Electromagnetic Fields: For Anna University

Cover......Page 1
Preface......Page 8
Acknowledgements......Page 10
Contents......Page 12
Introduction......Page 22
 Applications of Electromagnetic Field Theory......Page 23
 Differences between Circuit Theory and Electromagnetic Field Theory......Page 25
 Notation of Scalar Parameters......Page 26
 Notation of Vector Parameters......Page 29
 Large Value Representation......Page 31
 Some Great Contributors to Electromagnetic Field Theory......Page 32
Chapter 1: Mathematical Preliminaries......Page 34
 1.1 Fundamentals of Scalars and Vectors......Page 35
  Cartesian Coordinate System......Page 36
  Cylindrical Coordinate Systeym......Page 37
  Spherical Coordinate System......Page 39
  Example and Features of Divergence......Page 43
 1.6 Curl of a Vector......Page 44
 1.7 Laplacian Operator......Page 46
 1.8 Dirac Delta......Page 47
 1.9 Decibel and Neper Concepts......Page 48
  Properties of Complex Numbers......Page 49
 1.11 Logarithmic Series and Identities......Page 50
 1.13 Cubic Equations......Page 51
 1.14 Determinants......Page 52
  Minor of a Determinant......Page 53
  Types of Matrices......Page 54
  Properties of Matrices......Page 55
 1.17 Permutations......Page 57
 1.19 Basic Series......Page 58
 1.21 Sine and Cosine Series......Page 59
 1.23 Hyperbolic Functions......Page 60
 1.24 Sine, Cosine, Tan and Cot Functions......Page 61
  Gamma function......Page 63
  Bessel function......Page 64
  Fresnel integral......Page 66
 1.26 Partial Derivative......Page 67
 1.27 Some Differentiation Formulae......Page 68
 1.28 Some Useful Integration Formulae......Page 70
 1.29 Radian and Steradian......Page 72
 1.30 Integral Theorems......Page 73
 Points/Formulae to Remember......Page 74
 Solved Problems......Page 75
 Objective Questions......Page 83
 Exercise Problems......Page 87
Chapter 2: Electrostatic Fields......Page 88
 2.2 Applications of Electrostatic Fields......Page 89
  Properties and Functions of Charges......Page 90
 2.4 Coulomb\'s Law......Page 92
 2.7 Electric Field Strength due to Point Charge......Page 98
 2.8 Salient Features of Electric Intensity......Page 99
 2.9 Electric Field due to Line Charge Density......Page 103
 2.10 Electric Field Strength due to Infinite Line Charge......Page 106
 2.11 Field due to Surface Charge Density, ρs(C/m2)......Page 113
 2.12 Field due to Volume Charge Density, ρv (C/m3)......Page 118
 2.13 Potential......Page 122
 2.14 Potential at a Point......Page 123
 2.15 Potential Difference......Page 126
 2.16 Salient Features of Potential Difference......Page 127
 2.18 Salient Features of Potential Gradient......Page 128
 2.20 Potential due to Electric Dipole......Page 129
 2.21 Electric Field due to Dipole......Page 133
 2.22 Electric Flux......Page 134
 2.23 Salient Features of Electric Flux......Page 135
 2.24 Faraday\'s Experiment to Define Flux......Page 136
 2.26 Salient Features of Electric Flux Density, D......Page 137
 2.27 Gauss\'s Law and Applications......Page 139
 2.28 Proof of Gauss\'s Law (on Arbitrary Surface)......Page 141
 2.29 Gauss\'s Law in Point Form......Page 142
 2.30 Divergence of a Vector, Electric Flux Density......Page 145
 2.33 Salient Features of Gauss\'s Law......Page 146
 2.34 Poisson\'s and Laplace\'s Equations......Page 147
 2.35 Applications of Poisson\'s and Laplace\'s Equations......Page 148
 2.36 Uniqueness Theorem......Page 149
 2.38 Proof of Boundary Conditions......Page 154
 2.40 Properties of Conductors......Page 157
 2.41 Electric Current......Page 158
 2.42 Current Densities......Page 159
 2.43 Equation of Continuity......Page 160
 2.44 Relaxation Time (Ty)......Page 161
 2.45 Relation between Current Density and Volume Charge Density......Page 162
  Diekectrics in Electric Field......Page 164
 2.49 Polarisation, P......Page 166
 2.50 Capacitance of Different Configurations......Page 170
 2.51 Energy Stored in an Electrostatic Field......Page 180
 2.52 Energy in a Capacitor......Page 183
 Points/Formulae to Remember......Page 185
