Electromagnetic fields and waves fundamentals of engineering

143 4A.2.2 Case of an Infinite Height Cylindrical Surface Charge Distribution with Uniform p, or Ø,.... 144 44.2.3 Case of a Cylindrical Shell of Charge Distribution with Infinite Hei

ELECTROMAGNETIC

FIELDS ano WAVES

Fundamentals of Engineering

Sedki M Riad | Iman M Salama

Electromagnetic

Fields and Waves

Fundamentals of Engineering

Sedki M Riad, Ph.D., PE

Professor Emeritus Virginia Tech

Iman M Salama, Ph.D

Northeastern University

[rant

THU VieN iB CONG DIE

McGraw Hill Education (India) Private Limited

Preface

Contents

Chapter] Introduction we(lp†0llasaiondidl c8 meh :

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13

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Why Start with Transmission Lines First?

Review of Transient and Harmonic Analysis Techniques and the Use of Complex Variables sac: cszesixxf2ii>ax6sv EU Ví SẼ săi 8ö Addendum 1Đ Transientand Harmonic Analysis of Linear Šystems ‹ -.‹-

1A.I 1A.2 1A.3 1A4 1A.5 1A.6 1A.7 THHOQBEUHÔN, - sao rat [ ban v2 C18 4g a2 401202314720 3 30 u89 E 2E k3 Time Domain and Frequency Domain

SUATES AIG ARES «sua uđố bó h4 «suy sn acannon’ fa eee Gp WS Se ges Phasors and Frequency-Domain (Harmonic) Analysis

Use of Phasors in Circuit Analysis (in the Frequency Domain)

Demonstration of Circuit Analysis in the Frequency Domain

1A.6.1 Starting with the Time-Domain Form

1A.6.2 Starting with the Frequency-Domain Form

The Frequency Domain and the Laplace Transform _

Addendum1B The Mystery of/ and lImaginaryNumbers

Chapter2 Transmission Lines—Wave Equations TT NT el 2.2 2.3 2.4 2.5 2.6 df 2.8 29 2.10 2.11 212 TRRROCUCHGE 2 fiptalss ex wuslail idpped laaniend wehbe ĐẪn r2 pae302106144 Transmission Line Analysis (Theory)_

Circuit Theory Analysis of a Two-Conductor Controlled Geometry TL is sabes naw ds vaared dowomdwns SMa towne veces an eee BC NHDđồI, s‹a 42922584624 kbasifebel,deoEssMlsesecxessl Transmission Line Circuit Analysis Using the Distributed RLGC Model: vines cds medantiaren rawmmtensS ấu di rrbat ie Kka hn: Steady-State Harmonic Analysis: “|, nails ducide dhersaneisnaarer eu eas ZBL SOTO „a»sxem + /Ae30Ou 30 1Bausszmasasotratassila RE biếu, THNEIWNIB 2201xxx/)056ebsveansbik lễ sxsa2sessissksebsiie 3.63 Caseo[lLossless LLÍR =Úand =0): si: 246vvii c.a

Physical Implications of Solutions: 0, ổ, Đ, and eụ

Physical Implications of $olutions: ÿ Z„, V”, and V—

Physical Impllcalans 066 luönN6Ï” s:/¿ssïisvv-0011 10 6L ca sat Two Special Cases: The Infinite Line and the Matched Load Line

Standing Waves and Standing Wave Ratio

AA Standing Wave Rate (2 (cesses ls saan wis cas vane te 2.11.2 Standing Wave Maxima and Minima

Standing Waves and the Bounce Diagram _

vi Contents

2.13 The Issues ofReflections and Standing Waves

28:2 MStfðÐSIDEINNES °66n0d000001 002227000) 000

2/015 Ñfmel']piWG 066781181 m mien

2.14 Combined Power and Signal Delivery Constraints

Addendum 2A DrivingPointlmpedance - cĂ con HHnHnHn ng ưu 2A.1 TL Driving Point Impedance and Input Impedance .,

