ENE 325
Electromagnetic Fields and
Waves
Lecture 1 Electrostatics
1
Syllabus





Dr. Ekapon Siwapornsathain, email:
sie4129@hotmail.com
Course webpage:
http://webstaffs.kmutt.ac.th/ekapon.siw
Lecture: 9:30pm-12:20pm Wednesday, Rm.
CB41004
Office hours :By appointment
Textbook: Fundamentals of Electromagnetics
with Engineering Applications by Stuart M.
Wentworth (Wiley, 2005)
2
Course Objectives
This is the course on beginning level electrodynamics. The
purpose of the course is to provide junior electrical engineering
students with the fundamental methods to analyze and
understand electromagnetic field problems that arise in various
branches of engineering science.
3
Agreement
The instruction will be given mostly in English.
You are not allowed to say the followings (or
anything of the similar nature and meaning):
 “อาจารย์ , พูดภาษาไทยเถอะ
ขอร้ อง”
 “อาจารย์ , เอาภาษาไทยครับ”
If you do, I will punish you by asking you to step
outside the lecture room. I will make a super
difficult exams and will not tutor you or review
the material for you before the exams.
4
Prerequisite knowledge and/or skills
 Basic physics background relevant to electromagnetism:
charge, force, SI system of units; basic differential and
integral vector calculus
 Concurrent study of introductory lumped circuit analysis
 Ability to visualize problems in 3-D is a must!
 Reflection: periodically review the material, ask
questions to yourself or to the instructor and discuss with
your classmates.
5
Course outline
Introduction to course:
 Review of vector operations
 Orthogonal coordinate systems and change of
coordinates
 Integrals containing vector functions
 Gradient of a scalar field and divergence of a vector field
6
Electrostatics:
 Fundamental postulates of electrostatics and
Coulomb's Law
 Electric field due to a system of discrete charges
 Electric field due to a continuous distribution of charge
 Gauss' Law and applications
 Electric Potential
 Conductors in static electric field
 Dielectrics in static electric fields
 Electric Flux Density, dielectric constant
 Boundary Conditions
 Capacitor and Capacitance
 Nature of Current and Current Density
7
Electrostatics:





Resistance of a Conductor
Joule’s Law
Boundary Conditions for the current density
The Electromotive Force
The Biot-Savart Law
8
Magnetostatics:
 Ampere’s
Force Law
 Magnetic Torque
 Magnetic Flux and Gauss’s Law for Magnetic Fields
 Magnetic Vector Potential
 Magnetic Field Intensity and Ampere’s Circuital Law
 Magnetic Material
 Boundary Conditions for Magnetic Fields
 Energy in a Magnetic Field
 Magnetic Circuits
 Inductance
9
Dynamic Fields:
Faraday's Law and induced emf
 Transformers
 Displacement Current
 Time-dependent Maxwell's equations and
electromagnetic wave equations
 Time-harmonic wave problems, uniform plane waves in
lossless media, Poynting's vector and theorem
 Uniform plane waves in lossy media
 Uniform plane wave transmission and reflection on
normal and oblique incidence

10
Grading

Homework
20%
Midterm exam 40%
Final exam
40%
Vision:
Providing opportunities for intellectual growth in the context
of an engineering discipline for the attainment of professional
competence, and for the development of a sense of the social
context of technology.
11
Examples of Electromagnetic fields

Electromagnetic fields
–
–
–
–

Solar radiation
Lightning
Radio communication
Microwave oven
Light consists of electric and magnetic fields. An
electromagnetic wave can propagate in a
vacuum with a speed velocity c=2.998x108 m/s
f = frequency (Hz)
 = wavelength (m)
c = f
12
Aurora Borealis (northern lights)
13
Vectors - Magnitude and direction
1. Cartesian coordinate system (x-, y-, z-)
14
Vectors - Magnitude and direction
2. Cylindrical coordinate system (, , z)
15
Vectors - Magnitude and direction
3. Spherical coordinate system (, , )
16
Manipulation of vectors

To find a vector from point m to n
A  ( xn  xm )a x  ( yn  ym )a y  ( zn  zm )a z

