Classical electromagnetism

__Classical Electromagnetism__ is built for readers who want to learn about the theory of electricity and magnetism. The text starts in historical order, moving through Coulomb's law and the magnetic law of Biot-Savart to Maxwell's unification of physics. Author Jerrold Franklin carefully develops each stage of the theory without oversimplifying. Throughout, he demonstrates how key principles can be defined on a more fundamental basis to enhance reader understanding. The mathematics and physics are unified so that readers learn the material in the context of real physics applications. Foundations of Electrostatics, Further Development of Electrostatics, Methods of Solution in Electrostatics, Spherical and Cylindrical Coordinates, Green's Functions, Electrostatics in Matter, Magnetostatics, Magnetization and Ferromagnetism, Time Varying Fields, Maxwell's Equations, Electromagnetic Plane Waves, Wave Guides and Cavities, Electromagnetic Radiation and Scattering, Special Relativity, The Electrodynamics of Moving Bodies For all readers interested in learning about the theory of electricity and magnetism. Front cover......Page 1 Title page......Page 3 Date-line......Page 4 Preface......Page 5 Contents......Page 7 1.1 Coulomb's Law......Page 17 1.2 The Electric Field......Page 20 1.3 Electric Potential......Page 22 1.3.1 Potential Gradient......Page 25 1.4 Gauss's Law......Page 28 1.4.1 Examples of Gauss's Law......Page 30 1.4.2 Spherically Symmetric Charge (and Mass) Distributions......Page 32 1.5 The Variation of $\vec{E}$......Page 35 1.5.1 Divergence......Page 36 1.5.2 Dirac Delta Function......Page 39 1.5.3 Curl......Page 41 1.6 Summary of Vector Calculus......Page 45 1.6.1 Operation by $\nabla$......Page 46 1.6.2 Integral Theorems......Page 48 1.7 Problems......Page 50 2.1 Conductors......Page 53 2.2 Electrostatic Energy......Page 56 2.3.1 Fields Due to Dipoles......Page 62 2.3.2 Forces and Torques on Dipoles......Page 64 2.3.3 Dipole Singularity at $\vec{r}=0$......Page 67 2.4 Electric Quadrupole Moment......Page 69 2.4.1 Dyadics......Page 70 2.4.2 Quadrupole Dyadic......Page 71 2.5 Problems......Page 76 3.1 Differential Form of Electrostatics......Page 79 3.1.1 Uniqueness Theorem......Page 80 3.2.1 Infinite Grounded Plane......Page 84 3.2.2 Conducting Sphere......Page 86 3.3.1 Cartesian Coordinates......Page 89 3.3.2 Fourier Series......Page 92 3.3.3 Fourier Sine Integrals......Page 95 3.4 Surface Green's Function......Page 98 3.5 Problems......Page 102 4.1 General Orthogonal Coordinate Systems......Page 105 4.2 Spherical Coordinates......Page 107 4.2.1 Separation of Variables in Spherical Coordinates......Page 109 4.2.2 Azimuthal Symmetry, Legendre Polynomials......Page 110 4.2.3 Boundary Value Problems with Azimuthal Symmetry......Page 116 4.2.4 Multipole Expansion......Page 120 4.2.5 Spherical Harmonics......Page 125 4.3 Cylindrical Coordinates......Page 133 4.3.1 Separation of Variables in Cylindrical Coordinates......Page 134 4.3.2 Two-Dimensional Cases (Polar Coordinates)......Page 135 4.3.3 Three-Dimensional Cases, Bessel Functions......Page 139 4.4 Problems......Page 148 5.2 Surface Boundary Conditions......Page 151 5.3 Green's Function Solution of Poisson's Equation......Page 152 5.5 Symmetry of the Green's Function......Page 153 5.6 Green's Reciprocity Theorem......Page 154 5.7 Green's Functions for Specific Cases......Page 156 5.8.1 Construction of the Green's Function from Eigenfunctions......Page 157 5.8.2 Reduction to a One-Dimensional Green's Function......Page 