Di Tom SPeclal Cases racer een gre er Ne ee ns sig ches Lis vee ve Addendum 2B Impedance Matching .ssssesseeseeseneeeeeeeseeerereensneseseeeneneaseeensneass OR How to, Achieve Matching $70.04 Walid lo cass 2B.2, 1-P1.1.MatchingiNebWorks 51110041 11190 0100 cu ch ca cái 283.1.Stubi MIAtehinb, de 30 bo 80M IÊ( VAO NHI cE TL cuc, 2B.4 The Quarter Wave Transformer as a Matching Network

2B.5 The Half Wave Transformer as a Matching Network

Addendum 2C The Frequency-Domain Bounce Diagram

Addendum2D TheTime-Domain Bounce Diagram _ -

213012 161L09/801141019012 0005206 tảo vấn co #nh sks noi an

2D.2 Time-Domain Bounce Diagram for Lossless Lines and Resistive WISCOMUMUIMES re tee, freee SE is cas uw h ay qe pe aan pwn eo + 2D.3 Time-Domain Reflectometry and the Bounce Diagram

2D.4 Time-Domain Reflectometry for Ideal Step Waveform Excitations

2D.5 Time-Domain Reflectometry for Ideal Dirac-Delta Impulse Waveform Excitations Addendum 2E 0 thị tiIu[8 hit TT TỡổCốẽ.Ũ

PU tMmmehitdioil vẽ nha D5 006 n0 1 ee 2E.2.1 The Magnitude of the Reflection Coefficient (|T |) Scale

2E.2.2 The Phase Angle of the Reflection Coefficient (ZI") Scale 2E.2.3 Normalized Distance Moved Scale

2E.3 Transmission Line Trace on the Smith Chart 2E.3.1 Case of Lossless TL, a=0 2E.3.2 Case of Lossy TL, #0 2E.4 How Does the Smith Chart Work? PE Erle otanting wit A(z Ord OO A) VP nes be cnc pac ene es 2E.4.2 Starting with the I(zor đ) Phasor -

2E.4.3 Finding Ƒ'(z, or đ,) [and Z(z, or d,)] Knowing I’ (z, or d,)

D2171 070/11 sake AON LO eames

2E.4.4 Special Case (Lossless TL), a=0

2E.5 The Admittance Smith Chart 0e0cccccccccccececcccececcececues 2E.6 Smith Chart Features and Short Cuts

2E.7 Matching Using the Smith Chart

Chapter 2 Problems

Chapter 2 Summary 99 92090290900060009090090000060690000000000090900000000000000060609060666 Chapter3 Transition to Electrostatics

3.1 Introduction

Contents

Addendum 3A (oordinateŠystems ccẰ nh nhe nhe nền nhe g 94

3A.1 Introduction ccc nh nh nh nh nh nh nh hi khinh ng 94 3A.2_ The Cartesian Coordinate Šyšsfem -‹ + nen nen hen 94

3A.3 The Cylindrical Coordinate System -‹ + chì nnìn 97 3A.4 The Spherical Coordinate System -. ‹ -‹ che hnhn 99

3A.5 Relationships between Coordinate Šystems . - +: 101 3A.6 Vector EXpresSi0nS c con hen nen nen nh hen ng 101

Midendum3B Vedtor(alculusand Vector ldentities -: -<<-*+< ch hhhhhhhhhhtheenheeh 102

3B.1 Vector Defnition and Examples -:© -+ + nh 102

3B.2 Vector Representations in Coordinate Šystems ‹ + 103

3B.2.1 Vector Representation in a Cartesian Coordinate System 103 3B.2.2 Vector Representation for a General Form Vector - +.+- 104 3B.2.3 Vector Representation in Cylindrical Coordinates .- 104

