1. 1 ENE 325 Electromagnetic Fields and Waves Lecture 1 Electrostatics

2. 2 Syllabus Dr. Rardchawadee Silapunt, rardchawadee.sil@kmutt.ac.th Dr. Rardchawadee Silapunt, rardchawadee.sil@kmutt.ac.th rardchawadee.sil@kmutt.ac.th Lecture: 9:30pm-12:20pm Wednesday, Rm. CB41004 Lecture: 9:30pm-12:20pm Wednesday, Rm. CB41004 Office hours :By appointment Office hours :By appointment Textbook: Fundamentals of Electromagnetics with Engineering Applications by Stuart M. Wentworth (Wiley, 2005) Textbook: Fundamentals of Electromagnetics with Engineering Applications by Stuart M. Wentworth (Wiley, 2005)

3. 3 This is the course on beginning level electrodynamics. The purpose of the course is to provide junior electrical engineering students with the fundamental methods to analyze and understand electromagnetic field problems that arise in various branches of engineering science. Course Objectives

4. 4  Basic physics background relevant to electromagnetism: charge, force, SI system of units; basic differential and integral vector calculus  Concurrent study of introductory lumped circuit analysis Prerequisite knowledge and/or skills

5. 5 Introduction to course:  Review of vector operations  Orthogonal coordinate systems and change of coordinates  Integrals containing vector functions  Gradient of a scalar field and divergence of a vector field Course outline

6. 6 Electrostatics:  Fundamental postulates of electrostatics and Coulomb's Law  Electric field due to a system of discrete charges  Electric field due to a continuous distribution of charge  Gauss' Law and applications  Electric Potential  Conductors in static electric field  Dielectrics in static electric fields  Electric Flux Density, dielectric constant  Boundary Conditions  Capacitor and Capacitance  Nature of Current and Current Density

7. 7 Electrostatics:  Resistance of a Conductor  Joule’s Law  Boundary Conditions for the current density  The Electromotive Force  The Biot-Savart Law

8. 8 Magnetostatics: Ampere’s Force Law Magnetic Torque Magnetic Flux and Gauss’s Law for Magnetic Fields Magnetic Vector Potential Magnetic Field Intensity and Ampere’s Circuital Law Magnetic Material Boundary Conditions for Magnetic Fields Energy in a Magnetic Field Magnetic Circuits Inductance

9. 9 Dynamic Fields : Faraday's Law and induced emf Faraday's Law and induced emf Transformers Transformers Displacement Current Displacement Current Time-dependent Maxwell's equations and electromagnetic wave equations Time-dependent Maxwell's equations and electromagnetic wave equations Time-harmonic wave problems, uniform plane waves in lossless media, Poynting's vector and theorem Time-harmonic wave problems, uniform plane waves in lossless media, Poynting's vector and theorem Uniform plane waves in lossy media Uniform plane waves in lossy media Uniform plane wave transmission and reflection on normal and oblique incidence Uniform plane wave transmission and reflection on normal and oblique incidence

10. 10 Homework 20% Homework 20% Midterm exam 40% Midterm exam 40% Final exam 40% Final exam 40% Grading Vision: Providing opportunities for intellectual growth in the context of an engineering discipline for the attainment of professional competence, and for the development of a sense of the social context of technology.

11. 11 Examples of Electromagnetic fields Electromagnetic fields Electromagnetic fields –Solar radiation –Lightning –Radio communication –Microwave oven Light consists of electric and magnetic fields. An electromagnetic wave can propagate in a Light consists of electric and magnetic fields. An electromagnetic wave can propagate in a vacuum with a speed velocity c=2.998x10 8 m/s vacuum with a speed velocity c=2.998x10 8 m/s c = f c = f f = frequency (Hz) = wavelength (m) = wavelength (m)

12. 12 Vectors - Magnitude and direction 1. Cartesian coordinate system (x-, y-, z-)

