Classical electromagnetism /
Franklin, Jerrold.
Classical electromagnetism / by Jerrold Franklin. - San Francisco : Pearson Addison-Wesley, c2012. - xiv, 469 p. : ill. ; 25 cm.
Includes bibliographical references (p. 459) and index.
*Contents
ContentsContents
chapter1Foundations of Electrostatics1
section1.1Coulomb's Law1
section1.2The Electric Field4
section1.3Electric Potential6
subsection1.3.1Potential Gradient9
section1.4Gauss's Law12
subsection1.4.1Examples of Gauss's Law14
subsubsectionPoint Charge14
subsection1.4.2Spherically Symmetric Charge (and Mass)Distributions16
subsubsectionLine Charge17
subsubsectionInfinite Plane18
section1.5The Variation of E19
subsection1.5.1Divergence20
subsection1.5.2Dirac Delta Function23
subsection1.5.3Curl25
section1.6Summary of Vector Calculus29
subsection1.6.1Operation by 30
subsection1.6.2Integral Theorems32
section1.7Problems34
chapter2Further Development of Electrostatics37
section2.1Conductors37
section2.2Electrostatic Energy40
section2.3Electric Dipoles46
subsection2.3.1Fields Due to Dipoles46
subsection2.3.2Forces and Torques on Dipoles48
subsection2.3.3Dipole Singularity at 51
section2.4Electric Quadrupole Moment53
subsection2.4.1Dyadics54
subsection2.4.2Quadrupole dyadic55
subsection2.4.3Multipole Expansion60
section2.5Problems60
chapter3Methods of Solution in Electrostatics63
section3.1Differential Form of Electrostatics63
subsection3.1.1Uniqueness Theorem64
paragraphDirichlet Boundary Condition:66
paragraphNeumann Boundary Condition:66
paragraphUniqueness Theorem of Electrostatics:66
paragraphUniqueness Theorem of Electrostatics in the Presence of Conductors:67
paragraphUniqueness Theorem for the Electrostatic Potential:67
section3.2Images68
subsection3.2.1Infinite Grounded Plane68
subsection3.2.2Conducting Sphere70
section3.3Separation of Variables for Laplace's Equation73
subsection3.3.1Cartesian Coordinates73
subsection3.3.2Fourier Series76
subsection3.3.3Fourier Sine Integrals79
section3.4Surface Green's Function82
section3.5Problems86
chapter4Spherical and Cylindrical Coordinates89
section4.1General Orthogonal Coordinate Systems89
section4.2Spherical Coordinates91
subsection4.2.1Separation of Variables in Spherical Coordinates93
subsection4.2.2Azimuthal Symmetry, Legendre Polynomials94
paragraphNormalization97
paragraphOrthogonality97
paragraphGenerating Function99
paragraphRecursion Relation100
paragraph, , 100
subsection4.2.3Boundary Value Problems with AzimuthalSymmetry100
subsubsectionPotential Outside a Sphere101
subsection4.2.4Multipole Expansion104
subsubsectionUniformly Charged Needle105
subsubsectionMutipole Expansion for a Point Charge, Derivation of the Generating Function for Legendre Polynomials107
subsubsectionPoint Charge and Grounded Sphere108
subsubsectionMultipole Moment by Integration108
subsection4.2.5Spherical Harmonics109
subsubsectionPotential Outside a Sphere112
subsubsectionMultipole Moments112
subsubsectionRotation of Axes113
subsubsectionAddition Theorem114
subsubsectionMultipole Moment by Integration115
section4.3Cylindrical Coordinates117
subsection4.3.1Separation of Variables in Cylindrical Coordinates118
subsection4.3.2Two-Dimensional Cases (Polar Coordinates)119
subsubsectionPotential Inside a Cylinder120
subsubsectionFourier Series120
subsubsectionIntersecting Grounded Planes121
subsection4.3.3Three-Dimensional Cases, Bessel Functions123
subsubsectionBessel Functions123
paragraphRecursion Relation126