3B.2.4 Vector Representation in Spherical Coordinates .-. -: 105

3B.3 Vector Operations cceseeeseeesereencntngersereneetentonsres 106

Addendum 3C 5patialDistributionsand Densities -++ *+++teeeretttnreeetreeree 108

3C.1 Static Distributions and Densities «0.0 see eee eect eee e tenn etnies 108 3C.2 Conversions between Static Density Expressions -‹‹ 109 3C.3 Dynamic Distributions and Densities + +++eeereereres sete ees 110 3C.4 Conversions between Dynamic Density Expressions - - - - - 111 Addendum30 Line,Surface,andVolume lntegrations - - -+=*+*****$ nh hhhthtteth 111

SDT THtreduction /:.⁄/2vx02(216<ccccczc tt nen 22569105990 08056 T9 SE 11

3D.2 Integrating Vector Quantities - + nen nh nen hen lll

3D.3 Integrating Scalar Quantities © sss sees eee ee esse seer tent ee sess 113 3D.4 Examples of Work and Energy Integratlons -.-‹-‹-‹-‹ 114

Chapter4 Electrostatic Fields: Electric Flux and 6auss law _ sale deealcasat seen

4.1 The Electric Charge .sseseeeetesenrenrensesesanennererencs 116 4.2 Charge Distributions and Charge Densities -‹ -‹©‹: 117

Á3 - Electric EluX ¿cv <c22/⁄⁄4962/900X6/XL NN Re nc nla class 118

4.4 Faradays Concentric Spheres Experiment ‹-‹‹‹‹ccccccị 120 4.5 Electric FluxDensity -cc cà nen nh nhe nh nh nh th 121 4.6 Gauss’ Law: The Integral Form sess eee eect eee reese eee cease 122 4.7 Application of Gauss’ Law in the Integral Form: Electric Flux due to

Symmetrical Charge Distributions -‹-++-c+ +: 124

4.8 Gauss’ Law in the Point Form (Differential FOLM)) se 128

4.8.1 Point Form versus [ntegral Form - 128 4.8.2 Cartesian Coordinates Differential Form of Gauss Law 129 4.9 The Divergence Theorem 1 sss eerste tere rs tees ee ee este ta ees 132 4.10 Application of Gausỷ Law in the Point Form -‹-c‹ccccị 132

Addendum4A Application of the Integral Form of Gauss’ Law to Symmetrical Charge Distributions 135

4A.1 Electric Flux Distributions for Charges of Spherical Symmetries

(No Variations with or @) oss seeeeeee nent nent eerste eee et et ee es 135

4A.1.1 Case of Point Charge q Located at the Origin

(Notice, We Use q or AQ for Point Charge Notation) 137

4A.1.2 Case of Spherical Surface Charge Distribution with

Uniform pe |ceniot selon nal âm (c1 1536 eee es 138

vil

viii Contents

4A.1.3 Case of Spherical Shell Charge Distribution with p,

WVanyinpiwitnrOnly, 02 MovomMena IAL 6 139 4A.1.4 Case of Spherical Volume Charge Distribution with p,

Varying withtmOniyinioe Viaswoa all LAL cs 140

4A.2 Electric Flux Distributions for Charges of Cylindrical Symmetries

(NO Variationsiwithiipong)io.! manwisd vyldaneelsd 2M 6 ec 14] 4A.2.1 Case of an Infinite Line Charge Uniformly Stretched

CLOT DAL EARS 6 SS ee bó ốc 143

4A.2.2 Case of an Infinite Height Cylindrical Surface Charge

Distribution with Uniform p, (or Ø,) 144

44.2.3 Case of a Cylindrical Shell of Charge Distribution with

Infinite Height and p, Varying withp Only 145 4A.2.4 Case of “Full” Cylindrical Charge Distribution with

Infinite Height and p, Varying with p Only 146 4A.3 Electric Flux Distributions for Charges of Planar Symmetries

UNG WWaraOns WINX OUP) ii ssaicxeitvaronssansuo canssnetswseacs 147 44.3.1 Case of Planar Surface Charge Distribution with Constant Ps

