0 Introduction Electromagnetic

Syllabus for Electromagnetic Theorem Fourth Stage Physics Department College of Science Chapter One: Vector Analysis and Coordinate Systems 1-1 Introduction 1-2 Scalar and Vectors 1-3 Unit Vector 1-4 Equality of Two Vectors 1-5 Vector Addition and Subtraction 1-6 Position and Distance Vector 1-7 Vector Multiplications 1-7-1 Simple Product 1-7-2 Scalar or dot Product 1-7-3 Vector or Cross Product 1-8 Scalar and Vector Triple Product 1-8-1 Scalar Triple Product 1-8-2 Vector Triple Product 1-9 Del ∇ Operator 1-9-1 Gradiant Operator 1-9-2 Divergence Operator and Divergence Theorem 1-9-3 Curl Operator and Stokes Theorem 1-10 Laplacian of a Vector 1-11 Integral Calculus 1-11-1 Line, Surface, and Volume Integrals 1-11-2 The Fundamental Theorem for Gradients 1-11-3 The Fundamental Theorem for Divergences 1-11-2 The Fundamental Theorem for Curls 1-12 Curvilinear Coordinates Systems 1-12-1 Cylindrical Coordinate 1-12-2 Spherical Coordinate 1-13 Transformation between Coordinate systems 1-13-1 Cartesian to Cylindrical Transformation 1-13-2 Cartesian to Spherical Transformation 1-13-3 Cylindrical to Spherical Transformation Chapter Two: Electrostatic Fields 2-1 The Electric Field 2-2 Coulomb’s Law 2-3 Continuous Charge Distributions 1

2-4 Electric field Intensity of a Uniform Charge Distributions 2-4-1 Uniform Line Charge Distribution 2-4-2 Uniform Surface Charge Distribution 2-4-3 Uniform Volume Charge Distribution 2-5 Gauss's Law and Applications 2-5-1 Application of gauss's Law on Point Charge 2-5-2 Application of gauss's Law on Line Charge Distribution 2-5-3 Application of gauss's Law on Surface Charge Distribution 2-5-4 Application of gauss's Law to Uniformly Charged Sphere 2-5-5 Application of gauss's Law to Coaxial Cable 2-6 Electric Potential 2-6-1 Poisson’s Equation and Laplace’s Equation 2-6-1 The Potential of a Localized Charge Distribution 2-7 Work and Energy in Electrostatics 2-7-1 The Work Done to Move a Charge 2-7-2 The Energy of a Point Charge Distribution 2-7-3 The Energy of a Continuous Charge Distribution 2-8 Capacitors Chapter Three: Special Techniques 3-1 Laplace’s Equation 3-1-1 Laplace’s Equation in One Dimension 3-1-1 Laplace’s Equation in Two Dimensions 3-1-1 Laplace’s Equation in Three Dimensions 3-1-2 Boundary Conditions and Uniqueness Theorem 3-2 The Method of Images 3-3 Separation of Variables 3-3-1 Cartesian Coordinates 3-3-2 Spherical Coordinates 3-4 The Monopole and Dipole Terms 3-5 The Electric Field of a Dipole Chapter Four: Electrostatic Field in Matter 4-1 Polarization 4-1-1 Dielectrics 4-1-2 Induced Dipoles 4-1-3 Alignment of Polar Molecules 4-2 The Field of a Polarized Object 4-2-1 Bound Charges 4-2-2 The Field Inside a Dielectric 4-3 The Electric Displacement 4-4 Gauss’s Law in The Presence of Dielectrics 4-5 Linear Dielectrics 4-5-1 Susceptibility, Permittivity, Dielectric Constant 4-5-2 Boundary Value Problems with Linear Dielectrics 4-5-3 Energy in Dielectric Systems 2

