Electromagnetic Field TheoryCourse Code EE2213

2nd Year EE Students

Prof. Dr. Magdi El-Saadawiwww.saadawi1.net

saadawi1@gmail.com

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