158 5.9 Problems......Page 163 6.1 Polarization......Page 165 6.2 The Displacement Vector $\vec{D}$......Page 166 6.3 Uniqueness Theorem with Polarization......Page 169 6.4.1 Boundary Conditions on $\vec{D}$, $\vec{E}$, and $\phi$......Page 170 6.4.2 Needle or Lamina......Page 172 6.4.3 Capacitance......Page 173 6.4.4 Images......Page 174 6.4.5 Dielectric Sphere in a Uniform Electric Field......Page 176 6.4.6 Dielectric Sphere and Point Charge......Page 177 6.5 Induced Dipole-Dipole Force, the Van der Waals Force......Page 179 6.6.1 Microscopic Electric Field......Page 180 6.6.2 Clausius-Mossotti Relation......Page 182 6.6.3 Models for Molecular Polarization......Page 183 6.7 Electrostatic Energy in Dielectrics......Page 185 6.8 Forces on Dielectrics......Page 186 6.9.1 Current Density and Continuity Equation......Page 190 6.9.2 Ohm's Law......Page 191 6.9.3 Relaxation Constant......Page 192 6.9.4 Effective Resistance......Page 193 6.10 Problems......Page 195 7.1 Magnetic Forces Between Electric Currents......Page 197 7.2 Units of Electricity and Magnetism......Page 199 7.3 The Magnetic Field $\vec{B}$......Page 202 7.4 Applications of the Biot-Savart Law......Page 203 7.5 Magnetic Effects on Charged Particles......Page 206 7.6.1 Volume Current Density $\vec{j}$......Page 209 7.6.2 Surface Current Density $\vec{K}$......Page 210 7.6.3 Magnetic Effects of Moving Charges......Page 211 7.7 Differential Form of Magnetostatics......Page 212 7.8.1 Gauge Transformation......Page 214 7.8.2 Poisson's Equation for $\vec{A}$......Page 215 7.9 Ampere's Circuital Law......Page 216 7.10 Magnetic Scalar Potential......Page 219 7.10.1 Magnetic Field of a Current Loop......Page 221 7.11.2 Magnetic Dipole Scalar Potential of a Current Loop......Page 225 7.11.3 Magnetic Dipole Vector Potential of a Current Loop......Page 226 7.11.4 Magnetic Dipole Moment of a Current Density......Page 228 7.11.5 Gyromagnetic Ratio......Page 229 7.11.6 The Zeeman Effect......Page 230 7.11.7 Magnetic Dipole Force, Torque, and Energy......Page 231 7.11.8 Fermi-Breit Interaction between Magnetic Dipoles......Page 234 7.12 Problems......Page 235 8.1 Magnetic Field Including Magnetization......Page 239 8.2 The $\vec{H}$ Field, Susceptibility, and Permeability......Page 241 8.3 Comparison of Magnetostatics and Electrostatics......Page 244 8.5 Hysteresis......Page 245 8.6 Permanent Magnetism......Page 247 8.7 Magnetization of a Ferromagnetic Sphere......Page 248 8.8 The Use of the H Field for a Permanent Magnet......Page 249 8.9 Bar Magnet......Page 250 8.10 Magnetic Images......Page 254 8.11 Problems......Page 255 9.1 Faraday's Law......Page 257 9.2 Inductance......Page 261 9.3 Displacement Current, Maxwell's Equations......Page 263 9.4 Electromagnetic Energy......Page 264 9.4.1 Potential Energy in Matter......Page 265 9.5 Magnetic Energy......Page 267 9.6 Electromagnetic Momentum, Maxwell Stress Tensor......Page 269 9.6.1 Momentum in the Polarization and Magnetization Fields......Page 272 9.7 Application of the Stress Tensor......Page 274 9.8 Magnetic Monopoles......Page 275 9.8.1 Dirac Charge Quantization......Page 276 9.9 Problems......Page 278 10.1 Electromagnetic Waves from Maxwell's Equations......Page 281 10.2 Energy and Momentum in an Electromagnetic Wave......Page 283 10.2.1 Radiation Pressure......Page 285 10.3.1 Polarized Light......Page 286 10.3.2 Circular Basis for Polarization......Page 287 10.3.3 Birefringence......Page 289 10.3.4 Unpolarized Light......Page 291 10.4 Reflection and Refraction at a Planar Interface......Page 