paragraphDerivative Recursion Relation126
paragraphAsymptotic Forms126
subsubsectionPotential Inside a Cylinder127
subsubsectionModified Bessel Functions130
section4.4Problems132
chapter5Green's Functions135
section5.1Application of Green's Second Theorem135
section5.2Surface Boundary Conditions135
section5.3Green's Function Solution of Poisson's Equation136
section5.4Surface Green's Function137
section5.5Symmetry of the Green's Function137
section5.6Green's Reciprocity Theorem138
section5.7Green's Functions for Specific Cases140
subsubsectionPlane Surface140
subsubsectionSphere140
section5.8Constructing Green's Functions141
subsection5.8.1Construction of the Green's Function fromEigenfunctions141
subsection5.8.2Reduction to a One-Dimensional Green's Function142
subsubsectionRectangular Coordinates142
subsubsectionSpherical Coordinates146
section5.9Problems147
chapter6Electrostatics in Matter149
section6.1Polarization149
section6.2The Displacement Vector D150
section6.3Uniqueness Theorem with Polarization153
section6.4Boundary Value Problems with Polarization154
subsection6.4.1Boundary Conditions on D, E, and 154
subsection6.4.2Needle or Lamina156
subsection6.4.3Capacitance157
subsection6.4.4Images158
subsection6.4.5Dielectric Sphere in a Uniform Electric Field160
subsection6.4.6Dielectric Sphere and Point Charge161
section6.5Induced Dipole--Dipole Force, the Van der Waals Force163
section6.6Molecular Polarizability164
subsection6.6.1Microscopic Electric Field164
subsection6.6.2Clausius--Mossotti Relation166
subsection6.6.3Models for Molecular Polarization167
section6.7Electrostatic Energy in Dielectrics169
section6.8Forces on Dielectrics170
section6.9Steady State Currents174
subsection6.9.1Current Density and Continuity Equation174
subsection6.9.2Ohm's Law175
subsection6.9.3Relaxation Constant176
subsection6.9.4Effective Resistance177
section6.10Problems179
chapter7Magnetostatics181
section7.1Magnetic Forces Between Electric Currents181
section7.2Units of Electricity and Magnetism183
section7.3The Magnetic Field B186
section7.4Applications of the Biot--Savart Law187
section7.5Magnetic Effects on Charged Particles190
section7.6Magnetic Effects of Current Densities193
subsection7.6.1Volume Current Density j193
subsection7.6.2Surface Current Density K194
subsection7.6.3Magnetic Effects of Moving Charges?195
section7.7Differential Form of Magnetostatics196
section7.8The Vector Potential A198
subsection7.8.1Gauge Transformation198
subsection7.8.2Poisson's Equation for A199
section7.9Ampere's Circuital Law200
section7.10Magnetic Scalar Potential203
subsection7.10.1Magnetic Field of a Current Loop205
section7.11Magnetic Dipole Moment209
subsection7.11.1Magnetic Multipole Expansion209
subsection7.11.2Magnetic Dipole Scalar Potential of a Current Loop209
subsection7.11.3Magnetic Dipole Vector Potential of a Current Loop210
subsection7.11.4Magnetic Dipole Moment of a Current Density212
subsection7.11.5Gyromagnetic Ratio213
subsection7.11.6The Zeeman Effect214
subsection7.11.7Magnetic Dipole Force, Torque, and Energy215
subsection7.11.8Fermi--Breit Interaction between Magnetic Dipoles218
section7.12Problems219
chapter8Magnetization and Ferromagnetism223
section8.1Magnetic Field Including Magnetization223
section8.2The H Field, Susceptibility, and Permeability225
section8.3Comparison of Magnetostatics and Electrostatics228
section8.4Ferromagnetism229
section8.5Hysteresis229
section8.6Permanent Magnetism231
