Designed for upper division electromagnetism courses or as a reference for electrical engineers and scientists, this book introduces Maxwell s equations and electromagnetic waves as soon as possible (i.e., in the first third of the book), and then discusses electrostatics, magnetostatics, induction, etc., in the light of those equations. The book also provides a thorough treatment of vector field theory which emphasizes the rotational invariance of the dot and cross products, together with div, grad, and curl, and thus gives a clear physical motivation for the use of those constructs to describe electric and magnetic fields. Unlike many competing books, Maxwell s Equations & the Principles of Electromagnetism covers topics such as advanced potentials, retarded fields, forces on dielectric liquids, antenna theory, and Faraday rotation. *BRIEF TABLE OF CONTENTS: 1. Introduction. 2. Vectors and Vector Fields. 3. Time-Independent Maxwell s Equations. 4. Time-Dependent Maxwell s Equations. 5. Electrostatic Calculations. 6. Dielectric and Magnetic Media. 7. Magnetic Induction.8.Electromagnetic Energy and Momentum. 9. Electromagnetic Radiation. 10. Relativity and Electromagnetism. Appendixes. Index.
Author(s): Richard Fitzpatrick
Series: Physics
Publisher: Infinity Science
Year: 2008
Language: English
Pages: 450
Introduction ......Page 13
2.2 Vector Algebra ......Page 17
2.3 Vector Areas ......Page 20
2.4 The Scalar Product ......Page 22
2.5 The Vector Product ......Page 24
2.6 Rotation ......Page 27
2.7 The Scalar Triple Product ......Page 29
2.8 The Vector Triple Product ......Page 30
2.9 Vector Calculus ......Page 31
2.10 Line Integrals ......Page 32
2.11 Vector Line Integrals ......Page 35
2.12 Surface Integrals ......Page 36
2.13 Vector Surface Integrals ......Page 38
2.14 Volume Integrals ......Page 39
2.15 Gradient ......Page 40
2.16 Divergence ......Page 44
2.17 The Laplacian ......Page 48
2.18 Curl ......Page 50
2.19 Polar Coordinates ......Page 55
2.20 Exercises ......Page 57
3.2 Coulomb’s Law ......Page 61
3.3 The Electric Scalar Potential ......Page 66
3.4 Gauss’ Law ......Page 69
3.5 Poisson’s Equation ......Page 78
3.6 Ampere’s` Experiments ......Page 80
3.7 The Lorentz Force ......Page 83
3.8 Ampere’s` Law ......Page 87
3.9 Magnetic Monopoles? ......Page 88
3.10 Ampere’s` Circuital Law ......Page 91
3.11 Helmholtz’s Theorem ......Page 98
3.12 The Magnetic Vector Potential ......Page 103
3.13 The Biot-savart Law ......Page 107
3.14 Electrostatics And Magnetostatics ......Page 109
3.15 Exercises ......Page 113
4.2 Faraday’s Law ......Page 119
4.3 Electric Scalar Potential? ......Page 124
4.4 Gauge Transformations ......Page 125
4.5 The Displacement Current ......Page 128
4.6 Potential Formulation ......Page 135
4.7 Electromagnetic Waves ......Page 136
4.8 Green’s Functions ......Page 144
4.9 Retarded Potentials ......Page 148
4.10 Advanced Potentials? ......Page 154
4.11 Retarded Fields ......Page 157
4.12 Maxwell’s Equations ......Page 161
4.13 Exercises ......Page 163
5.2 Electrostatic Energy ......Page 169
5.3 Ohm’s Law ......Page 175
5.4 Conductors ......Page 177
5.5 Boundary Conditions On The Electric Field ......Page 183
5.6 Capacitors ......Page 184
5.7 Poisson’s Equation ......Page 190
5.8 The Uniqueness Theorem ......Page 191
5.9 One-dimensional Solutions Of Poisson’s Equation ......Page 196
5.10 The Method Of Images ......Page 198