(No Variations with x or y), with Infinite Extension in

Bothecdndty Coordinates’ 400) 79000 Bacco ccc 148 44.3.2 Case of Planar “Slab” of Charge Distribution with p, Varying

with z Only (No Variations with x or y), Again with iantute mandy tensions, ice is ain seeder nsioW + +61 sata 150 44.4 Flux Density Distribution in Some Familiar Combinations of

3ymmetrical Charge Distributions 153 4A.4.1 Two Concentric Spherical Surfaces (Spherical Capacitor) 153 44.4.2 Two Coaxial Cylindrical Surfaces (Cylindrical Capacitor/

Coaxial Capacitor/Coaxial Transmission Line) 154 44.4.3 Two Parallel Planar Surfaces (Planar Capacitor/Parallel

Plateiapaciton is XAMI3.M119A13;2014143/06426x1asl3, „.È 3eigs¿ 155

eM Re cri eet ec canaaaus 156

Chapter 4 DI HAT 2 2 122cc v(56001/2 cn So's 'g coin ved View Geox oun van saw ewes 159

Chapter5 Electric Force, Field, Energy, and Potential Su nh: UG

ae al Mới 2U cU OF cows 164

52/02 mlDniet To: xe teietansi A002 BA 164

S0 17117 170 7095) 0JNUỚ(C 166

5-4 Electric Field Evaluation Using the “Incrementation” Scheme 168 3.5 Electric Field due to Famous Examples of Charge Distributions 169

5.5.1 Case of Charges Distributed Uniformly in a Finite Length Bey esh een ae cee saussnosnmsan si ¥ete 169 5.5.2 Case of Charges Distributed Uniformly in an Infinite

Benatingiraiphtl bined tenvel livpstai-aiidowiitenilngs .Akmubne 172

26 Energy in a Systenmen Chargesiin iil, xy oi sooldevdefdesuesvnes eee iz

9.7 Examples of Energy ina SystemiofCharges : : - 175

5.7.1 Energy ina System of Point HAY DI ÍuifwarsavvLre te eee 175

a at Energy in Other Forms of Charge Distributions .+- 176

°.8.1 The Electric Potential due to the Field of a Point Charge 178

Contents

5.9 PotentialiGradient, cm cssaaes vec sas emlo cette vette: ¥ 0/7) 0° 179

5.10 Electric Potential Evaluation Using the “Incrementation’ Scheme 181

5.11 Conservative Nature of Electrostatic Potential 182

5.12 Energy Density in Electrostatic Fields - 183

Addendum 5A EFlectricField due to Famous Examples of Charge Distributions -.-. -: 185

5A.1 Charges Distributed Uniformly in a Circular Ring - 185

5A.2 Charges Distributed Uniformly in a Circular Disc - 187

5A.3 Alternative Integration Approaches to the Finite Disc Case .- 189

5A.4 Charges Distributed Uniformly in an Infinitely Extended Sheet of Charges (Figure 5A.6) .-cc che 191 5A.5 Important Remark .:cscseesatecesaeeereserecerncerecses 192 Addendum 5B _ Electric Potential (and Field) due to Famous Examples of Charge Distributions .+ 192

5B.1 Charges Distributed Uniformly in a Circular Ring - 192

5B.2 Charges Distributed Uniformly in a Circular Disc (Figure 5B.2) 193

5B.3 Electric Dipole (Field and Potential) - 194

Chapter 5 Problems_ - << nọ nh nh kÝ nh nh nh t 197 (hapter 5 §ummary _ -.‹-.‹‹ccccc nnnỲ nh nh nh hoc 203 (hapter6 Materials: Conductors and DielectriG v6 6244885558180 1007202 61 HIrOdUEHOD -+:iraxcso2atsmssehaeaEtsaas t9 20021070616 11011k 206 62-:GHdHGLOES:- '22211265/7156660571/8SS1EEÿNV LH TPE T119 011779 rt 207 6.2.1 Conductors under Static Conditions - 207

