Dr. Naser Abu-Zaid; Lecture notes in electromagnetic theory 1; Referenced to Engineering electromagnetics by Hayt, 8 th edition 2012; Text Book

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1 Text Book Dr. Naser Abu-Zaid Page 1 9/4/2012

2 Course syllabus Electroagnetic 2 (63374) Seester Language Copulsory / Elective Prerequisites Course Contents Course Objectives Learning Outcoes and Copetences ELECTICAL ENGINEEING 5 th & 6 th English Copulsory course for electrical engineering and counication engineering students. Electroagnetic theory (1) and preferred after a course on differential equations. Magnetic Forces; Magnetic Circuits; Inductance; Faraday s Law; Displaceent Current and tie varying Maxwell s equations; Transission lines; Plane electroagnetic waves; eflection and transission of plane EM waves; Introduction to waveguides. To understand Faraday s Law and its applications; To analyze guided propagation through Transission lines, and solve associated probles; To predict the existence of EM waves for tie varying Maxwell s equations; To understand EM wave propagation in unbounded edia and study the characteristics and paraeters of plane EM waves and solutions of wave equations; To study the effect of dispersion in counication channels; To study basic applications of EM theory including TL's and waveguides; To be prepared for ore advanced courses. To appreciate and feel the iportance of electroagnetic theory in our daily life. 1. Be able to apply knowledge of coplex A 50% calculus, vector algebra and vector calculus to EM field probles (DC and tie varying fields). 2. Be able to analyze and design coponents and/or progras in relation to field probles. C&K 10% 3. Attain the ability to solve basic electroagnetic wave propagation, reflection and refraction probles. E 40% Textbook and eferences Assessent Criteria 1. Engineering Electroagnetics, Willia H. Hayt and John A. Buck; 7 th Edition; McGraw-Hill International Editions, Field and Wave Electroagnetics, David K. Cheng; Addison- Wesley Publishing Copany; Second Edition If any,ark as (X) Percent (%) Dr. Naser Abu-Zaid Page 2 9/4/2012

3 Midter Exas X 40 Quizzes X 10 Hoework s Projects Ter Paper Laboratory Work Other Final Exa X 50 Instructor(s) Assist. Prof. Dr. Naser A. Abu-Zaid; naser_res@yahoo.co Week Subject 1-2 Magnetic Forces: Lorentz Force equation; Magnetic Forces and Torques; Magnetic aterials and pereability; Magnetic Boundary conditions; Magnetic Circuits; Magneto-static energy; Inductance and Mutual inductance; Suary of Maxwell s equations for static and steady fields. 3-4 Tie-Varying Fields and Maxwell s Equations: Magnetic forces and torques; Magnetic aterials and agnetic circuits; 3-4 Faraday s Law and applications; Displaceent current; Point for and Integral fors of Maxwell s equations; Electroagnetic Boundary Conditions; 5 Transission Lines: General Transission Line Equations; TL Paraeters; Lossless propagation; Lossless propagation of sinusoidal voltages; Coplex analysis of sinusoidal waves; Solution of Transission line equations in phasor for; lossless and low loss propagation; Power transission and losses; First Exa 6 Wave reflections; VSW; Finite length TL; TL s as circuit eleents; Sith Chart; Transient Analysis(possible); 7 Unifor Plane Electroagnetic Waves: Wave equations and their solutions; Propagation in free space; Propagation in dielectrics; propagation constant; intrinsic ipedance; phase velocity, phase constant; attenuation constant, wave length; 8 Flow of electroagnetic power and Poynting's Vector (Poynting s Th.); Propagation in good conductors; Skin effect; Polarization of waves; 9-10 eflection and Dispersion: Noral Incidence at a Plane Dielectric Boundary; Noral Incidence at Plane Conducting Boundary; SW; eflection fro ultiple interfaces; Propagation in arbitrary directions; Second Exa 13 Oblique Incidence at a Plane Dielectric Boundary (Perpendicular Dr. Naser Abu-Zaid Page 3 9/4/2012

4 Polarization and Parallel Polarization); Oblique Incidence at Plane Conducting Boundary; 14 Total eflection and Total Transission; Dispersion and Pulse expansion; Introduction to etallic waveguides. 15 General eview Dr. Naser Abu-Zaid Page 4 9/4/2012

