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# Classical Electromagnetism in a NutshellAnupam Garg

 TABLE OF CONTENTS:Preface xvList of symbols xxiSuggestions for using this book xxxiChapter 1 Introduction 11The field concept 12The equations of electrodynamics 23A lightspeed survey of electromagnetic phenomena 74SI versus Gaussian 10Chapter 2 Review of mathematical concepts 185Vector algebra 186Derivatives of vector fields 257Integration of vector fields 308The theorems of Stokes and Gauss 329Fourier transforms, delta functions, and distributions 3710Rotational transformations of vectors and tensors 4511Orthogonal curvilinear coordinates 51Chapter 3 Electrostatics in vacuum 5512Coulomb's law 5513The electrostatic potential 5714Electrostatic energy 5815Differential form of Coulomb's law 6316Uniqueness theorem of electrostatics 6517Solving Poisson's equation: a few examples 6818Energy in the electric field 7119The multipole expansion 7320Charge distributions in external fields 80Chapter 4 Magnetostatics in vacuum 8221Sources of magnetic field 8222The law of Biot and Savart 8923Differential equations of magnetostatics; Ampere's law 9324The vector potential 10125Gauge invariance 10526∇ B and ∇×B for a point dipole 10827Magnetic multipoles 112Chapter 5 Induced electromagnetic fields 11428Induction 11429Energy in the magnetic field--Feynman's argument 11730Energy in the magnetic field--standard argument 12031Inductance 12132The Ampere-Maxwell law 12533Potentials for time-dependent fields 128Chapter 6 Symmetries and conservation laws 13234Discrete symmetries of the laws of electromagnetism 13235Energy flow and the Poynting vector 13736Momentum conservation 14037Angular momentum conservation∗ 14438Relativity at low speeds 14839Electromagnetic mass∗ 150Chapter 7 Electromagnetic waves 15240The wave equation for E and B 15241Plane electromagnetic waves 15442Monochromatic plane waves and polarization 15643Nonplane monochromatic waves; geometrical optics∗ 16044Electromagnetic fields in a laser beam∗ 16545Partially polarized (quasimonochromatic) light∗ 16846Oscillator representation of electromagnetic waves 17147Angular momentum of the free electromagnetic field∗ 174Chapter 8 Interference phenomena 17848Interference and diffraction 17849Fresnel diffraction 18250Fraunhofer diffraction 18651Partially coherent light 18752The Hanbury-Brown and Twiss effect; intensity interferometry∗ 19153The Pancharatnam phase∗ 195Chapter 9 The electromagnetic field of moving charges 20054Green's function for the wave equation 20055Fields of a uniformly moving charge 20456Potentials of an arbitrarily moving charge--the Lienard-Wiechert solutions 20757Electromagnetic fields of an arbitrarily moving charge 21058Radiation from accelerated charges: qualitative discussion 214Chapter 10 Radiation from localized sources 21759General frequency-domain formulas for fields 21760Far-zone fields 21961Power radiated 22362The long-wavelength electric dipole approximation 22763Higher multipoles∗ 22964Antennas 23365Near-zone fields 23766Angular momentum radiated∗ 23967Radiation reaction 241Chapter 11 Motion of charges and moments in external fields 24568The Lorentz force law 24569Motion in a static uniform electric field 24670Motion in a static uniform magnetic field 24871Motion in crossed E and B fields; E < B 25172Motion in a time-dependent magnetic field; the betatron 25573Motion in a quasiuniform static magnetic field--guiding center drift∗ 25774Motion in a slowly varying magnetic field--the first adiabatic invariant∗ 26175The classical gyromagnetic ratio and Larmor's theorem 26476Precession of moments in time-dependent magnetic fields∗ 268Chapter 12 Action formulation of electromagnetism 27377Charged particle in given field 27378The free field 27679The interacting system of fields and charges 27980Gauge invariance and charge conservation 283Chapter 13 Electromagnetic fields in material media 28581Macroscopic fields 28682The macroscopic charge density and the polarization 28983The macroscopic current density and the magnetization 29384Constitutive relations 29785Energy conservation 300Chapter 14 Electrostatics around conductors 30286Electric fields inside conductors, and at conductor surfaces 30387Theorems for electrostatic fields 30688Electrostatic energy with conductors; capacitance 30889The method of images 31390Separation of variables and expansions in basis sets 32091The variational method∗ 32992The relaxation method 33493Microscopic electrostatic