6.2.2 Conductors under Dynamic Conditions 207

6.3 Electric Currentand Current Densities - 208

6.4 The Continuity Equation . -< << 209 6.5 Conductivity and Resistance {nằee nhe 210 6.5.1 Power Dissipated due to Conductivity/Resistivity 211

6.5.2 Resistance and Conductance - 211

6.5.3 The Resistance as a Circuit Element - 212

6.6 Dielectrics (Insulators) and Polarization - 213

6.6.1 The Polarization Vector che 214 6.6.2 Energy in Dielectric Polarizatlon 217

6.7 CApACÍADC€ on nh nh nh nh ni kh nh nh ng 218 6.7.1 The Capacitance as a Circuit Element - 219

68 Boundary Conditions c ch nh he heo 224 6.8.1 Dielectric-Dielectric Interface - 224

6.8.2 Surface Charges at the Interface: Free and Bound (PolarizafOH): «(042x926 he Gieeerats impels 8 226 6.8.3 Conductor-Conductor Interface - 228

6.8.4 Conductor-Dielectric Interface -.- 229

Addendum6A Resistance Evaluafion - -c sen nh nh nh nh kh nh nh kh bu 230 6A.1 TResistanee Evaluation- - -‹.-.-7:/7775/02/001 05, 8962/2000 0-0 230 6A.1.1 Using Vand J for Resistance Evaluation [Equation (6.19)] [0.)20000 SARI SAB cicie eae 230 6A.1.2 Using AR for Resistance Evaluation [Equation (6A.1)] .- 230

6A.2 Coaxial Cable Transmission Line R and G, Parameters 232

6A.2.1 Conductance of TL Insulator, Gypp sess sees eee e eee eens 233

ix

X Contents

Addendum 6B Capacitance Evaluation ssseseseseeeeeeeeseessseeneeeeeeseseeaneeeeessseeen

eens

6blm@apacitancelevaluaviony AGAMA 2W094694.3181492 (HH

6B.1.1 Using Vand ự for Capacitance Evaluation

6B.1.2 Using AC for Capacitance Evaluation

6B.2 Examples of “Controlled Geometry” Capacitances

GB 2eanParalleliplate Capacitance: vài a2 22 vapicny anes vase

Addendum 6C Resistors and Capacitors as Œircuit Flements

6C.1 Resistance Circuit Relationships: Current, Voltage, Power, ShQ EHCTEVE các 0 ái 0-8 0XELL).0 010/11 19109112 ck kv ken ese cece 6C.1.1 Current-Voltage Relationship

6C.1.2 1OWer jn Resistance/Conductance

6C.1.3 Resistances/Conductances in Series

6C.1.4 Resistances/Conductances in Parallel

6C.2_ Capacitance Circuit Relationships: Current, Voltage, Power, BS Me Ve creda icles n ac ead oii wars v ov able b'sos cipide wai vo esde 6 om 6C;2:1- - Current-Voltage Relationship - : :

O22 Bower M Capacitance o's as ois x qasisasin® Peanemesi «cu aves oe 6C.2.3 Energy Stored in Capacitance

K2 L1 C CHÚC CHIẾN c2 (2.2002 3222-0562 csvsss Si 0 0001110 ri uc ovoxosnv vi v2 5V, đ 11341219 n9 Trẻ mẽ ẽ -

Chapter 6 Summary CTP e meee eee eee reser ee ee ee seen eee EO ee eee e ene eeeeeeeeeereseers Chapter7 Poisson's and Laplace's Equations and Solution Methods _

