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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, McGraw-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 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 A4 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 (i.e., the maximum score for a make up will be 90). President University Erwin Sitompul EEM 1/4 Engineering Electromagnetics Grade Policy 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 Electric and magnetic field exist nearly everywhere. President University Erwin Sitompul EEM 1/8 Engineering Electromagnetics Applications 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 Electromagnetic fields are used in induction heaters for melting, forging, annealing, surface hardening, and soldering operation. 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 Scalar refers to a quantity whose value may be represented by a single (positive or negative) real number. Some examples include distance, temperature, mass, density, pressure, volume, and time. A vector quantity has both a magnitude and a direction in space. We especially concerned with two- and threedimensional spaces only. 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 AB BA A (B + C) (A B) + C A B A (B) A 1 A n n AB 0 A B President University Erwin Sitompul EEM 1/13 Chapter 1 Vector Analysis Rectangular Coordinate System • Differential surface units: dx dy dy dz dx dz • Differential volume unit : dx dy dz President University Erwin Sitompul EEM 1/14 Chapter 1 Vector Analysis Vector Components and Unit Vectors RPQ ? r xyz r xax ya y zaz ax , a y , az : unit vectors RPQ rQ rP (2ax 2a y az ) (1ax 2a y 3az ) ax 4a y 2a z President University Erwin Sitompul EEM 1/15 Chapter 1 Vector Analysis Vector Components and Unit Vectors For any vector B, B Bxax Bya y + Bzaz : B Bx2 By2 Bz2 B aB B Bx2 By2 Bz2 B B Magnitude of B Unit vector in the direction of B Example Given points M(–1,2,1) and N(3,–3,0), find RMN and aMN. RMN (3ax 3a y 0az ) (1ax 2a y 1az ) 4a x 5a y a z a MN 4a x 5a y 1a z R MN 0.617a x 0.772a y 0.154a z 2 2 2 R MN 4 (5) (1) President University Erwin Sitompul EEM 1/16 Chapter 1 Vector Analysis The Dot Product 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: A B A B cos AB The dot product is a scalar, and it obeys the commutative law: A B BA For any vector A Axax Aya y + Azaz and B Bxax Bya y + Bzaz , A B Ax Bx Ay By + Az Bz President University Erwin Sitompul EEM 1/17 Chapter 1 Vector Analysis The Dot Product 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 Ba • The vector component of B in the direction of the unit vector a is (Ba)a B a B a cosBa B cosBa President University Erwin Sitompul EEM 1/18 Chapter 1 Vector Analysis The Dot Product 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. B R AB (2ax 3a y 4az ) (6ax a y 2az ) 8a x 4a y 6a z R AC (3ax 1a y 5az ) (6ax a y 2az ) 9a x 2a y 3a z BAC R AB R AC R AB R AC cosBAC cos BAC R R AB AC R AB R AC C A (8a x 4a y 6a z ) (9a x 2a y 3a z ) (8) (4) (6) 2 2 2 (9) (2) (3) 2 2 2 62 116 0.594 94 BAC cos1 (0.594) 53.56 President University Erwin Sitompul EEM 1/19 Chapter 1 Vector Analysis The Dot Product 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. R AB on R AC R AB a AC a AC (9a x 2a y 3a z ) (8a x 4a y 6a z ) (9)2 (2)2 (3)2 (9a x 2a y 3a z ) 2 2 2 (9) (2) (3) 62 (9a x 2a y 3a z ) 94 94 5.963a x 1.319a y 1.979a z President University Erwin Sitompul EEM 1/20 Chapter 1 Vector Analysis The Cross Product Given two vectors A and B, the magnitude of the cross product, or vector product, written as AB, is defines as the product of the magnitude of A, the magnitude of B, and the sine of the smaller angle between them. The direction of AB 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. A B aN A B sin AB The cross product is a vector, and it is not commutative: ax a y az a y az ax az ax a y (B A) (A B) President University Erwin Sitompul EEM 1/21 Chapter 1 Vector Analysis The Cross Product Example Given A = 2ax–3ay+az and B = –4ax–2ay+5az, find AB. A B ( Ay Bz Az By )ax ( Az Bx Ax Bz )a y ( Ax By Ay Bx )az (3)(5) (1)(2) ax (1)(4) (2)(5) a y (2)(2) (3)(4) az 13a x 14a y 16a z 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: d dz d dz d d • Relation between the rectangular and the cylindrical coordinate systems x cos y sin • Differential volume unit : d d dz President University zz Erwin Sitompul x2 y 2 1 y tan x zz EEM 1/24 Chapter 1 Vector Analysis The Cylindrical Coordinate System ? az az A Ax a x Ay a y + Az a z A A a A a + Az a z ay A A a ( Axax Aya y + Azaz ) a Axax a Aya y a + Azaz a Ax cos Ay sin • Dot products of unit vectors in cylindrical and rectangular coordinate systems A A a ( Axax Aya y + Azaz ) a Axax a Aya y a + Azaz a Ax sin Ay cos a a ax Az A a z ( Axax Aya y + Azaz ) az Axax az Aya y az + Azaz az Az 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: dr rd dr r sin d rd r sin d • Differential volume unit : dr rd r sin d President University Erwin Sitompul EEM 1/27 Chapter 1 Vector Analysis The Spherical Coordinate System • Relation between the rectangular and the spherical coordinate systems x r sin cos r x2 y2 z 2 , r 0 y r sin sin cos 1 z r cos tan 1 z x y z 2 2 2 , 0 180 y x • 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 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. r x 2 y 2 z 2 (3) 2 (2) 2 (1) 2 3.742 cos1 tan 1 z x2 y 2 z 2 cos 1 1 74.50 3.742 y 1 2 tan 33.69 180 146.31 x 3 C (r 3.742, 74.50, 146.31) D( x 0.585, y 1.607, z 4.698) President University Erwin Sitompul EEM 1/29 Chapter 1 Vector Analysis Homework 1 D1.4. D1.6. D1.8. All homework problems from Hayt and Buck, 7th Edition. Due: Next week 17 April 2012, at 08:00. President University Erwin Sitompul EEM 1/30