5.11 Complex Analysis ......Page 207
5.12 Separation Of Variables ......Page 214
5.13 Exercises ......Page 221
6.2 Polarization ......Page 227
6.3 Electric Susceptibility And Permittivity ......Page 229
6.4 Boundary Conditions For E And D ......Page 230
6.5 Boundary Value Problems With Dielectrics ......Page 232
6.6 Energy Density Within A Dielectric Medium ......Page 238
6.7 Force Density Within A Dielectric Medium ......Page 240
6.8 The Clausius-mossotti Relation ......Page 242
6.9 Dielectric Liquids In Electrostatic Fields ......Page 245
6.11 Magnetization ......Page 249
6.12 Magnetic Susceptibility And Permeability ......Page 252
6.13 Ferromagnetism ......Page 253
6.14 Boundary Conditions For B And H ......Page 255
6.15 Boundary Value Problems With Ferromagnets ......Page 256
6.16 Magnetic Energy ......Page 261
6.17 Exercises ......Page 263
7.2 Inductance ......Page 267
7.3 Self-inductance ......Page 269
7.4 Mutual Inductance ......Page 273
7.5 Magnetic Energy ......Page 276
7.6 Alternating Current Circuits ......Page 282
7.7 Transmission Lines ......Page 286
7.8 Exercises ......Page 292
8.2 Energy Conservation ......Page 295
8.3 Electromagnetic Momentum ......Page 299
8.4 Momentum Conservation ......Page 303
8.5 Angular Momentum Conservation ......Page 306
8.6 Exercises ......Page 309
9.2 The Hertzian Dipole ......Page 311
9.3 Electric Dipole Radiation ......Page 318
9.4 Thompson Scattering ......Page 319
9.5 Rayleigh Scattering ......Page 322
9.6 Propagation In A Dielectric Medium ......Page 324
9.7 Dielectric Constant Of A Gaseous Medium ......Page 325
9.8 Dispersion Relation Of A Plasma ......Page 326
9.9 Faraday Rotation ......Page 330
9.10 Propagation In A Conductor ......Page 334
9.11 Dispersion Relation Of A Collisional Plasma ......Page 336
9.12 Normal Reflection At A Dielectric Boundary ......Page 338
9.13 Oblique Reflection At A Dielectric Boundary ......Page 342
9.14 Total Internal Reflection ......Page 348
9.15 Optical Coatings ......Page 351
9.16 Reflection At A Metallic Boundary ......Page 354
9.17 Wave-guides ......Page 355
9.18 Exercises ......Page 360
10.2 The Relativity Principle ......Page 363
10.3 The Lorentz Transformation ......Page 364
10.4 Transformation Of Velocities ......Page 369
10.5 Tensors ......Page 371
10.6 Physical Significance Of Tensors ......Page 376
10.7 Space-time ......Page 377
10.8 Proper Time ......Page 382
10.9 4-velocity And 4-acceleration ......Page 383
10.10 The Current Density 4-vector ......Page 384
10.12 Gauge Invariance ......Page 386
10.13 Retarded Potentials ......Page 387
10.14 Tensors And Pseudo-tensors ......Page 389
10.15 The Electromagnetic Field Tensor ......Page 393
10.16 The Dual Electromagnetic Field Tensor ......Page 396
10.17 Transformation Of Fields ......Page 398
10.18 Potential Due To A Moving Charge ......Page 399
10.19 Field Due To A Moving Charge ......Page 400
10.20 Relativistic Particle Dynamics ......Page 403
10.21 Force On A Moving Charge ......Page 405
10.22 The Electromagnetic Energy Tensor ......Page 406
10.23 Accelerated Charges ......Page 409
10.24 The Larmor Formula ......Page 414
10.25 Radiation Losses ......Page 418
10.26 Angular Distribution Of Radiation ......Page 419
10.27 Synchrotron Radiation ......Page 421
10.28 Exercises ......Page 424
Physical Constants ......Page 429
Useful Vector Identities ......Page 431
Gaussian Units ......Page 433
Further Reading ......Page 437