13. 13 Vectors - Magnitude and direction 2. Cylindrical coordinate system ( , , z)

14. 14 Vectors - Magnitude and direction 3. Spherical coordinate system ( , ,  )

15. 15 Manipulation of vectors To find a vector from point m to n To find a vector from point m to n Vector addition and subtraction Vector addition and subtraction Vector multiplication Vector multiplication – vector  vector = vector – vector  scalar = vector

16. 16 Ex1: Point P (0, 1, 0), Point R (2, 2, 0) The magnitude of the vector line from the origin (0, 0, 0) to point P The magnitude of the vector line from the origin (0, 0, 0) to point P The unit vector pointed in the direction of vector The unit vector pointed in the direction of vector

17. 17 Ex2: P (0,-4, 0), Q (0,0,5), R (1,8,0), and S (7,0,2) a) Find the vector from point P to point Q a) Find the vector from point P to point Q b) Find the vector from point R to point S b) Find the vector from point R to point S

18. 18 c) Find the direction of c) Find the direction of

19. 19 Coulomb’s law Law of attraction: positive charge attracts negative charge Law of attraction: positive charge attracts negative charge Same polarity charges repel one another Same polarity charges repel one another Forces between two charges Forces between two charges Coulomb’s Law Q = electric charge (coulomb, C)  0 = 8.854x10 -12 F/m 

20. 20 Electric field intensity An electric field from Q 1 is exerted by a force between Q 1 and Q 2 and the magnitude of Q 2 An electric field from Q 1 is exerted by a force between Q 1 and Q 2 and the magnitude of Q 2 or we can write or we can write

21. 21 Electric field lines

22. 22 Spherical coordinate system orthogonal point (r, ,  ) orthogonal point (r, ,  ) r = a radial distance from the origin to the point (m) r = a radial distance from the origin to the point (m)  = the angle measured from the positive axis (0     )  = the angle measured from the positive axis (0     )  = an azimuthal angle, measured from x-axis (0    2  )  = an azimuthal angle, measured from x-axis (0    2  ) A vector representation in the spherical coordinate system:

23. 23 Point conversion between cartesian and spherical coordinate systems A conversion from P(x,y,z) to P(r, ,  ) A conversion from P(r, ,  ) to P(x,y,z)

24. 24 Unit vector conversion (Spherical coordinates)

25. 25 differential element volume: dv = r 2 sin  drd  d  surface vector : Take the dot product of the vector and a unit vector in the desired direction to find any desired component of a vector. Find any desired component of a vector

26. 26 Ex3 Transform the vector field into spherical components and variables

27. 27 Ex4 Convert the Cartesian coordinate point P(3, 5, 9) to its equivalent point in spherical coordinates.

28. 28 Line charges and the cylindrical coordinate system orthogonal point ( , , z) orthogonal point ( , , z)  = a radial distance (m)  = a radial distance (m)  = the angle measured from x axis to the projection of the radial line onto x-y plane  = the angle measured from x axis to the projection of the radial line onto x-y plane z = a distance z (m) z = a distance z (m) A vector representation in the cylindrical coordinate system:

29. 29 Point conversion between cartesian and cylindrical coordinate systems A conversion from P(x,y,z) to P(r, , z) A conversion from P(r, , z) to P(x,y,z)

30. 30 Unit vector conversion (Cylindrical coordinates)

31. 31 differential element volume: dv =  d  d  dz surface vector : (top) (side) Take the dot product of the vector and a unit vector in the desired direction to find any desired component of a vector. Find any desired component of a vector

32. 32 Ex5 Transform the vector into cylindrical coordinates.

33. 33 Ex6 Convert the Cartesian coordinate point P(3, 5, 9) to its equivalent point in cylindrical coordinates.

34. 34 Ex7 A volume bounded by radius  from 3 to 4 cm, the height is 0 to 6 cm, the angle is 90  -135 , determine the volume.