5 Magnetic Forces, Materials and Inductance Lorentz force equation The electric force on a particle whether its oving or stationary is Fe QE Positive charge iplies force and field are in sae direction, while negative charge iplies opposite directions. The agnetic force on a oving particle in a agnetic flux density B with velocity v is: F Qv B The total force is the superposition of both F Fe F Q E v B Lorentz forceequation 6 Exaple 9.1: A point charge Q 18nC, is oving with a velocity of 10 s direction specified by aˆ v 0.6ˆ a x 0.75ˆ a force exerted on the oving particle by the field: 1) B 3aˆ 4ˆ a 6aˆ T. x 2) E 3aˆ 4ˆ a 6aˆ KV x y. 3) Bothe fields acting together. y z z y 0.3aˆ z 5 in a. Find the agnitude of the vector Dr. Naser Abu-Zaid Page 5 9/4/2012

6 Force on a differential current eleent Consider a sall section of current: dl External Field I q q v v Total charge dq vdv Differential volue dv contains a large nuber of charged particles Idl Jdv Kds The force on each charged particle due to otion in a agnetic field is: But And since Hence df df dqvb dq vdv df vdv vb J v JBdv KBds Idl B The total force on a conductor carrying current is: For unifor B F JBdv K Bds Idl B I B v s F v Idl B c c dl Dr. Naser Abu-Zaid Page 6 9/4/2012

7 Exaple 9.2: In the figure shown. Find the net force on the closed loop due to the field produced by the straight filaent. z x 1,1,0 15A 1,3,0 3,1,0 3,3,0 2 A y Dr. Naser Abu-Zaid Page 7 9/4/2012

8 Force between differential current eleents The agnetic field at point 2 due to a current eleent at point 1 was found to be The differential force on a differential current eleent is letting be (the differential flux density at point 2 caused by current eleent 1), by identifying as, and by sybolizing the differential aount of our differential force on eleent 2 as The total force between two filaentary circuits is obtained by integrating twice: Dr. Naser Abu-Zaid Page 8 9/4/2012

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10 The Magnetic Dipole Sall loop of current with radius ; First find then. Using Binoial expansion with the assuption, one can obtain; Define the agnetic dipole oent as; Let the center of the loop be located at expressions aybe written as; (H), then, the previously written Copare with electric dipole Dr. Naser Abu-Zaid Page 10 9/4/2012

11 The torque T is defined as: z Forces and Torques on closed circuits T F F y T is to plane containing and F. The origin about which Torque is to be calculated ust be defined. The point at which force is applied ust also be defined. x P Consider a differential current loop in an applied B : y B I dy x d T I ds Differential vector area B Defining the differential agnetic dipole oent as; Then d IdS d T db So, the torque on a planar loop of any size or shape in a unifor B is: dx T I SB B The applied B would produce a torque which tends to turn the loop so as to align the agnetic field produced by the loop with the applied agnetic field. Dr. Naser Abu-Zaid Page 11 9/4/2012

12 B 0.6 aˆ y 0.8 aˆ z T z 4 A y x 1,2,0 Dr. Naser Abu-Zaid Page 12 9/4/2012

13 In free space Magnetization and Pereability In aterial edia, the agnetization oent per unit volue, defined as the agnetic dipole Its units ust be the sae as for H, aperes per eter. for linear isotropic edia where a agnetic susceptibility χ can be defined: Dr. Naser Abu-Zaid Page 13 9/4/2012

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15 Magnetic Boundary Conditions (DC) Dr. Naser Abu-Zaid Page 15 9/4/2012

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17 Magnetic Circuits and Hysteresis Magnetic Circuits Analogy with Electric Circuits Electrostatics Magnetostatics E dl V H dl NI V chosen path S J ds I B ds ef V f V I esistance d d S S V I V C S eluctance Obtaining the previous analogy 2 Consider a toroid with N turns, square cross-cross sectional area W, ean radius o and a steady coil current I. Dr. Naser Abu-Zaid Page 17 9/4/2012

18 Toroid with circular cross section Side view of toroid with square cross section Top view of toroid with square cross section Dr. Naser Abu-Zaid Page 18 9/4/2012

19 Apers law iplies: Then: Knowing that: So: But, its well known that: And its clear that: C H dl NI V H B S NI 2 o NI 2 o B ds o NI W 2 2 V NI A. t 1 W 2 2 o d 1 H 2 W S V V I I V V d S d S And the toroid circuit is replaced by the electric circuit given below: o 2 Dr. Naser Abu-Zaid Page 19 9/4/2012