292 10.4.1 Snell'sLaw......Page 293 10.4.2 Perpendicular Polarization......Page 294 10.4.3 Parallel Polarization......Page 296 10.4.5 Polarization by Reflection......Page 297 10.4.6 Total Internal Reflection......Page 299 10.4.7 Nonreflective Coating......Page 301 10.5 Problems......Page 303 11.1 Electromagnetic Waves in a Conducting Medium......Page 306 11.1.1 Poor Conductor......Page 308 11.2.1 Perfect Conductor......Page 309 11.2.2 Radiation Pressure......Page 310 11.2.3 Interface with a Good Conductor......Page 311 11.3.1 Molecular Model for Permittivity......Page 314 11.3.2 Dispersion and Absorption......Page 315 11.3.3 Conduction Electrons......Page 316 11.4 Causal Relation between $\vec{D}$ and $\vec{E}$......Page 317 11.5 Wave Packets......Page 320 11.5.1 Natural Line Width......Page 322 11.6.1 Group Velocity and Phase Velocity......Page 323 11.6.2 Spread of a Wave Packet......Page 325 11.6.3 No Electromagnetic Wave Travels Faster Than $c$......Page 326 11.7 Problems......Page 329 12.1 Cylindrical Wave Guides......Page 331 12.1.1 Phase and Group Velocities in a Wave Guide......Page 332 12.2 Eigenmodes in a Waveguide......Page 333 12.2.1 TEM Waves......Page 334 12.2.3 TE Waves......Page 336 12.2.4 Summary of TM and TE Modes......Page 337 12.2.5 Rectangular Wave Guides......Page 338 12.2.6 Circular Wave Guides......Page 340 12.3.1 Power Transmitted......Page 341 12.3.2 Losses and Attenuation......Page 343 12.4.1 Resonant Modes of a Cavity......Page 344 12.4.3 Circular Cylindrical Cavity......Page 346 12.4.4 Electromagnetic Energy in a Cavity......Page 347 12.4.5 Power Loss, Quality Factor......Page 349 12.5 Problems......Page 351 13.1 Wave Equation with Sources......Page 353 13.2 The Lorentz Gauge......Page 354 13.3 Retarded Solution of the Wave Equation......Page 355 13.4 Radiation Solution of the Wave Equation......Page 358 13.5 Center Fed Linear Antenna......Page 361 13.6 Electric Dipole Radiation......Page 364 13.7 Radiation by Atoms......Page 367 13.8 Larmor Formula for Radiation by an Accelerating Charge......Page 368 13.9 Magnetic Dipole Radiation......Page 371 13.10 Electric Quadrupole Radiation......Page 372 13.11.1 Electric Dipole Scattering......Page 376 13.11.2 Scattering by a Conducting Sphere, Magnetic Dipole Scattering......Page 379 13.12 Problems......Page 381 14.1 The Need for Relativity......Page 384 14.2 Mathematical Basis of Special Relativity, the Lorentz Transformation......Page 387 14.3.1 Relativistic Addition of Velocities......Page 390 14.3.2 Lorentz Contraction......Page 392 14.3.3 Time Dilation......Page 393 14.4 Mathematics of the Lorentz Transformation......Page 394 14.4.1 Three-Dimensional Rotations......Page 395 14.4.2 Lorentz Four-Vectors and Scalar Invariants......Page 398 14.5 Relativistic Space-Time......Page 402 14.5.1 The Light Cone......Page 403 14.5.2 Proper Time......Page 404 14.6.1 Four-Velocity......Page 406 14.6.2 Energy-Momentum Four-Vector......Page 407 14.6.3 $E = mc^2$......Page 408 14.7 Doppler Shift and Stellar Aberration......Page 409 14.8 Natural Relativistic Units, No More $c$......Page 411 14.9 Relativistic "Center of Mass"......Page 412 14.10.1 Charge-Current Four-Vector $j^\mu$......Page 414 14.10.2 Lorentz Invariance of Charge......Page 415 14.10.3 The Four-Potential $A^\mu$......Page 416 14.10.4 The Electromagnetic Field Tensor $F^\mu\nu$......Page 417 14.11 Problems......Page 420 15.1.1 Covariant Extension of $\vec{F} = m\vec{a}$......Page 423 15.1.2 Motion in a Magnetic Field......Page 424 15.1.3 Linear Accelerator......Page 