 Objective Questions......Page 188
  Answers......Page 191
 Multiple Choice Questions......Page 192
  Answers......Page 197
 Exercise Problems......Page 198
Chapter 3: Steady Magnetic Fields......Page 200
 3.3 Fundamentals of Steady Magnetic Fields......Page 201
 3.4 Faraday\'s Law of Induction......Page 202
 3.5 Magnetic Flux Density, B (wb/m2)......Page 203
 3.7 Field due to Infinitely Long Current Element......Page 206
 3.8 Field due to a Finite Current Element......Page 208
 3.9 Ampere\'s Work Law or Ampere\'s Circuit Law......Page 210
 3.10 Differential Form of Ampere\'s Circuit Law......Page 212
 3.11 Stoke\'s Theorem......Page 218
 3.12 Force on a Moving Charge due to Electric and Magnetic Fields......Page 219
 3.14 Force on a Current Element in a Magnetic Field......Page 221
 3.15 Ampere\'s Force Law......Page 222
 3.16 Boundary Conditions on H and B......Page 224
  Characteristics of Scalar Magnetic Potential (Vm)......Page 227
 3.18 Vector Magnetic Potential......Page 228
  Characteristics of Vector Magnetic Potential......Page 229
 3.19 Force and Torque on a Loop or Coil......Page 230
  Diamagnetic Materials......Page 232
  Ferromagnetic Materials......Page 233
 3.21 Magnetisation in Materials......Page 234
  Magnetic Dipole Moment, m......Page 235
 3.22 Inductance......Page 238
  Toroid......Page 239
  Solenoid......Page 240
  Parallel Conductors of Radius, a......Page 241
 3.24 Energy Density in a Magnetic Field......Page 243
 3.25 Energy Stored in an Inductor......Page 245
 3.26 Expression for Inductance, L, in Terms of Fundamental Parameters......Page 246
  Coefficient of Coupling......Page 248
 3.28 Comparison between Electric and Magnetic Fields/Circuits/Parameters......Page 249
 Points/Formulae to Remember......Page 252
 Objective Questions......Page 255
  Answers......Page 257
 Multiple Choice Questions......Page 258
  Answers......Page 259
 Exercise Problems......Page 260
Chapter 4: Maxwell\'s Equations......Page 262
 4.1 Introduction......Page 263
 4.2 Equation of Continuity for Time Varying Fields......Page 264
 4.3 Maxwell\'s Equations for Time Varying Fields......Page 265
 4.4 Meaning of Maxwell\'s Equations......Page 266
 4.5 Conversion of Differential Form of Maxwell\'s Equation to Integral Form......Page 267
 4.6 Maxwell\'s Equations for Static Fields......Page 268
 4.9 Maxwell\'s Equations for Static Fields in Free Space......Page 269
 4.10 Proof of Maxwell\'s Equations......Page 270
 4.11 Sinusoidal Time Varying Field......Page 272
 4.12 Maxwell\'s Equations in Phasor Form......Page 273
 4.14 Types of Media......Page 274
 4.15 Summary of Maxwell\'s Equations for Different Cases......Page 284
 4.17 Proof of Boundary Conditions on E, D, H and B......Page 285
 4.19 Boundary Conditions in Vector Form......Page 289
 4.20 Time Varying Potentials......Page 291
 4.21 Retarded Potentials......Page 292
 4.22 Maxwell\'s Equations Approach to Relate Potentials, Fields and Their Sources......Page 293
 4.24 Lorentz Gauge Condition......Page 294
 Points/Formulae to Remember......Page 297
 Objective Questions......Page 299
  Answers......Page 300
 Multiple Choice Questions......Page 301
  Answers......Page 303
 Exercise Problems......Page 304
Chapter 5 Electromagnetic Fields and Waves......Page 306
 5.3 Wave Equations in Free Space......Page 307
 5.4 Wave Equations for a Conducting Medium......Page 308
 5.5 Uniform Plane Wave Equation......Page 309
 5.6 General Solution of Uniform Plane Wave Equation......Page 312
 5.7 Relation between E and H in Uniform Plane Wave......Page 313
 5.9 Wave Equations in Phasor Form......Page 316
 5.10 Wave Propagation in Lossless Medium......Page 317
 5.11 Propagation Characteristics of EM Waves in Free Space......Page 318
 5.12 Propagation Characteristics of EM Waves in Conducting Medium......Page 322
 5.13 Summary of Propagation Characteristics of EM Waves in a Conducting Medium......Page 325
 5.15 Wave Propagation Characteristics in Good Dielectrics......Page 328
 5.16 Summary of the Propagation Characteristics of EM Waves in Good Dielectrics......Page 330
