EKT 242/3 & EKT 241/4 1. INTRODUCTION

1. EKT 242/3 & EKT 241/41. INTRODUCTION Ruzelita Ngadiran

2. Chapter 1 Overview • Electrostatic vs magnetostatic • EM applications • EM Timeline • Dimensions & Unit • Fundamental Forces of Nature • The EM spectrum • Complex number (Revision)

3. Electrostatic vs. Magnetostatic

4. Examples of EM Applications

5. Dimensions and Units

6. EM in 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.

10. Fundamental Forces of Nature

11. Gravitational Force Force exerted on mass 2 by mass 1 Gravitational field induced by mass 1

12. Charge: Electrical property of particles Units: coulomb One coulomb: amount of charge accumulated in one second by a current of one ampere. 1 coulomb represents the charge on ~ 6.241 x 1018 electrons The coulomb is named for a French physicist, Charles-Augustin de Coulomb (1736-1806), who was the first to measure accurately the forces exerted between electric charges. Charge of an electron e = 1.602 x 10-19 C Charge conservation Cannot create or destroy charge, only transfer

13. Electrical Force Force exerted on charge 2 by charge 1

14. Electric Field In Free Space Permittivity of free space

15. Electric Field Inside Dielectric Medium Polarization of atoms changes electric field New field can be accounted for by changing the permittivity Permittivity of the material Another quantity used in EM is the electric flux density D:

16. Magnetic Field Electric charges can be isolated, but magnetic poles always exist in pairs. Magnetic field induced by a current in a long wire Magnetic permeability of free space Electric and magnetic fields are connected through the speed of light:

17. Static vs. Dynamic Static conditions: charges are stationary or moving, but if moving, they do so at a constant velocity. Under static conditions, electric and magnetic fields are independent, but under dynamic conditions, they become coupled.

18. 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.

19. where = radial unit vector pointing away from charge Electric Fields Electric field intensity, E due to q UNIVERSITI MALAYSIA PERLIS

20. Electric Fields Electric flux density, D UNIVERSITI MALAYSIA PERLIS where E = electric field intensityε = electric permittivity of the material

21. 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. UNIVERSITI MALAYSIA PERLIS

22. 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. UNIVERSITI MALAYSIA PERLIS north pole south pole

23. Magnetic Fields • Velocity of light in free space, c where µ0 = magnetic permeability of free space = 4π x 10-7 H/m • Magnetic flux density, B (unit: Tesla) where H = magnetic field intensity UNIVERSITI MALAYSIA PERLIS

24. 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; UNIVERSITI MALAYSIA PERLIS

25. Permeability • The degree of magnetization of a material that responds linearly to an applied magnetic field. • The constant value μ0 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; UNIVERSITI MALAYSIA PERLIS

26. Material Properties

27. The EM Spectrum

29. Electromagnetic Applications

30. Complex Numbers We will find it is useful to represent sinusoids as complex numbers Rectangular coordinates Polar coordinates Relations based on Euler’s Identity

31. Review of Complex Numbers • You can use calculator . • 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) UNIVERSITI MALAYSIA PERLIS

32. Forms of Complex Numbers • Using Trigonometry, convert from rectangular to polar form, • Alternative polar form, UNIVERSITI MALAYSIA PERLIS

33. Forms of complex numbers • Relations between rectangular and polar representations of complex numbers. UNIVERSITI MALAYSIA PERLIS

34. Forms of complex numbers UNIVERSITI MALAYSIA PERLIS NB: θ in degrees

35. 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. UNIVERSITI MALAYSIA PERLIS

36. Equality • z1 = z2 if and only if x1=x2 AND y1=y2 • Or equivalently, UNIVERSITI MALAYSIA PERLIS

37. Addition & Subtraction UNIVERSITI MALAYSIA PERLIS

38. Multiplication in Rectangular Form • Given two complex numbers z1 and z2; • Multiplication gives; UNIVERSITI MALAYSIA PERLIS

39. Multiplication in Polar Form • In polar form, UNIVERSITI MALAYSIA PERLIS

40. Division in Polar Form • For UNIVERSITI MALAYSIA PERLIS

41. Division in Polar Form UNIVERSITI MALAYSIA PERLIS

42. Powers • For any positive integer n, • And, UNIVERSITI MALAYSIA PERLIS

43. Powers • Useful relations UNIVERSITI MALAYSIA PERLIS

44. Exercise 1 • V = 3-j4 • I = -(2+j3) • A) polar form • B) VI • C) VI* • D)V/I • E)sqrt(I)

45. Exercise 2 • Express in polar form : • Z = (4-j3)^2 • Z = (4-j3)^1/2

46. Summary