NT 7 cha eee aig 7.2 Poisson's and Laplace's Equations 75a) ol NGNLEO era 0) 1150) delete al DI 7.4 Demonstration of Solving Poisson's ĐỊT HO v2 ils scadenastire wietosattia's wereceral 7.5 Solving Poisson's Equation for Nonsymmetrical Charge Distributions Addendum 7A The Method of Images S99 990906909600990000006906060069000000000000606060000000900096060600000066 E00 NHelailahidi le 3/21J942y 54a 2 - 7B.1 Introduction 7B.2 7B.3 Numerical Analysis of Electrostatic Problems _

Demonstration of Numerical Solution of Laplaces Equation S0 09050 ///72/2190D0)) bảo s„ 7B.4 Demonstration of Iterative Solution of Laplace's Equation in 2D

7B.5 Graphical Methods

7B.6

7B.7 Field Intensity and Flux Density Evaluation

Capacitance Evaluation

Chapter 7 Problems Chapter 7 Summary

Contents

Chapter8 MagneticFields and Flux -. - 5< <<©+<+ „ 289

8.1 Introduction s+¿¿2 402224 //00941114/010221-1.11222142 2x1 ^: 92n0000 290 8.2 Amperes Law for Magnetic Force -. ‹‹‹- << 291 8.3 Magnetic Field Intensity and Magnetic Flux Density 292

8.4 Biot-SavariLAW con nh nh như kh nh nh nà 293 8.5 Magnetic Flux and Gauss’ Law for Magnetism - 294

8.6 Ampere§ Circuital LAW cc cành nen hen nhe 295 8.7 Magnetic Field Evaluation Schemes - 296

8.8 Magnetic Field Evaluation Using the “Incrementation” Scheme ssissssss.sGotessbvg49s1810 82-400 siôn 7c ng 296 8.8.1 Case 1: Magnetic Field due to a Finite Length Thin Straight Current-Carrying Conductor (Figure 8.8) - 296

8.8.2 Case 2: Magnetic Field due to an Infinite Length Thin Straight Current-Carrying Conductor (Figure 8.8) 298

8.8.3 Case 3: Magnetic Field due to a Thin Circular Current-Carrying Conductor (Loop) (Figure 8.13) soe ae 300 8.8.4 Case 4: Magnetic Field due to a Finite Height Circular Solenoid (Figure 8.17) esse erence teen ee eee e eens 302 8.8.5 Case 5: Magnetic Field due to an Infinite Height Circular Solenoid (Figure8.17) 6 See cece nee eee 303 8.9 Magnetic Field Evaluation Using Ampere’s Circuital Law Scheme + iacev Quan 5 SAN eee | Pe GRRE CO eiert eerie ete ate 303 8.10 Category A: Magnetic Field due to Infinite Length Axial/Coaxial Current Distributions with Cylindrical Symmetries (Figure 8.19) 304

8.10.1 Case al: Magnetic Field due to an Infinite Length Thin Straight Current-Carrying Conductor (Leftof Figure 8.19) :: ((( 2220002212 305 8.10.2 Case a2: Magnetic Field due to an Infinite Length Thick Straight Current-Carrying Conductor (Center Figure 8.19) seseeneeer erect eeeeeneeeeeaees 305 8.10.3 Case a3: Magnetic Field due to an Infinite Length Coaxial Transmission Line (Right of Figure 8.19) 306

8.11 Category B: Magnetic Field due to Planar Current Distributions with Planar Smmetries - << Ÿ nhe 308 8.11.1 Case bl: Magnetic Field due to an Infinite Extension Thin Current Sheet (Figure 8.21) cssqsigess sees sere eannmienen 308 8.12 Category C: Magnetic Field due to Toroidal and Solenoidal Current Distributions with Uniform Linear Current Densities .+ 309