section8.7Magnetization of a Ferromagnetic Sphere232
section8.8The Use of the H Field for a Permanent Magnet233
section8.9Bar Magnet234
section8.10Magnetic Images238
section8.11Problems239
chapter9Time Varying Fields, Maxwell's Equations241
section9.1Faraday's Law241
section9.2Inductance245
section9.3Displacement Current, Maxwell's Equations247
section9.4Electromagnetic Energy248
subsection9.4.1Potential Energy in Matter249
section9.5Magnetic Energy251
section9.6Electromagnetic Momentum, Maxwell Stress Tensor253
subsection9.6.1Momentum in the Polarization and MagnetizationFields256
section9.7Application of the Stress Tensor258
section9.8Magnetic Monopoles259
subsection9.8.1Dirac Charge Quantization260
section9.9Problems262
chapter10Electromagnetic Plane Waves265
section10.1Electromagnetic Waves from Maxwell's Equations265
section10.2Energy and Momentum in an Electromagnetic Wave267
subsection10.2.1Radiation Pressure269
section10.3Polarization270
subsection10.3.1Polarized Light270
subsection10.3.2Circular Basis for Polarization271
subsection10.3.3Birefringence273
subsection10.3.4Unpolarized Light275
section10.4Reflection and Refraction at a Planar Interface276
subsection10.4.1Snell's Law277
subsection10.4.2Perpendicular Polarization278
subsection10.4.3Parallel Polarization280
subsection10.4.4Normal Incidence281
subsection10.4.5Polarization by Reflection281
subsection10.4.6Total Internal Reflection283
subsection10.4.7Nonreflective Coating285
section10.5Problems287
chapter11Electromagnetic Waves in Matter290
section11.1Electromagnetic Waves in a Conducting Medium290
subsection11.1.1Poor Conductor292
subsection11.1.2Good Conductor293
section11.2Electromagnetic Wave at the Interface of a Conductor293
subsection11.2.1Perfect Conductor293
subsection11.2.2Radiation Pressure294
subsection11.2.3Interface with a Good Conductor295
subsubsectionEnergy Absorption at the Interface297
subsubsectionEffective Surface Current298
section11.3Frequency Dependence of Permittivity298
subsection11.3.1Molecular Model for Permittivity298
subsection11.3.2Dispersion and Absorption299
subsection11.3.3Conduction Electrons300
section11.4Causal Relation between D and E301
section11.5Wave Packets304
subsection11.5.1Natural Line Width306
section11.6Wave Propagation in a Dispersive Medium307
subsection11.6.1Group Velocity and Phase Velocity307
subsection11.6.2Spread of a Wave Packet309
subsection11.6.3No Electromagnetic Wave Travels Faster Than 310
section11.7Problems313
chapter12Wave Guides and Cavities315
section12.1Cylindrical Wave Guides315
subsection12.1.1Phase and Group Velocities in a Wave Guide316
section12.2Eigenmodes in a Waveguide317
subsection12.2.1TEM Waves318
subsubsectionCoaxial Wave Guide319
subsubsectionParallel-Wire Wave Guide319
subsection12.2.2TM Waves320
subsection12.2.3TE Waves320
subsection12.2.4Summary of TM and TE Modes321
subsection12.2.5Rectangular Wave Guides322
subsubsectionTM Modes:322
subsubsectionTE Modes:323
subsection12.2.6Circular Wave Guides324
section12.3Power Transmission and Attenuation in Wave Guides325
subsection12.3.1Power Transmitted325
subsection12.3.2Losses and Attenuation327
section12.4Cylindrical Cavities328
subsection12.4.1Resonant Modes of a Cavity328
subsection12.4.2Rectangular Cavity330
subsection12.4.3Circular Cylindrical Cavity330
subsection12.4.4Electromagnetic Energy in a Cavity331
subsection12.4.5Power Loss, Quality Factor333
section12.5Problems335
chapter13Electromagnetic Radiation and Scattering337
