• Instead of cutting off power in an
defense.
area, an e-bomb would destroy
• Unit cost US$ 284,000 – US$
most machines that use
870,000.
electricity.
• Generators, cars,
telecommunications would be
non operable.
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Engineering Electromagnetics
Chapter 1
Vector Analysis
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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
AB BA
A  (B + C)  ( A  B) + C
A  B  A  ( B )
A 1
 A
n n
AB  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
R PQ ?
r  xyz
r  xa x  ya y  za z
a x , a y , a z : unit vectors
R PQ  rQ  rP
 (2a x  2a y  a z )  (1a x  2a y  3a z )
 a x  4a y  2a z
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Chapter 1
Vector Analysis
Vector Components and Unit Vectors
 For any vector B, B  Bxa x  By a y + Bz a z :
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.
R MN  (3a x  3a y  0a z )  (1a x  2a y  1a z )  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  BA
 For any vector A  Axa x  Ay a y + Az a z and B  Bxa x  By a y + Bz a z ,
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 Ba
• The vector component of B in the direction
of the unit vector a is (Ba)a
B  a  B a cosBa  B cosBa
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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  (2a x  3a y  4a z )  (6a x  a y  2a z )  8a x  4a y  6a z
R AC  (3a x  1a y  5a z )  (6a x  a y  2a z )  9a x  2a y  3a z
 BAC
A
R AB  R AC  R AB R AC cosBAC
 cos  BAC
R R
 AB AC 
R AB R AC
C
(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  cos 1 (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 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B 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  a N 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 AB.
A  B  ( Ay Bz  Az By )a x  ( Az Bx  Ax Bz )a y  ( Ax By  Ay Bx )a z
  (3)(5)  (1)(2)  ax   (1)(4)  (2)(5)  a y   (2)(2)  (3)(4)  a z
 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 
• Differential volume unit :
d    d  dz
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y    sin 
  x2  y 2
1 y
  tan
zz
zz
x
EEM 1/28
Chapter 1
Vector Analysis
The Cylindrical Coordinate System
?
az
az
A  Axa x  Ay a y + Az a z  A  A a   A a + Az a z
ay
A  A  a 
 ( Axa x  Ay a y + Az a z )  a 
 Axa x  a   Ay a y  a  + Az a z  a 
 Ax cos   Ay sin 
• Dot products of unit vectors in
cylindrical and rectangular
coordinate systems
A  A  a
 ( Ax a x  Ay a y + Az a z )  a
 Axa x  a  Ay a y  a + Az a z  a
  Ax sin   Ay cos 
a
a
ax
Az  A  a z
 ( Ax a x  Ay a y + Az a z )  a z
 Axa x  a z  Ay a y  a z + Az a z  a z
 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  y 2  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
  cos
z
1
  tan 1
x2  y 2  z 2
 cos 1
1
 74.50
3.742
y
2
 tan 1
 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: Monday, 15 April 2013.
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