ENE 325 Electromagnetic Fields and Waves Lecture 1 Electrostatics
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Transcript ENE 325 Electromagnetic Fields and Waves Lecture 1 Electrostatics
ENE 325
Electromagnetic Fields and
Waves
Lecture 1 Electrostatics
1
Syllabus
Dr. Rardchawadee Silapunt,
[email protected]
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)
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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.
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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
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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
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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
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Electrostatics:
Resistance of a Conductor
Joule’s Law
Boundary Conditions for the current density
The Electromotive Force
The Biot-Savart Law
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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
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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
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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.
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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
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Vectors - Magnitude and direction
1. Cartesian coordinate system (x-, y-, z-)
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Vectors - Magnitude and direction
2. Cylindrical coordinate system (, , z)
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Vectors - Magnitude and direction
3. Spherical coordinate system (, , )
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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 B y )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
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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
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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
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c) Find the direction of A B
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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
109
F /m
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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
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Electric field lines
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Spherical coordinate system
orthogonal point (r,, )
r = a radial distance from the origin to the point (m)
= the angle measured from the positive 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
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Point conversion between cartesian and
spherical coordinate systems
A conversion from
P(x,y,z) to P(r,, )
r x2 y 2 z 2
1
z
cos
r
A conversion from
P(r,, ) to P(x,y,z)
x r sin cos
y r sin sin
z r cos
1
y
tan
x
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Unit vector conversion (Spherical
coordinates)
ar
a
a
ax
sin cos
cos cos
sin
ay
sin sin
cos sin
cos
az
cos
sin
0
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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 ar
A A a
A A a
differential element
volume:
dv = r2sindrdd
surface vector: ds r 2 sin d d ar
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Ex3 Transform the vector field
G ( xz / y )a x into spherical components and
variables
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Ex4 Convert the Cartesian coordinate point P(3, 5,
9) to its equivalent point in spherical coordinates.
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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
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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 y 2
x cos
y sin
zz
1
y
tan
x
zz
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Unit vector conversion (Cylindrical
coordinates)
a
a
az
ax
cos
sin
0
ay
sin
cos
0
az
0
0
1
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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 ar
A A a
Az A a z
differential element
volume:
dv = dddz
surface vector: ds d d az
(top)
ds ddza
(side)
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Ex5 Transform the vector B ya x xa y za z
into cylindrical coordinates.
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Ex6 Convert the Cartesian coordinate point P(3, 5,
9) to its equivalent point in cylindrical coordinates.
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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.
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