section13.1Wave Equation with Sources337
section13.2The Lorentz Gauge338
section13.3Retarded Solution of the Wave Equation339
section13.4Radiation Solution of the Wave Equation342
section13.5Center Fed Linear Antenna345
section13.6Electric Dipole Radiation348
section13.7Radiation by Atoms351
section13.8Larmor Formula for Radiation by an Accelerating Charge352
section13.9Magnetic Dipole Radiation355
section13.10Electric Quadrupole Radiation356
section13.11Scattering of Electromagnetic Radiation360
subsection13.11.1Electric Dipole Scattering360
subsection13.11.2Scattering by a Conducting Sphere, Magnetic Dipole Scattering363
section13.12Problems365
chapter14Special Relativity368
section14.1The Need for Relativity368
section14.2Mathematical Basis of Special Relativity, the Lorentz Transformation371
section14.3Spatial and Temporal Consequences of the Lorentz Transformation374
subsection14.3.1Relativistic Addition of Velocities374
subsection14.3.2Lorentz Contraction376
subsection14.3.3Time Dilation377
section14.4Mathematics of the Lorentz Transformation378
subsection14.4.1Three-Dimensional Rotations379
subsection14.4.2Lorentz Four-Vectors and Scalar Invariants382
section14.5Relativistic Space-Time386
subsection14.5.1The Light Cone387
subsection14.5.2Proper Time388
section14.6Relativistic Kinematics390
subsection14.6.1Four-Velocity390
subsection14.6.2Energy-Momentum Four-Vector391
subsection14.6.3392
section14.7Doppler Shift and Stellar Aberration393
section14.8Natural Relativistic Units, No More c395
section14.9Relativistic ``Center of Mass''396
section14.10Covariant Electromagnetism398
subsection14.10.1Charge-Current Four-Vector 398
subsection14.10.2Lorentz Invariance of Charge399
subsection14.10.3The Four-Potential 400
subsection14.10.4The Electromagnetic Field Tensor 401
section14.11Problems404
chapter15The Electrodynamics of Moving Bodies407
section15.1Relativistic Electrodynamics407
subsection15.1.1Covariant Extension of 407
subsection15.1.2Motion in a Magnetic Field408
subsection15.1.3Linear Accelerator409
section15.2Lagrange's and Hamilton's Equations for Electrodynamics410
subsection15.2.1Nonrelativistic Lagrangian410
subsection15.2.2Relativistic Lagrangian412
subsection15.2.3Hamiltonian for Electrodynamics414
section15.3Fields of a Charge Moving with Constant Velocity415
subsection15.3.1Energy Loss of a Moving Charge417
subsection15.3.2Interaction between Moving Charges419
section15.4Electromagnetic Fields of a Moving Charge421
subsection15.4.1Covariant Solution of the Wave Equation421
subsection15.4.2Lienard--Wiechert Potentials and Fields of a Moving Charge424
subsection15.4.3Constant Velocity Fields427
section15.5Electromagnetic Radiation by a Moving Charge428
subsection15.5.1Radiation with Acceleration Parallel to Velocity429
subsection15.5.2Radiation with Acceleration Perpendicular to Velocity431
subsection15.5.3Radiation from a Circular Orbit433
subsection15.5.4Relativistic Larmor formula436
section15.6Problems437
chapter16Classical Electromagnetism in a Quantum World439
section16.1Looking Back439
section16.2Electromagnetism as a Gauge Theory441
section16.3Local Gauge Invariance as the Grand Unifier of Interactions444
section16.4Classical Electromagnetism and Quantum Electrodynamics446
section16.5Natural Units448
section16.6451
chapterAConversion of Units457
chapterBDerivatives of the Retarded Time459
chapterRecommended Reading461
chapterIndex463
9788131709740 (pbk)
2004030193
Electromagnetism--Textbooks.