4-5-4 Forces on Dielectrics Chapter Five: Magnetostatics Field 5-1 The Lorentz Force Law 5-2 The Biot-Savart Law 5-3 The Magnetic Field of a Steady Current 5-4 Straight-Line Currents 5-5 The Divergence and Curl of B 5-6 Application of Ampere's Law 5-6-1 Infinite Line Current 5-6-2 Infinite Sheet Current 5-6-3 Infinitely Long Coaxial Transmission Line 5-6-4 Infinite Solenoid Coil 5-6-5 Toroidal Coil 5-7 Comparison of Magnetics and Electrostatics 5-8 Magnetic Vector Potential Chapter Six: Magnetic Fields in Matter 7-1 Magnetization 7-2 Diamagnets, Paramagnets, Ferromagnets 7-3 Torques and Forces on Magnetic Dipoles 7-4 Effect of a Magnetic Field on Atomic Orbits 7-5 The Field of a Magnetized Objet 7-5-1 Bound Currents 7-5-2 The Magnetic Field Inside Matter 7-6 The Auxiliary Field H 7-7 Ampere’s Law in Magnetized Materials 7-8 Linear and Nonlinear Media 7-9 Magnetic Susceptibility and Permeability Chapter Seven: Electrodynamics Fields 7-1 Electromotive Force emf 7-2 Ohm’s Law 7-3 Transformer and Motional electromotive forces emf 7-3-1 Stationary Loop in Time-Varying Magnetic Field 7-3-2 Moving Loop in Static Magnetic Field 7-3-3 Moving Loop in Time Varying Magnetic Field 7-4 Electromagnetic Induction 7-4-1 Faraday’s Law 7-4-2 The Induced Electric Field 7-4-3 Inductance 7-4-4 Energy in Magnetic Fields 7-5 Electrodynamics before Maxwell 7-6 How Maxwell Fixed Ampere’s Law 3

7-7 Displacement Current 7-8 Maxwell’s Equations in Final Forms 7-9 Maxwell’s Equations in Matter 7-10 Propagation of Electromagnetic Waves in Different Medium 7-10-1 In Free Space 7-10-2 In Lossy Medium 7-10-3 In Perfect Dielectric 7-10-4 In Good Conductor 7-11 Power and the Poynting Vector Reffrences [1] David J. Griffiths, and Reed College, “Introduction to Electrodynamics”, Prentice-Hall, Inc. (1999). [2] Herbert P. Neff, “Introductory Electromagnetics”, John Wiley & Sons, Inc., (1991). [3] Matthew N. O. Sadiku, “Elements of Electromagnetics”, Fourth Edition, Oxford University Press, Inc., (2007). [4] Joseph A. Edminister, “Schaum’s outline of Theory and Problems of Electromagnetis”, Second Edition, The McGraw-Hill Companies, Inc. (1993).

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History of Electric and Magnetic Phenomenon • ca. 900 Legend has it that while walking across a field in northern

Greece, a shepherd named Magnus experiences a pull on the iron nails in his sandals by the black rock he was standing on. The region was later named Magnesia and the rock became known as magnetite [a form of iron with permanent magnetism].

• ca. 600 Greek philosopher Thales describes how amber, after being

rubbed with cat fur, can pick up feathers [static electricity].

• ca. 1000 Magnetic compass used as a navigational device.

• 1600 William Gilbert (English) coins the term electric after the Greek

word for amber (elektron), and observes that a compass needle points north-south because the Earth acts as a bar magnet.

• 1671 Isaac Newton (English) demonstrates that white light is a

mixture of all the colors.

• 1733 Charles-Francois du Fay (French) discovered that electric

charges are of two forms, and that like charges repel and unlike charges attract.

• 1745 Pieter van Musschenbroek (Dutch) invents the Leyden jar, the

first electrical capacitor.

• 1752 Benjamin Franklin (American) invents the lightning rod and

demonstrates that lightning is electricity.

• 1785 Charles-Augustin de Coulomb (French) demonstrates that the

electrical force between charges is proportional to the inverse of the square of the distance between them.

• 1800 Alessandro Volta (Italian) develops the first electric battery.

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• 1820

Hans Christian Oersted (Danish) demonstrates the interconnection between electricity and magnetism through his discovery that an electric current in a wire causes a compass needle to orient itself perpendicular to the wire.

• 1820 Andre-Marie Ampere (French) notes that parallel currents in

wires attract each other and opposite currents repel.

• 1820 Jean-Baptiste Biot (French) and Felix Savart (French) develop

the Biot-Savart law relating the magnetic field induced by a wire segment to the current flowing through it.

• 1827 Georg Simon Ohm (German) formulates Ohm’s law relating

electric potential to current and resistance.

• 1827 Joseph Henry (American) introduces the concept of inductance

and built one of the earliest electric motors. He also assisted Samuel Morse in the development of the telegraph.

• 1831 Michael Faraday (English) discovers that a changing magnetic

flux can induce an electromotive force.

• 1835 Carl Friedrich Gauss (German) formulates Gauss’s law relating

the electric flux flowing through an enclosed surface to the enclosed electric charge.

• 1873 James Clerk Maxwell (Scottish) publishes his Treatise on

Electricity and Magnetism in which he unites the discoveries of Coulomb, Oersted, Ampere, Faraday, and others into four elegantly constructed mathematical equations known today as Maxwell’s Equations.

• 1887 Heinrich Hertz (German) builds a system that can generate

electromagnetic waves (at radio frequencies) and detect them.

