Syllabus for Electromagnetic Theorem

Fourth StagePhysics DepartmentCollege of Science

Chapter One: Vector Analysis and Coordinate Systems

1-1 Introduction 1-2 Scalar and Vectors1-3 Unit Vector1-4 Equality of Two Vectors1-5 Vector Addition and Subtraction1-6 Position and Distance Vector1-7 Vector Multiplications

1-7-1 Simple Product1-7-2 Scalar or dot Product1-7-3 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 Theorem1-10 Laplacian of a Vector1-11 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 Curls1-12 Curvilinear Coordinates Systems

1-12-1 Cylindrical Coordinate 1-12-2 Spherical Coordinate1-13 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 Field2-2 Coulomb’s Law2-3 Continuous Charge Distributions

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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 Distribution2-5 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 Cable2-6 Electric Potential

2-6-1 Poisson’s Equation and Laplace’s Equation2-6-1 The Potential of a Localized Charge Distribution

2-7 Work and Energy in Electrostatics2-7-1 The Work Done to Move a Charge2-7-2 The Energy of a Point Charge Distribution2-7-3 The Energy of a Continuous Charge Distribution

2-8 Capacitors

Chapter Three: Special Techniques

3-1 Laplace’s Equation3-1-1 Laplace’s Equation in One Dimension3-1-1 Laplace’s Equation in Two Dimensions3-1-1 Laplace’s Equation in Three Dimensions3-1-2 Boundary Conditions and Uniqueness Theorem

3-2 The Method of Images3-3 Separation of Variables

3-3-1 Cartesian Coordinates3-3-2 Spherical Coordinates

3-4 The Monopole and Dipole Terms3-5 The Electric Field of a Dipole

Chapter Four: Electrostatic Field in Matter

4-1 Polarization4-1-1 Dielectrics4-1-2 Induced Dipoles4-1-3 Alignment of Polar Molecules

4-2 The Field of a Polarized Object4-2-1 Bound Charges4-2-2 The Field Inside a Dielectric

4-3 The Electric Displacement4-4 Gauss’s Law in The Presence of Dielectrics4-5 Linear Dielectrics

4-5-1 Susceptibility, Permittivity, Dielectric Constant4-5-2 Boundary Value Problems with Linear Dielectrics4-5-3 Energy in Dielectric Systems

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4-5-4 Forces on Dielectrics

Chapter Five: Magnetostatics Field

5-1 The Lorentz Force Law5-2 The Biot-Savart Law5-3 The Magnetic Field of a Steady Current5-4 Straight-Line Currents5-5 The Divergence and Curl of B 5-6 Application of Ampere's Law

5-6-1 Infinite Line Current5-6-2 Infinite Sheet Current 5-6-3 Infinitely Long Coaxial Transmission Line5-6-4 Infinite Solenoid Coil5-6-5 Toroidal Coil

5-7 Comparison of Magnetics and Electrostatics5-8 Magnetic Vector Potential

Chapter Six: Magnetic Fields in Matter

7-1 Magnetization7-2 Diamagnets, Paramagnets, Ferromagnets7-3 Torques and Forces on Magnetic Dipoles7-4 Effect of a Magnetic Field on Atomic Orbits7-5 The Field of a Magnetized Objet

7-5-1 Bound Currents7-5-2 The Magnetic Field Inside Matter

7-6 The Auxiliary Field H7-7 Ampere’s Law in Magnetized Materials7-8 Linear and Nonlinear Media7-9 Magnetic Susceptibility and Permeability

Chapter Seven: Electrodynamics Fields

7-1 Electromotive Force emf7-2 Ohm’s Law7-3 Transformer and Motional electromotive forces emf

7-3-1 Stationary Loop in Time-Varying Magnetic Field7-3-2 Moving Loop in Static Magnetic Field 7-3-3 Moving Loop in Time Varying Magnetic Field

7-4 Electromagnetic Induction7-4-1 Faraday’s Law7-4-2 The Induced Electric Field7-4-3 Inductance7-4-4 Energy in Magnetic Fields

7-5 Electrodynamics before Maxwell7-6 How Maxwell Fixed Ampere’s Law

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7-7 Displacement Current7-8 Maxwell’s Equations in Final Forms7-9 Maxwell’s Equations in Matter7-10 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:

No BranchesFrequency

(Hz)Wavelength (m) Energy (ev) Sources Applications

1. Cosmic Ray > 1024 <10-12 > 106 Cosmic Astronomy

2. Gamma Ray 1019-1023 10-10 – 10-12 104 - 106 Radioactive elements

Cancer therapy

3. X-Ray 1016-1019 10-10 - 10-8 102 –104 X-Ray machine

Medical diagnosis

4. 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 - 5Radiant Heater

Photography

7. Microwave 108-1011 10-3 - 1 10-6–10-3

1.Microwave oven

2. Mobile phone towers

Tv, radar & Satellite

communication

8. Radio Wave 101-108 1 - 108 <10-6

Tv, FM radio & AM Radio towers with Power lines

Telephone, Navigation &

Radio Broadcasting

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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)GHzNot 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

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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:

Where,

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