425 15.2.1 Nonrelativistic Lagrangian......Page 426 15.2.2 Relativistic Lagrangian......Page 428 15.2.3 Hamiltonian for Electrodynamics......Page 430 15.3 Fields of a Charge Moving with Constant Velocity......Page 431 15.3.1 Energy Loss of a Moving Charge......Page 433 15.3.2 Interaction between Moving Charges......Page 435 15.4.1 Covariant Solution of the Wave Equation......Page 437 15.4.2 Lienard-Wiechert Potentials and Fields of a Moving Charge......Page 440 15.4.3 Constant Velocity Fields......Page 443 15.5 Electromagnetic Radiation by a Moving Charge......Page 444 15.5.1 Radiation with Acceleration Parallel to Velocity......Page 445 15.5.2 Radiation with Acceleration Perpendicular to Velocity......Page 447 15.5.3 Radiation from a Circular Orbit......Page 449 15.5.4 Relativistic Larmor formula......Page 452 15.6 Problems......Page 453 16.1 Looking Back......Page 455 16.2 Electromagnetism as a Gauge Theory......Page 457 16.3 Local Gauge Invariance as the Grand Unifier of Interactions......Page 460 16.4 Classical Electromagnetism and Quantum Electrodynamics......Page 462 16.5 Natural Units......Page 464 16.6 $\alpha$......Page 467 A Conversion of Units......Page 471 B Derivatives of the Retarded Time......Page 473 Recommended Reading......Page 475 Index......Page 477 Back cover......Page 486 {\rtf1\mac\ansicpg10000\cocoartf102 {\fonttbl\f0\fmodern\fcharset77 Courier;} 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The text starts in historical order, moving through Coulomb's law and the magnetic law of Biot-Savart to Maxwell's unification of physics. Author Jerrold Franklin carefully develops each stage of the theory without oversimplifying. Throughout, he demonstrates how key principles can be defined on a more fundamental basis to enhance reader understanding. The mathematics and physics are unified so that readers learn the material in the context of real physics applications. Foundations of Electrostatics, Further Development of Electrostatics, Methods of Solution in Electrostatics, Spherical and Cylindrical Coordinates, Green's Functions, Electrostatics in Matter, Magnetostatics, Magnetization and Ferromagnetism, Time Varying Fields, Maxwell's Equations, Electromagnetic Plane Waves, Wave Guides and Cavities, Electromagnetic Radiation and Scattering, Special Relativity, The Electrodynamics of Moving Bodies For all readers interested in learning about the theory of electricity and magnetism.}

classical Electromagnetism Is Built For Readers Who Want To Learn About The Theory Of Electricity And Magnetism. The Text Starts In Historical Order, Moving Through Coulomb's Law And The Magnetic Law Of Biot-savart To Maxwell's Unification Of Physics. Author Jerrold Franklin Carefully Develops Each Stage Of The Theory Without Oversimplifying. Throughout, He Demonstrates How Key Principles Can Be Defined On A More Fundamental Basis To Enhance Reader Understanding. The Mathematics And Physics Are Unified So That Readers Learn The Material In The Context Of Real Physics Applications.

foundations Of Electrostatics, Further Development Of Electrostatics, Methods Of Solution In Electrostatics, Spherical And Cylindrical Coordinates, Green's Functions, Electrostatics In Matter, Magnetostatics, Magnetization And Ferromagnetism, Time Varying Fields, Maxwell's Equations, Electromagnetic Plane Waves, Wave Guides And Cavities, Electromagnetic Radiation And Scattering, Special Relativity, The Electrodynamics Of Moving Bodies

for All Readers Interested In Learning About The Theory Of Electricity And Magnetism.