• 1888 Nikola Tesla (Serbian-American) invents the ac (alternating

current) electric motor.

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• 1895 Wilhelm Roentgen (German) discovers Xrays. One of his first X-

ray images was of the bones in his wife’s hand. [1901 Nobel Prize in physics.]

• 1897 Joseph John Thomson (English) discovers the electron and

measures its charge-to-mass ratio. [1906 Nobel Prize in physics.]

• 1905 Albert Einstein (German-American) explains the photoelectric

effect discovered earlier by Hertz in 1887. [1921 Nobel Prize in physics.]

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Table (1): Branches of electromagnetic spectrum in terms of their frequencies, wavelengths and energies:

Branches

Frequency (Hz)

1.

Cosmic Ray

> 1024

<10-12

2.

Gamma Ray

1019-1023

3.

X-Ray

4.

No

Sources

Applications

> 106

Cosmic

Astronomy

10-10 – 10-12

104 - 106

Radioactive elements

Cancer therapy

1016-1019

10-10 - 10-8

102 –104

X-Ray machine

Medical diagnosis

Ultra Violet

1015-1017

10-9 - 10-7

101 –103

Arc Welding

Sterilization

5.

Visible light

1014-1015

10-7 - 10-6

5–7

The Sun

Vision

6.

Infrared

1011-1015

10-6 - 10-3

10-3 - 5

Radiant Heater

Photography

10 –10

1.Microwave oven 2. Mobile phone towers

Tv, radar & Satellite communication

<10-6

Tv, FM radio & AM Radio towers with Power lines

Telephone, Navigation & Radio Broadcasting

7.

8.

Microwave

Radio Wave

8

10 -10

11

101-108

Wavelength (m) Energy (ev)

-3

-6

10 - 1

1 - 108

8

-3

Table (2): Branches of Radio Wave Frequencies with Their Applications

No

Branches

Frequency (Hz)

Applications

1.

ELF

(3-30)Hz

Detection of buried metal or objects

2.

SLF

(30-300)Hz

Sensing or earth’s ionosphere

3.

ULF

(300-3000)Hz

Sensing or earth’s ionosphere

4.

VLF

(3-30)kHz

Submarine communication

5.

LF

(30-300)kHz

Short distance communication and radio broadcasting

6.

MF

(300-3000)kHz

AM- Radio Broadcasting

7.

HF

(3-30)MHz

Long distance communication and radio broadcasting

8.

VHF

(30-300)MHz

FM-Radio broadcast and TV

9.

UHF

(300-3000)MHz

Radar , Colure TV and Mobile communication

10.

SHF

(3-30)GHz

Aircraft radar, Satellites communication

11.

EHF

(30-300)GHz

Not used due to the high attenuation by atmospheric region

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Electromagnetic Field: Is a branch of physics or electrical engineering which studies the electric and magnetic phenomenon. Electromagnetic Field: Is a science which studies the electric and magnetic phenomenon with their engineering applications. Wave: Generally the wave is defined as a form of energy in move. Field: Is defined as the action at a distance between two objects without direct contact, such as Electric, Magnetic and Gravitational fields. The source of the production of electric, magnetic and electromagnetic field 10

ELECTROSTATICS Field: Stationary Charges produce E-field. This field and their phenomenon’s have been studied by many scientists: Coulomb, Ohm, Gauss, Kirschofe and Volta. ELECTROSTATICS – The electric charges do not change position in time. Therefore, ρ, E and D are constant and there is nomagnetic field H, since there is no current density J. MAGNETOSTATICS – The charge crossing a given crosssection (current) does not vary in time. Therefore, J, H and B are constant. Although charges are moving, the steady current maintains a constant charge density ρ in space and the electric field E is static. MAGNETOSTATICS Field: Moving charges or stationary current lead to the production of magnetic field. This field and their phenomenon’s have been studied by many scientists: Oerestd, Ampere, Biot-Savart, Henry, Lenz, Lorentz and Faraday. Electromagnetic Field: Time varying current or when the charge is accelerated (i.e. moving with varying velocity) the field which produced is known as electromagnetic field. This theory has been constructed by Maxwell who unified the theory of electricity and magnetism through a set of four equations known as the Maxwell’s equation:   ∇⋅ D = ρv    ∂B ∇× E = − ∂t   ∇⋅ B =0     ∂D ∇× H = J + ∂t

D =Electric

flux density

E =Electric

field Intensity

B =Magnetic H =Magnetic

Where,

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( N / C ) or (V / m)

flux density ( Web / m 2 ) field Intensity ( A / m)

ρv =Ch arg e density J =Current

( C / m2 )

density

( C / m3 ) ( A / m2 )