537 / FRA-C 2012 2005
Classical electromagnetism / by Jerrold Franklin. - San Francisco : Pearson Addison-Wesley, c2012. - xiv, 469 p. : ill. ; 25 cm.
Includes bibliographical references (p. 459) and index.
*Contents
ContentsContents
chapter1Foundations of Electrostatics1
section1.1Coulomb's Law1
section1.2The Electric Field4
section1.3Electric Potential6
subsection1.3.1Potential Gradient9
section1.4Gauss's Law12
subsection1.4.1Examples of Gauss's Law14
subsubsectionPoint Charge14
subsection1.4.2Spherically Symmetric Charge (and Mass)Distributions16
subsubsectionLine Charge17
subsubsectionInfinite Plane18
section1.5The Variation of E19
subsection1.5.1Divergence20
subsection1.5.2Dirac Delta Function23
subsection1.5.3Curl25
section1.6Summary of Vector Calculus29
subsection1.6.1Operation by 30
subsection1.6.2Integral Theorems32
section1.7Problems34
chapter2Further Development of Electrostatics37
section2.1Conductors37
section2.2Electrostatic Energy40
section2.3Electric Dipoles46
subsection2.3.1Fields Due to Dipoles46
subsection2.3.2Forces and Torques on Dipoles48
subsection2.3.3Dipole Singularity at 51
section2.4Electric Quadrupole Moment53
subsection2.4.1Dyadics54
subsection2.4.2Quadrupole dyadic55
subsection2.4.3Multipole Expansion60
section2.5Problems60
chapter3Methods of Solution in Electrostatics63
section3.1Differential Form of Electrostatics63
subsection3.1.1Uniqueness Theorem64
paragraphDirichlet Boundary Condition:66
paragraphNeumann Boundary Condition:66
paragraphUniqueness Theorem of Electrostatics:66
paragraphUniqueness Theorem of Electrostatics in the Presence of Conductors:67
paragraphUniqueness Theorem for the Electrostatic Potential:67
section3.2Images68
subsection3.2.1Infinite Grounded Plane68
subsection3.2.2Conducting Sphere70
section3.3Separation of Variables for Laplace's Equation73
subsection3.3.1Cartesian Coordinates73
subsection3.3.2Fourier Series76
subsection3.3.3Fourier Sine Integrals79
section3.4Surface Green's Function82
section3.5Problems86
chapter4Spherical and Cylindrical Coordinates89
section4.1General Orthogonal Coordinate Systems89
section4.2Spherical Coordinates91
subsection4.2.1Separation of Variables in Spherical Coordinates93
subsection4.2.2Azimuthal Symmetry, Legendre Polynomials94
paragraphNormalization97
paragraphOrthogonality97
paragraphGenerating Function99
paragraphRecursion Relation100
paragraph, , 100
subsection4.2.3Boundary Value Problems with AzimuthalSymmetry100
subsubsectionPotential Outside a Sphere101
subsection4.2.4Multipole Expansion104
subsubsectionUniformly Charged Needle105
subsubsectionMutipole Expansion for a Point Charge, Derivation of the Generating Function for Legendre Polynomials107
subsubsectionPoint Charge and Grounded Sphere108
subsubsectionMultipole Moment by Integration108
subsection4.2.5Spherical Harmonics109
subsubsectionPotential Outside a Sphere112
subsubsectionMultipole Moments112
subsubsectionRotation of Axes113
subsubsectionAddition Theorem114
subsubsectionMultipole Moment by Integration115
section4.3Cylindrical Coordinates117
subsection4.3.1Separation of Variables in Cylindrical Coordinates118
subsection4.3.2Two-Dimensional Cases (Polar Coordinates)119
subsubsectionPotential Inside a Cylinder120
subsubsectionFourier Series120
subsubsectionIntersecting Grounded Planes121
subsection4.3.3Three-Dimensional Cases, Bessel Functions123
subsubsectionBessel Functions123
paragraphRecursion Relation126
paragraphDerivative Recursion Relation126
