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

2 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 Field strength: Volts per meter (V/m) Field strength: Amperes per meter (A/m) Fields exist anywhere as long as there was a potential difference Fields exist as soon as current flows We will see how charged dielectric produces an electrostatic fields We will see how current flows through conductor and produces magnetostatic fields Example of electrostatics: vigorously rubbing a rubber rod with a piece of fur and bring to a piece of foil – foil will be attracted to the charged rod Example of magnetostatics: Current passes through a coil produces magnetic field about each turn of coil – combined will produce two-pole field, south & north pole

3 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.

4  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

5  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

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

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

8 The Nature of Electromagnetism Physical universe is governed by 4 forces: 1.nuclear force – strongest of the four but its range is limited to submicroscopic systems, such as nuclei 2.weak-interaction force – strength is only that of the nuclear force. Interactions involving certain radioactive particles. 3.electromagnetic force – exists between all charged particles. The dominant force in microscopic systems such as atoms and molecules. Strength is of the order of the nuclear force 4.gravitational force – weakest of all four forces. Strength is of the order that of the nuclear force. Dominant force in macroscopic systems, e.g solar system

9 The Electromagnetic Force Where; m 2, m 1 = masses R 12 = distance G = gravitational constant = unit vector from 1 to 2 Gravitational force – between two masses

Electric fields Electric fields exist whenever a positive or negative electrical charge is present. The strength of the electric field is measured in volts per meter (V/m). The field exists even when there is no current flowing. E.g rubbing a rubber sphere with a piece of fur. 10

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

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

Magnetic Fields Magnetic field arise from the motion of electric charges. Magnetic field strength (or intensity) is measured in amperes per meter (A/m). Magnetic field only exist when a device is switched on and current flows. The higher the current, the greater the strength of the magnetic field. 13

Magnetic Fields Magnetic field lines are induced by current flow through coil. Magnetic field strength or magnetic field intensity is denoted as H, the unit is A/m. 14 north pole south pole

15 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 (unit: Tesla) where H = magnetic field intensity

16 Permittivity  Describes how an electric field affects and is affected by a dielectric medium  Relates to the ability of a material to transmit (or “permit”) an electric field.  Each material has a unique value of permittivity.  Permittivity of free space;  Relative permittivity;

17  The degree of magnetization of a material that responds linearly to an applied magnetic field.  The constant value μ 0 is known as the magnetic constant, i.e permeability of free space;  Most materials have permeability of except ferromagnetic materials such as iron, where is larger than.  Relative permeability; Permeability

18 The Electromagnetic Spectrum

Electromagnetic Applications 19

20 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 Hence, x =Re (z), y =Im (z)

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

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

23 Forms of complex numbers NB: θ in degrees

24 Complex conjugate Complex conjugate, z* Opposite sign (+ or -) & with * superscript (asterisk) Product of a complex number z with its complex conjugate is always a real number. Important in division of complex number.

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

26 Addition & Subtraction

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

28 Multiplication in Polar Form In polar form,

29 Division in Polar Form For

30 Division in Polar Form

31 Powers For any positive integer n, And,

32 Powers Useful relations