Engineering Electromagnetics Lecture 1 Dr Ing Erwin Sitompul

Engineering Electromagnetics Lecture 1 Dr. -Ing. Erwin Sitompul President University http: //zitompul. wordpress. com President University Erwin Sitompul EEM 1/1

Engineering Electromagnetics Textbook and Syllabus Textbook: “Engineering Electromagnetics”, William H. Hayt, Jr. and John A. Buck, Mc. Graw-Hill, 2006. Syllabus: Chapter 1: Vector Analysis Chapter 2: Coulomb’s Law and Electric Field Intensity Chapter 3: Electric Flux Density, Gauss’ Law, and Divergence Chapter 4: Energy and Potential Chapter 5: Current and Conductors Chapter 6: Dielectrics and Capacitance Chapter 8: The Steady Magnetic Field Chapter 9: Magnetic Forces, Materials, and Inductance President University Erwin Sitompul EEM 1/2

Engineering Electromagnetics Grade Policy: Final Grade = 10% Homework + 20% Quizzes + 30% Midterm Exam + 40% Final Exam + Extra Points § Homeworks will be given in fairly regular basis. The average of homework grades contributes 10% of final grade. § Homeworks are to be written on A 4 papers, otherwise they will not be graded. § Homeworks must be submitted on time. If you submit late, < 10 min. No penalty 10 – 60 min. – 20 points > 60 min. – 40 points § There will be 3 quizzes. Only the best 2 will be counted. The average of quiz grades contributes 20% of final grade. President University Erwin Sitompul EEM 1/3

Engineering Electromagnetics Grade Policy • Heading of Homework Papers (Required) Grade Policy: § Midterm and final exam schedule will be announced in time. § Make up of quizzes and exams will be held one week after the schedule of the respective quizzes and exams. § The score of a make up quiz or exam can be multiplied by 0. 9 (the maximum score for a make up is 90). President University Erwin Sitompul EEM 1/4

Engineering Electromagnetics Grade Policy: § Extra points will be given every time you solve a problem in front of the class. You will earn 1 or 2 points. § Lecture slides can be copied during class session. It also will be available on internet around 3 days after class. Please check the course homepage regularly. http: //zitompul. wordpress. com President University Erwin Sitompul EEM 1/5

Engineering Electromagnetics What is Electromagnetics? Electric field Produced by the presence of electrically charged particles, and gives rise to the electric force. Magnetic field Produced by the motion of electric charges, or electric current, and gives rise to the magnetic force associated with magnets. President University Erwin Sitompul EEM 1/6

Engineering Electromagnetics Electromagnetic Wave Spectrum President University Erwin Sitompul EEM 1/7

Engineering Electromagnetics Why do we learn Engineering Electromagnetics n Electric and magnetic field exist nearly everywhere. President University Erwin Sitompul EEM 1/8

Engineering Electromagnetics Applications n Electromagnetic principles find application in various disciplines such as microwaves, x-rays, antennas, electric machines, plasmas, etc. President University Erwin Sitompul EEM 1/9

Engineering Electromagnetics Applications n Electromagnetic fields are used in induction heaters for melting, forging, annealing, surface hardening, and soldering operation. n Electromagnetic devices include transformers, radio, television, mobile phones, radars, lasers, etc. President University Erwin Sitompul EEM 1/10

Engineering Electromagnetics Applications Transrapid Train • A magnetic traveling field moves the vehicle without contact. • The speed can be continuously regulated by varying the frequency of the alternating current. President University Erwin Sitompul EEM 1/11

Chapter 1 Vector Analysis Scalars and Vectors n Scalar refers to a quantity whose value may be represented by a single (positive or negative) real number. n Some examples include distance, temperature, mass, density, pressure, volume, and time. n A vector quantity has both a magnitude and a direction in space. We especially concerned with two- and three-dimensional spaces only. n Displacement, velocity, acceleration, and force are examples of vectors. • Scalar notation: A or → A (italic or plain) • Vector notation: A or A (bold or plain with arrow) President University Erwin Sitompul EEM 1/12

Chapter 1 Vector Analysis Vector Algebra President University Erwin Sitompul EEM 1/13

