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Electromagnetic Field TheoryCourse Code EE2213
2nd Year EE Students
Prof. Dr. Magdi El-Saadawiwww.saadawi1.net
2017/2018
cOntents
Chapter 1 Introduction and Course Objectives
Chapter 2 Vector Algebra &Maxwell’s Equations
Chapter 3 Electrostatic Field Theorems
Chapter 4 Stationary Current Fields
Chapter 5 Stationary Magnetic Fields
Chapter 6 Time-Varying Fields and Maxwell’s Equations
Chapter 7 Electromagnetic Wave Propagation
Chapter 1
intrOductiOn
And
cOurse Outlines
Chapter 1Introduction and Course Outlines
1.1. What is Electromagnetics?
1.2. Course Aims
1.3. Course Attributes
1.4. Assessment Scheduling and Weighting
1.4.1 Student Assessment Methods
1.4.2 Assessment Schedule
1.4.3 Weighting of Class Grading for
1.5. List of References
EM principles find applications in:
microwaves, antennas, electric machines, satellitecommunications, bio-electromagnetics, plasmas,nuclear research, fiber optics, electromagneticinterference and compatibility …….
1.1. What is Electromagnetics?
1.1. What is Electromagnetics?
EM devices include:
Transformers, electric relays, radio/TV, telephone,electric motors, transmission lines, waveguides,antennas, optical fibers, radars, and lasers.
The design of these devices requires thoroughknowledge of the laws and principles of EM.
1.2. Course Aims
This course aims to provide students with an
understanding of electromagnetic field theory and
wave propagation in the context of applications in
electrical engineering.
1.3. Course Attributes سمات -خصائص
• Apply knowledge of mathematics and
engineering concepts related to electromagnetic
and electrostatic field.
• Manage activities related to electromagnetics,
using the techniques, skills, and appropriate
engineering tools.
1.4. Students’ Assessment كیفیة تقییم الطالب
جدید
1.6. List of References
1. F. M. Youssef, “Electromagnetic Field Theory”, 4th editionMansoura University Press, 2012.
2. P. J. Nolan, “The Fundamentals of Electromagnetic Theory”, StateUniversity of New York, 2009.
3. N. N. Rao, “Fundamentals of Electromagnetics for Electrical andComputer Engineering”, Illinois Ece Series, 2008.
4. R. Bansal, “Fundamentals of Engineering Electromagnetics”, Taylor& Francis Group, 2006.
5. R. Bansal, “Handbook of Engineering Electromagnetics”, MarcelDekker, Inc., 2004.
1.6. List of References
6. W.H. Hayt, J.A. Buck, “Engineering Electromagnetics”, 6th edition,McGraw Companies, 2001.
7. C. R. Paul, K. W. Whites, and S. A. Nasar “Introduction toElectromagnetic Fields”, Mcgraw-Hill, 1997.
8. H. P. Neff, “Introductory Electromagnetics”, John Wiley & Sons Inc.,1991.
9. M. N. Sadiku, “Elements of Electromagnetics”, The Oxford Series inElectrical and Computer Engineering, Oxford University Press2010.
10. D. K. Cheng, “Field and wave Electromagnetics”, Addison-WeselyPublishing Company, 1983
Chapter 2
VectOr AlgebrA
Contents
2.0. Introduction
2.1. A Preview of the Course
2.2. Vector Analysis
2.3. Vector Multiplication
2.4. Components of a vector
2.5. Coordinate Systems
2.6. DEL Operator
2.7. The Gradient
2.8. Divergence of a vector and Divergence Theorem
2.9. The curl of a vector and Stock’s theorem
2.10. The Laplacian
2.10. Important Vector Identities
2.0 Introduction
In this introductory chapter:
• A brief review of the vector algebra.
• Presentation of the three most common coordinate systems, Cartesian, Cylindrical, and Spherical coordination
• Explanation of more complicated operations, such as divergence of a vector, gradient of a scalar, curl of a vector, line integral, flux of a vector.