Vector addition and subtraction
A  B  ( Ax  Bx )a x  ( Ay  By )a y  ( Az  Bz )a z
A  B  ( Ax  Bx )a x  ( Ay  By )a y  ( Az  Bz )a z

Vector multiplication
– vector  vector = vector Q  4a x  5a y  20a z
– vector  scalar = vector Q  4 p  4a y
17
Ex1:

Point P (0, 1, 0), Point R (2, 2, 0)
The magnitude of the vector line from the origin
(0, 0, 0) to point P
op  1a y

The unit vector pointed in the direction of vectorR
R(2, 2, 0)  R  2a x  2a y
R  Ra R
R  R  22  22  2 2
R (2a x  2a y )
aR  
R
2 2
18
Ex2:
P (0,-4, 0), Q (0,0,5), R (1,8,0), and S
(7,0,2)

a) Find the vector from point P to point Q

b) Find the vector from point R to point S
19

c) Find the direction of A  B
20
Coulomb’s law
Law of attraction: positive charge attracts
negative charge
 Same polarity charges repel one another


Forces between two charges
Coulomb’s Law
F 12
Q1Q2

a
2 12
4 0 R12
Q = electric charge (coulomb, C)
0 = 8.854x10-12 F/m
 109
F /m
36
21
Electric field intensity

An electric field from Q1 is exerted by a force
between Q1 and Q2 and the magnitude of Q2
F 12
E1 
Q2

V/m
or we can write
E
Q
4 0 R
2
aR
V/m
22
Electric field lines
23
Spherical coordinate system




orthogonal point (r,, )
r = a radial distance from the origin to the point (m)
 = the angle measured from the positive z-axis (0    )
 = an azimuthal angle, measured from x-axis (0    2)
A vector representation in the spherical coordinate system:
A  Ar a r  A a  A a
24
Point conversion between cartesian and
spherical coordinate systems
A conversion from
P(x,y,z) to P(r,, )
r  x2  y 2  z 2
z
 
1  y 
  tan  
x
  cos 1  
r
A conversion from
P(r,, ) to P(x,y,z)
x  r sin  cos 
y  r sin  sin 
z  r cos 
25
Unit vector conversion (Spherical
coordinates)
ar
a
a
ax 
sin  cos 
cos  cos 
 sin 
ay 
sin  sin 
cos  sin 
cos 
az 
cos 
 sin 
0
26
Find any desired component of a vector
Take the dot product of the vector and a unit vector in the
desired direction to find any desired component of a vector.
Ar  A  a r
A  A  a
A  A  a
differential element
volume:
dv = r2sindrdd
surface vector: ds  r 2 sin  d dar
27
Ex3 Transform the vector field
G  ( xz / y)a x into spherical components and
variables
28
Ex4 Convert the Cartesian coordinate point P(3, 5,
9) to its equivalent point in spherical coordinates.
29
Line charges and the cylindrical coordinate
system
orthogonal point (, , z)
  = a radial distance (m)
  = the angle measured from x axis to the projection of
the radial line onto x-y plane
 z = a distance z (m)

A vector representation in the cylindrical coordinate system:
A  A a   A a  Az a z
30
Point conversion between cartesian and
cylindrical coordinate systems
A conversion from
P(x,y,z) to P(r,, z)
A conversion from
P(r,, z) to P(x,y,z)
  x2  y2
x   cos 
y   sin 
zz
1 
y
  tan  
x
zz
31
Unit vector conversion (Cylindrical
coordinates)
a
a
az
ax 
cos 
 sin 
0
ay 
sin 
cos 
0
az 
0
0
1
32
Find any desired component of a vector
Take the dot product of the vector and a unit vector in the
desired direction to find any desired component of a vector.
Ar  A  a r
A  A  a
Az  A  a z
differential element
volume:
dv = dddz
surface vector: ds  d d az
(top)
ds  ddza
(side)
33
Ex5 Transform the vector B  ya x  xa y  za z
into cylindrical coordinates
34
Ex6 Convert the Cartesian coordinate point P(3, 5,
9) to its equivalent point in cylindrical coordinates.
35
Ex7 A volume bounded by radius  from 3 to 4 cm,
the height is 0 to 6 cm, the angle is 90-135,
determine the volume.
36