paragraphAsymptotic Forms126
subsubsectionPotential Inside a Cylinder127
subsubsectionModified Bessel Functions130
section4.4Problems132
chapter5Green's Functions135
section5.1Application of Green's Second Theorem135
section5.2Surface Boundary Conditions135
section5.3Green's Function Solution of Poisson's Equation136
section5.4Surface Green's Function137
section5.5Symmetry of the Green's Function137
section5.6Green's Reciprocity Theorem138
section5.7Green's Functions for Specific Cases140
subsubsectionPlane Surface140
subsubsectionSphere140
section5.8Constructing Green's Functions141
subsection5.8.1Construction of the Green's Function fromEigenfunctions141
subsection5.8.2Reduction to a One-Dimensional Green's Function142
subsubsectionRectangular Coordinates142
subsubsectionSpherical Coordinates146
section5.9Problems147
chapter6Electrostatics in Matter149
section6.1Polarization149
section6.2The Displacement Vector D150
section6.3Uniqueness Theorem with Polarization153
section6.4Boundary Value Problems with Polarization154
subsection6.4.1Boundary Conditions on D, E, and 154
subsection6.4.2Needle or Lamina156
subsection6.4.3Capacitance157
subsection6.4.4Images158
subsection6.4.5Dielectric Sphere in a Uniform Electric Field160
subsection6.4.6Dielectric Sphere and Point Charge161
section6.5Induced Dipole--Dipole Force, the Van der Waals Force163
section6.6Molecular Polarizability164
subsection6.6.1Microscopic Electric Field164
subsection6.6.2Clausius--Mossotti Relation166
subsection6.6.3Models for Molecular Polarization167
section6.7Electrostatic Energy in Dielectrics169
section6.8Forces on Dielectrics170
section6.9Steady State Currents174
subsection6.9.1Current Density and Continuity Equation174
subsection6.9.2Ohm's Law175
subsection6.9.3Relaxation Constant176
subsection6.9.4Effective Resistance177
section6.10Problems179
chapter7Magnetostatics181
section7.1Magnetic Forces Between Electric Currents181
section7.2Units of Electricity and Magnetism183
section7.3The Magnetic Field B186
section7.4Applications of the Biot--Savart Law187
section7.5Magnetic Effects on Charged Particles190
section7.6Magnetic Effects of Current Densities193
subsection7.6.1Volume Current Density j193
subsection7.6.2Surface Current Density K194
subsection7.6.3Magnetic Effects of Moving Charges?195
section7.7Differential Form of Magnetostatics196
section7.8The Vector Potential A198
subsection7.8.1Gauge Transformation198
subsection7.8.2Poisson's Equation for A199
section7.9Ampere's Circuital Law200
section7.10Magnetic Scalar Potential203
subsection7.10.1Magnetic Field of a Current Loop205
section7.11Magnetic Dipole Moment209
subsection7.11.1Magnetic Multipole Expansion209
subsection7.11.2Magnetic Dipole Scalar Potential of a Current Loop209
subsection7.11.3Magnetic Dipole Vector Potential of a Current Loop210
subsection7.11.4Magnetic Dipole Moment of a Current Density212
subsection7.11.5Gyromagnetic Ratio213
subsection7.11.6The Zeeman Effect214
subsection7.11.7Magnetic Dipole Force, Torque, and Energy215
subsection7.11.8Fermi--Breit Interaction between Magnetic Dipoles218
section7.12Problems219
chapter8Magnetization and Ferromagnetism223
section8.1Magnetic Field Including Magnetization223
section8.2The H Field, Susceptibility, and Permeability225
section8.3Comparison of Magnetostatics and Electrostatics228
section8.4Ferromagnetism229
section8.5Hysteresis229
section8.6Permanent Magnetism231
section8.7Magnetization of a Ferromagnetic Sphere232