• The use for these vector operations in Maxwell’s equations and in practical applications such as lines, guides, and antennas.
2.1 A Preview of the Course
The subject of EM phenomena in this book can be summarized in Maxwell's equations:
So, we have to study vectors in details
where
2.2. Vector Analysis
Vector analysis is a mathematical tool with which
electromagnetic (EM) concepts are most
conveniently express
سیةتحلیل المتجھات ھو أداة ریاضیة لتسھیل التعبیر عن المفاھیم الكھرومغناطی
2.2.1 Scalars and Vectors
Scalar refers to a quantity whose value may be
represented by its magnitude (a single real number).
For example: temperature, mass, density, pressure,
voltage, …..
2.2.1 Scalars and Vectors
A vector quantity has both a magnitude and a direction in space.
We shall be concerned with two-and three dimensional spaces only but vectors may be defined in n-dimensional space in more advanced applications.
examples for vectors are: Force, velocity, acceleration, …..
2.2.1 Scalars and Vectors
EM theory is a study of some particular fields.
A field is a function that specifies a particular quantity everywhere in a region.
The field is said to be a scalar (or vector) field.
2.2.2 Unit Vector
2.2.2 Unit Vector
2.2.2 Unit Vector
2.2.3 Vector addition and subtraction
• Two vectors are equal if they have the samemagnitude, and direction.
• Adding two vectors produces a new one
2.2.3 Vector addition and subtraction (cont.)
The vector addition obeys both:
commutative law:
قانون التبادل
associative law:
قانون التجمیع
2.2.3 Vector addition and subtraction (cont.)
Vector Subtraction
2.2.3 Vector addition and subtraction (cont.)
Vectors may be multiplied by scalars. Multiplication of a vector by a scalar also obeys the associative and distributive laws of algebra, leading to:
Solved Example
2.3. Vector Multiplication
Vectors may be multiplied by scalars: The magnitude of the vector changes, but its direction does not when the scalar is positive.
In case of vector multiplication:
the dot product (also called scalar product)
the cross product (also called vector product).
2.3.1 The dot product
Two vectors and are said to be orthogonal (or perpendicular) with each other if
2.3.1 The dot product (cont.)
The dot product obeys the following identities:
2.3.1 The dot product (cont.)
OR
2.3.1 The dot product (cont.)
The most common application of the dot product is:
The mechanical work W, where a constant force F applied over a straight displacement L does an amount of work i.e.
Another example is the magnetic fields Φ, where
2.3.2 The cross product
2.3.2 The cross product (cont.)
2.3.2 The cross product (cont.)
2.4. Components of a Vector
The unit vectors in the Cartesian coordinate system are ax, ay, and az.
They are directed along the x, y, and z axes
Any vector in
Cartesian coordinate
system can be
represented by means
of its components
2.4. Components of a Vector
Example 3
Example 3 (cont.)
2.5 Coordinate Systems
Coordinate systems that will be used in this textbook are: the Cartesian (rectangular), circular cylindrical, and spherical coordinate systems.
In three dimension space, any point are defined by three crossing perpendicular planes
Cartesian: x, y , z
Cylindrical: ρ,φ, z
Spherical: r, θ, φ
Representation of a point in Cartesian coordinates
Unit vectors
Differential elements of volume
Differential elements of vector length, vector area, and scalar volume
Cylindrical Coordinates
Unit vectors
Differential elements of volume
Differential elements of vector length, vector area, and scalar volume
Unit vectors
Unit vectors
Differential elements of volume
Differential elements of vector length, vector area, and scalar volume
Transformation between coordinate system
Transformation between coordinate system
Cross Product in Cylindrical and Spherical coordinates
Example 4
Example 4
Video Links
Cylindrical coordinate system
https://www.youtube.com/watch?v=EthQB3325GM
Spherical coordinate system
https://www.youtube.com/watch?v=cImmxNYiNeg