ELECTROMAGNETIC THEORY EKT 241/4: ELECTROMAGNETIC THEORY PREPARED BY: NORDIANA MOHAMAD SAAID CHAPTER 1 - INTRODUCTION

2  Optical transmission  Coaxial transmission line  Antenna system  High voltage transmission Electromagnetic Applications

3 Electrostatic vs. Magnetostatic ElectrostaticMagnetostatic Fields arise from a potential difference or voltage gradient Fields arise from the movement of charge carriers, i.e flow of current Volts per meter (V/m)Amperes per meter (A/m) Fields exist anywhere as long as there was a potential difference Fields exist as soon as current flows

4 Timeline for Electromagnetics in the Classical Era  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.

5  1835 Carl Friedrich Gauss (German) formulates Gauss’s law relating the electric flux flowing through an enclosed surface to the enclosed electric charge. Timeline for Electromagnetics in the Classical Era

6  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, now known as Maxwell’s Equations. Timeline for Electromagnetics in the Classical Era

7 Units and Dimensions  SI Units  French name ‘Systeme Internationale’  Based on six fundamental dimensions

8 Multiple & Sub-Multiple Prefixes Example:  4 x F becomes 4 pF

9 The Nature of Electromagnetism Physical universe is governed by 4 forces: 1.nuclear force 2.weak-interaction force 3.electromagnetic force 4.gravitational force

10 The Electromagnetic Force Analogy: The Gravitational Force Where; m 2, m 1 = masses R 12 = distance G = gravitational constant = unit vector from 1 to 2 Gravitational force

11 The Electric Fields Coulomb’s law Where; Fe 21 = electrical force q 1,q 2 = charges R 12 = distance between the two charges = unit vector ε 0 = electrical permittivity of free space

12 The Electric Fields Electric field intensity, E due to q where = radial unit vector pointing away from charge

13 The Electric Fields TWO important properties for electric charge: 1.Law of conservation of electric charge 2.Principle of linear superposition

14 The Electric Fields Electric flux density, D where E = electric field intensity ε = electric permittivity of the material

15 The Magnetic Fields  Velocity of light in free space, c where µ 0 = magnetic permeability of free space = 4π x H/m  Magnetic flux density, B where H = magnetic field intensity

16 Permittivity  Describes how an electric field affects and is affected by a dielectric medium  Ability of material to polarize in response to field  Reduce the total electric field inside the material  Permittivity of free space;  Relative permittivity

17  The degree of magnetization of a material  Responds linearly to an applied magnetic field.  The constant value μ 0 is known as the magnetic constant, i.e permeability of free space;  Relative permeability Permeability

18 The Electromagnetic Spectrum

19 Review of Complex Numbers A complex number z is written in the rectangular form Z = x ± jy x is the real ( Re ) part of Z y is the imaginary ( Im ) part of Z Value of j = −1. Hence, x =Re (z), y =Im (z)

20 Forms of Complex Numbers Using Trigonometry, convert from rectangular to polar form, Alternative polar form,

21 Forms of complex numbers Relations between rectangular and polar representations of complex numbers.

22 Forms of complex numbers

23 Complex conjugate Complex conjugate, z* Opposite sign (+ or -) & with * superscript (asterisk) Product of complex number z with its complex conjugate is always a real number;

24 Equality z 1 = z 2 if and only if x 1 =x 2 AND y 1 =y 2 Or equivalently,

25 Addition & Subtraction

26 Multiplication in Rectangular Form Given two complex numbers z 1 and z 2 ; Multiplication gives;

27 Multiplication in Polar Form In polar form,

28 Division in Polar Form For

29 Division in Rectangular Form

30 Powers For any positive integer n, And,

31 Powers Useful relations