Chapter 1 Vector Analysis Rectangular Coordinate System • Differential surface units: • Differential volume unit : President University Erwin Sitompul EEM 1/14

Chapter 1 Vector Analysis Vector Components and Unit Vectors President University Erwin Sitompul EEM 1/15

Chapter 1 Vector Analysis Vector Components and Unit Vectors n For any vector B, : Magnitude of B Unit vector in the direction of B n Example Given points M(– 1, 2, 1) and N(3, – 3, 0), find RMN and a. MN. President University Erwin Sitompul EEM 1/16

Chapter 1 Vector Analysis The Dot Product n Given two vectors A and B, the dot product, or scalar product, is defines as the product of the magnitude of A, the magnitude of B, and the cosine of the smaller angle between them: n The dot product is a scalar, and it obeys the commutative law: n For any vector President University and Erwin Sitompul , EEM 1/17

Chapter 1 Vector Analysis The Dot Product n One of the most important applications of the dot product is that of finding the component of a vector in a given direction. • The scalar component of B in the direction of the unit vector a is B a • The vector component of B in the direction of the unit vector a is (B a)a President University Erwin Sitompul EEM 1/18

Chapter 1 Vector Analysis The Dot Product n Example The three vertices of a triangle are located at A(6, – 1, 2), B(– 2, 3, – 4), and C(– 3, 1, 5). Find: (a) RAB; (b) RAC; (c) the angle θBAC at vertex A; (d) the vector projection of RAB on RAC. President University Erwin Sitompul EEM 1/19

Chapter 1 Vector Analysis The Dot Product n Example The three vertices of a triangle are located at A(6, – 1, 2), B(– 2, 3, – 4), and C(– 3, 1, 5). Find: (a) RAB; (b) RAC; (c) the angle θBAC at vertex A; (d) the vector projection of RAB on RAC. President University Erwin Sitompul EEM 1/20

Chapter 1 Vector Analysis The Cross Product n Given two vectors A and B, the magnitude of the cross product, or vector product, written as A B, is defines as the product of the magnitude of A, the magnitude of B, and the sine of the smaller angle between them. n The direction of A B is perpendicular to the plane containing A and B and is in the direction of advance of a right-handed screw as A is turned into B. n The cross product is a vector, and it is not commutative: President University Erwin Sitompul EEM 1/21

Chapter 1 Vector Analysis The Cross Product n Example Given A = 2 ax– 3 ay+az and B = – 4 ax– 2 ay+5 az, find A B. President University Erwin Sitompul EEM 1/22

Chapter 1 Vector Analysis The Cylindrical Coordinate System President University Erwin Sitompul EEM 1/23

Chapter 1 Vector Analysis The Cylindrical Coordinate System • Differential surface units: • Relation between the rectangular and the cylindrical coordinate systems • Differential volume unit : President University Erwin Sitompul EEM 1/24

Chapter 1 Vector Analysis The Cylindrical Coordinate System • Dot products of unit vectors in cylindrical and rectangular coordinate systems President University Erwin Sitompul EEM 1/25

Chapter 1 Vector Analysis The Spherical Coordinate System President University Erwin Sitompul EEM 1/26

Chapter 1 Vector Analysis The Spherical Coordinate System • Differential surface units: • Differential volume unit : President University Erwin Sitompul EEM 1/27

Chapter 1 Vector Analysis The Spherical Coordinate System • Relation between the rectangular and the spherical coordinate systems • Dot products of unit vectors in spherical and rectangular coordinate systems President University Erwin Sitompul EEM 1/28

Chapter 1 Vector Analysis The Spherical Coordinate System n Example Given the two points, C(– 3, 2, 1) and D(r = 5, θ = 20°, Φ = – 70°), find: (a) the spherical coordinates of C; (b) the rectangular coordinates of D. President University Erwin Sitompul EEM 1/29

Chapter 1 Vector Analysis Homework 1 n D 1. 4. (p. 14) n D 1. 6. (p. 19) n D 1. 8. (p. 22) n Due: Next week 18 January 2011, at 07: 30. President University Erwin Sitompul EEM 1/30