section8.8The Use of the H Field for a Permanent Magnet233
section8.9Bar Magnet234
section8.10Magnetic Images238
section8.11Problems239
chapter9Time Varying Fields, Maxwell's Equations241
section9.1Faraday's Law241
section9.2Inductance245
section9.3Displacement Current, Maxwell's Equations247
section9.4Electromagnetic Energy248
subsection9.4.1Potential Energy in Matter249
section9.5Magnetic Energy251
section9.6Electromagnetic Momentum, Maxwell Stress Tensor253
subsection9.6.1Momentum in the Polarization and MagnetizationFields256
section9.7Application of the Stress Tensor258
section9.8Magnetic Monopoles259
subsection9.8.1Dirac Charge Quantization260
section9.9Problems262
chapter10Electromagnetic Plane Waves265
section10.1Electromagnetic Waves from Maxwell's Equations265
section10.2Energy and Momentum in an Electromagnetic Wave267
subsection10.2.1Radiation Pressure269
section10.3Polarization270
subsection10.3.1Polarized Light270
subsection10.3.2Circular Basis for Polarization271
subsection10.3.3Birefringence273
subsection10.3.4Unpolarized Light275
section10.4Reflection and Refraction at a Planar Interface276
subsection10.4.1Snell's Law277
subsection10.4.2Perpendicular Polarization278
subsection10.4.3Parallel Polarization280
subsection10.4.4Normal Incidence281
subsection10.4.5Polarization by Reflection281
subsection10.4.6Total Internal Reflection283
subsection10.4.7Nonreflective Coating285
section10.5Problems287
chapter11Electromagnetic Waves in Matter290
section11.1Electromagnetic Waves in a Conducting Medium290
subsection11.1.1Poor Conductor292
subsection11.1.2Good Conductor293
section11.2Electromagnetic Wave at the Interface of a Conductor293
subsection11.2.1Perfect Conductor293
subsection11.2.2Radiation Pressure294
subsection11.2.3Interface with a Good Conductor295
subsubsectionEnergy Absorption at the Interface297
subsubsectionEffective Surface Current298
section11.3Frequency Dependence of Permittivity298
subsection11.3.1Molecular Model for Permittivity298
subsection11.3.2Dispersion and Absorption299
subsection11.3.3Conduction Electrons300
section11.4Causal Relation between D and E301
section11.5Wave Packets304
subsection11.5.1Natural Line Width306
section11.6Wave Propagation in a Dispersive Medium307
subsection11.6.1Group Velocity and Phase Velocity307
subsection11.6.2Spread of a Wave Packet309
subsection11.6.3No Electromagnetic Wave Travels Faster Than 310
section11.7Problems313
chapter12Wave Guides and Cavities315
section12.1Cylindrical Wave Guides315
subsection12.1.1Phase and Group Velocities in a Wave Guide316
section12.2Eigenmodes in a Waveguide317
subsection12.2.1TEM Waves318
subsubsectionCoaxial Wave Guide319
subsubsectionParallel-Wire Wave Guide319
subsection12.2.2TM Waves320
subsection12.2.3TE Waves320
subsection12.2.4Summary of TM and TE Modes321
subsection12.2.5Rectangular Wave Guides322
subsubsectionTM Modes:322
subsubsectionTE Modes:323
subsection12.2.6Circular Wave Guides324
section12.3Power Transmission and Attenuation in Wave Guides325
subsection12.3.1Power Transmitted325
subsection12.3.2Losses and Attenuation327
section12.4Cylindrical Cavities328
subsection12.4.1Resonant Modes of a Cavity328
subsection12.4.2Rectangular Cavity330
subsection12.4.3Circular Cylindrical Cavity330
subsection12.4.4Electromagnetic Energy in a Cavity331
subsection12.4.5Power Loss, Quality Factor333
section12.5Problems335
chapter13Electromagnetic Radiation and Scattering337
section13.1Wave Equation with Sources337