8.12.1 Case cl: Magnetic Field due to a Toroid (Figure 8.23) 309

8.12.2 Case c2: Magnetic Field due to an Infinite Height Solenoid (Discuss Shape of Cross Section) (Figure 8.25) + 311

8.13 Magnetostatic Diferential (Point) Forms_ 312

8.13.1 Point Form ofGaus$ Law in Magnetism 312

8.13.2 Point Form of Ampere§ Circuital Law 312

8.14 Stokes’ Theorem, ‹‹.‹‹⁄55ỐỐ309552 251112432 26162060 1V V0 314 8.15 Static Form of Maxwell§ Equations -++++ + 315

8.16 Scalarand Vector Magnetic Potential -+ - 315

8.16.1 Scalar Magnetic Potential -c+ chì 315 8.16.2 Vector Magnetic Potential -©+ +**+ 316

XI

xii Contents

Addendum 8A Analogieswith ElectrostaticQuantities 2+2 317

icField Evaluation Using the “Incrementation” Scheme 318

ae a nad 1: Magnetic Field due to a Finite Length Thin Straight Gitrtent: Careyiny|CONGUCIOL rere coc serene a cue st heacces vies es iis 318 8B.2 Case 2: Magnetic Field due to an Infinite Length Thin Straight @urrent- Carrying CONGUCIOE - 71 - e¿ — 319 8B.3 Case 3: Magnetic Field due to a Thin Circular Current-Carrying €ôriductfff.LLD0D)/2 9 neo cv cay peuarss sen ¬— 320 8B.4 Case 4: Magnetic Field due to a Segment of a Thin Circular Current-Carrying Conductor (Loop)_ 322

8B.5 Case 5: Magnetic Field due to a Finite Height Circular Solenoid 323

8B.6 Case 6: Magnetic Field due to an Infinite Height Circular Solenoid 325

Addendum 8C Magnetic Field Evaluation Using Ampere’s CircuitalLawScheme 326

8C.1 Case 1: Magnetic Field due to an Infinite Length Thin Straight Gurrent= Carrying Conductor isc ssees hess cedseseeccececccccecceess 326 8C.2 Case 2: Magnetic Field due to an Infinite Length Thick Straight Current Carving COndtcton gst Hộ (ah và xác con sa nang 327 8C.3 Case 3: Magnetic Field due to an Infinite Length Coaxial 12mm Eb2n)0i18sá4xaxaasaezzr 7 77a 329 8C.4 Case 4: Magnetic Field due to an Infinite Extension Thin Current Sheet 330

8C.5 Case 5: Magnetic Field duetoaToroid 332

8C.6 Case 6: Magnetic Field due to an Infinite Height Solenoid 335

KiapterSiroblems areca MOGI tery 337 M2521 10 1 07 t8 10m0 1T 2T 343 Chapter 9 Magnetic Materials, Magnetic Circuits, and Inductance sevee 347 Poe ee Ốc 348 9.2 Magnetic Force and NÓ Ho ee eich so sence vnceescaccesesers 348 3.2.1 Ampere§ Law for MAROC EATER ot có, vabassasvuyv seo, 348 9.2.2 Magnetic Force on Moving Charge 349

9.2.3 Magnetic Force and Torque ona Current Loop 349

9.3 Energy Stored in ‘i aU lame ne leech es VỐ: 353 9.4 Magnetic Properties of TT ca ca 2i ế 356 etc en ese ee 356 “3⁄56: 3oEotilittoiftrueidbee mem: xusina "05 TESU Anh IS 356 3-43 Dipole Moments and Magnetization Vector 356

9.4.4 peter ee 358 nã 6 ga 00 00 Cy) 00707 358 9.4.6 Residual Magnetism (Permanent IMAP IIIS 123i od as dean oe 359 ge MagieticBoundary Conditions 7 All 360 9.5.1 Interface between Two Different Magnetic Materials 360

9.5.2 Interface between Two Nonmagnetic Materials (eg., P aramagnetic/Diamagnetic with Paramagnetic/Diamagnetic) 363

9.5.3 Interface between Nonmagnetic and Magnetic Materials (eg., Ferromagnetic with Paramagnetic/Diamagnetic) aie a 363 95.4 Magnetic Flux Confinement in Magnetic Materials 363