 5.17 Wave Propagation Characteristics in Good Conductors......Page 331
 5.19 Depth of Penetration, (m)......Page 332
  Linear Polarisation......Page 334
  Elliptical Polarisation......Page 335
 5.22 Direction Cosines of a Vector Field......Page 336
 5.23 Wave on a Perfect Conductor-Normal Incidence......Page 340
 5.24 Waves on Dielectric-Normal Incidence......Page 342
  Parallel Polarisation......Page 345
  Parallel Polarisation......Page 346
  Perpendicular Polarisation......Page 350
  Parallel Polarisation......Page 351
  Perpendicular Polarisation......Page 354
 5.28 Brewster Angle......Page 355
 5.29 Total Internal Reflection......Page 356
 5.30 Surface Impedance......Page 357
 5.31 Poynting Vector and Flow of Power......Page 359
 5.32 Complex Poynting Vector......Page 363
 Points/Formulae to Remember......Page 365
 Objective Questions......Page 367
  Answers......Page 368
 Multiple Choice Questions......Page 369
  Answers......Page 371
 Exercise Problems......Page 372
Chapter 6: Guided Waves......Page 374
 6.3 Derivation of Field Equations between Parallel Palates and Propagation Parameters......Page 375
 6.4 Field Components for TE Waves (Ez = 0)......Page 379
 6.5 Field Components of TM Waves (Hz = 0)......Page 381
 6.6 Propagation Parameters of TE and TM Waves......Page 383
 6.7 Guide Wavelength......Page 384
 6.8 Transverse Electromagnetic Wave (TEM Wave)......Page 386
 6.9 Velocities of Propagation......Page 387
 6.10 Attenuation in Parallel Plate Guides......Page 388
 6.11 Wave Impedances......Page 389
 6.13 Derivation of Field Equations in Rectangular Hollow Waveguides......Page 392
  Transverse Magnetic (TM) Waves in Rectangular Waveguide......Page 396
  Transverse Electric Waves......Page 400
 6.14 Propagation Parameters of TE and TM Waves in Rentangular Waveguides......Page 403
 6.15 TEM Wave does not Exist in Hollow Waveguides......Page 407
 6.16 Excitation Methods for Defferent TE and TM Waves/Modes......Page 409
 6.18 Wave Impedance in Waveguide......Page 410
  Power Dessipation in a Lossy Waveguide......Page 411
 6.20 Waveguide Resonators......Page 415
  TM Mode (Hz = 0)......Page 416
  Degenerate Mode......Page 417
 6.21 Salient Features of Cavity Resonators......Page 418
 6.22 Circular Waveguides......Page 422
 6.23 Salient Features of Circular Waveguides......Page 423
 Points/Formulate to Remember......Page 427
 Objective Questions......Page 429
  Answers......Page 432
 Multiple Choice Questions......Page 433
  Answers......Page 435
 Exercise Problems......Page 436
Chapter 7: Transmission Lines......Page 438
 7.2 Types of Transmission Lines......Page 439
 7.4 Equivalent Circuit of a Pair of Transmission Lines......Page 441
 7.5 Primary Constants......Page 442
 7.6 Transmission Line Equations......Page 445
 7.7 Input Impedance of a Transmission Line......Page 447
 7.8 Secondary Constants......Page 449
 7.9 Lossless Transmission Lines......Page 450
 7.10 Distortionless Line......Page 451
 7.11 Phase and Group Velocities......Page 453
 7.13 Input Impedance of Lossless Transmission Line......Page 454
 7.14 RF Lines......Page 456
 7.15 Relation between Reflection Coefficient, Load and Characteristic Impedances......Page 457
 7.16 Relation between Reflection Coefficient and Voltage Standing Wave Ratio (VSWR)......Page 458
 7.17 Lines of Different Length......Page 459
  Copper Loss......Page 461
  Radiation Losses......Page 462
  Construction of Smith Chart......Page 474
  Application of Smith Chart......Page 476
  Dedign of Single Stub Matching......Page 477
 7.21 Double Stubs......Page 484
  Design Methodology......Page 485
 Points/Formulae to Remember......Page 487
 Objective Questions......Page 490
  Answers......Page 492
 Multiple Choice Questions......Page 494
  Answers......Page 496
 Exercise Problems......Page 497
 Model Question Paper I......Page 498
 Model Question Paper II......Page 500
 Solutions to Model Question Paper I......Page 502
 Solurions to Model Questions Paper II......Page 503