20 Actually KVL for agnetic Circuits ay by written as: V i i Suof allf's fro sourcecoils j j j Suof allf drops alongthe core Siilarly, KCL for agnetic circuits ay be obtained by considering the boundary condition across a core junction: B n 1S 1 Bn2S2 Bn3S3 i i 0 0 Dr. Naser Abu-Zaid Page 20 9/4/2012

21 Exaple 4: Air core toroid with 500 turns, circular cross-section of radius of 15 c, and coil current of 4A. Find H. 2 6c, ean Solution: If Apers law is used: NI H o Using electrical circuit analogy, then toroid circuit is replaced by the electric circuit given above: d S S B H V source H Wb B o T 2120A. t Dr. Naser Abu-Zaid Page 21 9/4/2012

22 Exaple 5: Deterine the agnetic flux through the airgap. r 1000, 4 2 S 10 everywhere, l1 0. 1, l g 0.1, l3 0. 3, and l4 0. 2, The source has 1000 turns of wire, with I 1A. Dr. Naser Abu-Zaid Page 22 9/4/2012

23 Dr. Naser Abu-Zaid Page 23 9/4/2012 Solution: H S l l S d o H S l l S d o g H S l l S d o H S l S d o g g Wb V g // Flux division gives: Wb g

24 Ferroagnetic aterials (evisited) Magnetic Hysteresis Dr. Naser Abu-Zaid Page 24 9/4/2012

25 Energy is lost. Dr. Naser Abu-Zaid Page 25 9/4/2012

26 Easily agnetized and deagnetized. (Soft agnetic aterials). (Hard to deagnetize once they are agnetized). Usefull for producing perenant agnets. Soft agnetic aterials: Iron (0.2% ipure), r ax 9000 B r 0.77( T ), saturation flux B s 2.15( T ), H c 80A, Hard agnetic aterials: Alinco (Aluinu-Nickel-Cobalt), 3 5, H c 60 KA, B r 1.25( T ), Curie Tep. 850( C o ) r POTENTIAL ENEGY AND FOCES ON MAGNETIC MATEIALS The total energy stored in a steady agnetic field in which is is linearly related to Letting, we have the equivalent forulations Think of this energy as being distributed throughout the volue with an energy density of To calculate the forces on nonlinear agnetic aterials, suppose a long solenoid with a silicon-steel core. A coil containing with a current surrounds it. Let the agnetic flux density be. Suppose that the core is coposed of two sei-infinite cylinders that are just touching.we now apply a echanical force to separate these two sections of the core while keeping the flux density constant. We apply a force over a distance, thus doing work. We use the principle of virtual work to deterine the work we have done in oving one core appearing as stored energy in the air gap we have created. This increase is Where is the core cross-sectional area. Thus Dr. Naser Abu-Zaid Page 26 9/4/2012

27 In suary, the principle of virtual work states that INDUCTANCE AND MUTUAL INDUCTANCE Dr. Naser Abu-Zaid Page 27 9/4/2012

28 Consider a coil of N turns in which a current I produces a total flux. We assue that this flux links or encircles each of the turns, and that each of the N turns links the total flux. The flux linkage is defined as the product of the nuber of turns N and the flux linking each of the. Definition of inductance (or self-inductance): the ratio of the total flux linkages to the current which they link; Illustration: To calculate the inductance per eter length of a coaxial cable of inner radius and outer radius. We ay take the expression for total flux developed previously, and obtain the inductance rapidly for a length d, or, on a per-eter basis, In this case, turn, and all the flux links all the current. Illustration: For a toroidal coil of turns and a current, we have If the diensions of the cross section are sall copared with the ean radius of the toroid, then the total flux is The inductance Assued that all the flux links all the turns. A definition for inductance using energy expression, Dr. Naser Abu-Zaid Page 28 9/4/2012

29 The interior of any conductor also contains agnetic flux. Internal inductance, which ust be cobined with the external inductance to obtain the total inductance. The internal inductance of a long, straight wire of circular cross section, radius a, and unifor current distribution is Mutual inductance: Try this one Mutual inductance between circuits 1 and 2, linkages,, in ters of utual flux where signifies the flux produced by which links the path of the filaentary Dr. Naser Abu-Zaid Page 29 9/4/2012

30 current, and is the nuber of turns in circuit 2. It can be shown that EXAMPLE 8.9 Dr. Naser Abu-Zaid Page 30 9/4/2012

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