field at metal surfaces; work function andcontact potential∗ 33915Electrostatics of dielectrics 34494The dielectric constant 34495Boundary value problems for linear isotropic dielectrics 34796Depolarization 35097Thermodynamic potentials for dielectrics 35498Force on small dielectric bodies 36099Models of the dielectric constant 361Chapter 16 Magnetostatics in matter 370100 Magnetic permeability and susceptibility 370101Thermodynamic relations for magnetic materials 371102Diamagnetism 375103Paramagnetism 378104The exchange interaction; ferromagnetism 378105Free energy of ferromagnets 382106Ferromagnetic domain walls∗ 391107Hysteresis in ferromagnets 394108Demagnetization 397109Superconductors∗ 399Chapter 17 Ohm's law, emf, and electrical circuits 404110Ohm's law 405111Electric fields around current-carrying conductors--a solvable example∗ 407112van der Pauw's method∗ 409113The Van de Graaff generator 412114The thermopile 413115The battery 414116Lumped circuits 417117The telegrapher's equation∗ 422118The ac generator 424Chapter 18 Frequency-dependent response of materials 427119The frequency-dependent conductivity 427120The dielectric function and electric propensity 429121General properties of the ac conductivity∗ 431122Electromagnetic energy in material media∗ 435123Drude-Lorentz model of the dielectric response 437124Frequency dependence of the magnetic response∗ 44119Quasistatic phenomena in conductors 443125Quasistatic fields 443126Variable magnetic field: eddy currents and the skin effect in a planar geometry 445127Variable magnetic field: eddy currents and the skin effect in finite bodies∗ 450128Variable electric field, electrostatic regime 455129Variable electric field, skin-effect regime 457130Eddy currents in thin sheets, Maxwell's receding image construction, and maglev∗ 459131Motion of extended conductors in magnetic fields∗ 465132The dynamo∗ 467Chapter 20 Electromagnetic waves in insulators 470133General properties of EM waves in media 470134Wave propagation velocities 472135Reflection and refraction at a flat interface (general case) 475136More reflection and refraction (both media transparent and nonmagnetic) 479137Reflection from a nonmagnetic opaque medium∗ 483Chapter 21 Electromagnetic waves in and near conductors 487138Plasma oscillations 487139Dispersion of plasma waves∗ 488140Transverse EM waves in conductors 490141Reflection of light from a metal 492142Surface plasmons∗ 493143Waveguides 496144Resonant cavities 502Chapter 22 Scattering of electromagnetic radiation 505145Scattering terminology 505146Scattering by free electrons 506147Scattering by bound electrons 508148Scattering by small particles 510149Scattering by dilute gases, and why the sky is blue 512150Raman scattering 515151Scattering by liquids and dense gases∗ 516Chapter 23 Formalism of special relativity 524152Review of basic concepts 524153Four-vectors 532154Velocity, momentum, and acceleration four-vectors 537155Four-tensors 540156Vector fields and their derivatives in space--time 543157Integration of vector fields∗ 544158Accelerated observers∗ 548Chapter 24 Special relativity and electromagnetism 553159Four-current and charge conservation 553160The four-potential 556161The electromagnetic field tensor 556162Covariant form of the laws of electromagnetism 559163The stress--energy tensor 561164Energy--momentum conservation in special relativity 564165Angular momentum and spin∗ 565166Observer-dependent properties of light 567167Motion of charge in an electromagnetic plane wave∗ 572168Thomas precession∗ 576Chapter 25 Radiation from relativistic sources 581169Total power radiated 581170Angular distribution of power 584171Synchrotron radiation--qualitative discussion 588172Full spectral, angular, and polarization distribution of synchrotronradiation∗ 589173Spectral distribution of synchrotron radiation∗ 592174Angular distribution and polarization of synchrotron radiation∗ 595175Undulators and wigglers∗ 597Appendix A: Spherical harmonics 605Appendix B: Bessel functions 617Appendix C: Time averages of bilinear quantities in electrodynamics 625Appendix D: Caustics 627Appendix E: Airy functions 633Appendix F: Power spectrum of a random function 637Appendix G: Motion in the earth's magnetic field--the Stormer problem 643Appendix H: Alternative proof of Maxwell's receding image construction 651Bibliography 655Index 659Return to Book DescriptionFile created: 4/21/2017 Questions and comments to: webmaster@press.princeton.eduPrinceton University Press