section13.2The Lorentz Gauge338
section13.3Retarded Solution of the Wave Equation339
section13.4Radiation Solution of the Wave Equation342
section13.5Center Fed Linear Antenna345
section13.6Electric Dipole Radiation348
section13.7Radiation by Atoms351
section13.8Larmor Formula for Radiation by an Accelerating Charge352
section13.9Magnetic Dipole Radiation355
section13.10Electric Quadrupole Radiation356
section13.11Scattering of Electromagnetic Radiation360
subsection13.11.1Electric Dipole Scattering360
subsection13.11.2Scattering by a Conducting Sphere, Magnetic Dipole Scattering363
section13.12Problems365
chapter14Special Relativity368
section14.1The Need for Relativity368
section14.2Mathematical Basis of Special Relativity, the Lorentz Transformation371
section14.3Spatial and Temporal Consequences of the Lorentz Transformation374
subsection14.3.1Relativistic Addition of Velocities374
subsection14.3.2Lorentz Contraction376
subsection14.3.3Time Dilation377
section14.4Mathematics of the Lorentz Transformation378
subsection14.4.1Three-Dimensional Rotations379
subsection14.4.2Lorentz Four-Vectors and Scalar Invariants382
section14.5Relativistic Space-Time386
subsection14.5.1The Light Cone387
subsection14.5.2Proper Time388
section14.6Relativistic Kinematics390
subsection14.6.1Four-Velocity390
subsection14.6.2Energy-Momentum Four-Vector391
subsection14.6.3392
section14.7Doppler Shift and Stellar Aberration393
section14.8Natural Relativistic Units, No More c395
section14.9Relativistic ``Center of Mass''396
section14.10Covariant Electromagnetism398
subsection14.10.1Charge-Current Four-Vector 398
subsection14.10.2Lorentz Invariance of Charge399
subsection14.10.3The Four-Potential 400
subsection14.10.4The Electromagnetic Field Tensor 401
section14.11Problems404
chapter15The Electrodynamics of Moving Bodies407
section15.1Relativistic Electrodynamics407
subsection15.1.1Covariant Extension of 407
subsection15.1.2Motion in a Magnetic Field408
subsection15.1.3Linear Accelerator409
section15.2Lagrange's and Hamilton's Equations for Electrodynamics410
subsection15.2.1Nonrelativistic Lagrangian410
subsection15.2.2Relativistic Lagrangian412
subsection15.2.3Hamiltonian for Electrodynamics414
section15.3Fields of a Charge Moving with Constant Velocity415
subsection15.3.1Energy Loss of a Moving Charge417
subsection15.3.2Interaction between Moving Charges419
section15.4Electromagnetic Fields of a Moving Charge421
subsection15.4.1Covariant Solution of the Wave Equation421
subsection15.4.2Lienard--Wiechert Potentials and Fields of a Moving Charge424
subsection15.4.3Constant Velocity Fields427
section15.5Electromagnetic Radiation by a Moving Charge428
subsection15.5.1Radiation with Acceleration Parallel to Velocity429
subsection15.5.2Radiation with Acceleration Perpendicular to Velocity431
subsection15.5.3Radiation from a Circular Orbit433
subsection15.5.4Relativistic Larmor formula436
section15.6Problems437
chapter16Classical Electromagnetism in a Quantum World439
section16.1Looking Back439
section16.2Electromagnetism as a Gauge Theory441
section16.3Local Gauge Invariance as the Grand Unifier of Interactions444
section16.4Classical Electromagnetism and Quantum Electrodynamics446
section16.5Natural Units448
section16.6451
chapterAConversion of Units457
chapterBDerivatives of the Retarded Time459
chapterRecommended Reading461
chapterIndex463
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Electromagnetism--Textbooks.
537 / FRA-C 2012 2005