Classical Electrodynamics, 3rd Edition

by Jackson, John David

• ISBN13: 9780471309321
• ISBN10: 047130932X
• Edition: 3rd
• Format: Hardcover
• Copyright: 1998-08-14
• Publisher: Wiley

Summary

A revision of the defining book covering the physics and classical mathematics necessary to understand electromagnetic fields in materials and at surfaces and interfaces. The third edition has been revised to address the changes in emphasis and applications that have occurred in the past twenty years.

Author Biography

John David Jackson is the author of Classical Electrodynamics, 3rd Edition, published by Wiley.

Table of Contents

Introduction and Survey	1	(23)
1.1 Maxwell Equations in Vacuum, Fields, and Sources	2	(3)
1.2 Inverse Square Law, or the Mass of the Photon	5	(4)
1.3 Linear Superposition	9	(4)
1.4 Maxwell Equations in Macroscopic Media	13	(3)
1.5 Boundary Conditions at Interfaces Between Different Media	16	(3)
1.6 Some Remarks on Idealizations in Electromagnetism	19	(3)
References and Suggested Reading	22	(2)
Chapter 1 Introduction to Electrostatics	24	(33)
1.1 Coulomb's Law	24	(1)
1.2 Electric Field	24	(3)
1.3 Gauss's Law	27	(1)
1.4 Differential Form of Gauss's Law	28	(1)
1.5 Another Equation of Electrostatics and the Scalar Potential	29	(2)
1.6 Surface Distributions of Charges and Dipoles and Discontinuities in the Electric Field and Potential	31	(3)
1.7 Poisson and Laplace Equations	34	(1)
1.8 Green's Theorem	35	(2)
1.9 Uniqueness of the Solution with Dirichlet or Neumann Boundary Conditions	37	(1)
1.10 Formal Solution of Electrostatic Boundary-Value Problem with Green Function	38	(2)
1.11 Electrostatic Potential Energy and Energy Density; Capacitance	40	(3)
1.12 Variational Approach to the Solution of the Laplace and Poisson Equations	43	(4)
1.13 Relaxation Method for Two-Dimensional Electrostatic Problems	47	(3)
References and Suggested Reading	50	(1)
Problems	50	(7)
Chapter 2 Boundary-Value Problems in Electrostatics: I	57	(38)
2.1 Method of Images	57	(1)
2.2 Point Charge in the Presence of a Grounded Conducting Sphere	58	(2)
2.3 Point Charge in the Presence of a Charged, Insulated, Conducting Sphere	60	(1)
2.4 Point Charge Near a Conducting Sphere at Fixed Potential	61	(1)
2.5 Conducting Sphere in a Uniform Electric Field by Method of Images	62	(2)
2.6 Green Function for the Sphere; General Solution for the Potential	64	(1)
2.7 Conducting Sphere with Hemispheres at Different Potentials	65	(2)
2.8 Orthogonal Functions and Expansions	67	(3)
2.9 Separation of Variables; Laplace Equation in Rectangular Coordinates	70	(2)
2.10 A Two-Dimensional Potential Problem; Summation of Fourier Series	72	(3)
2.11 Fields and Charge Densities in Two-Dimensional Corners and Along Edges	75	(4)
2.12 Introduction to Finite Element Analysis For Electrostatics	79	(5)
References and Suggested Reading	84	(1)
Problems	85	(10)
Chapter 3 Boundary-Value Problems in Electrostatics: II	95	(50)
3.1 Laplace Equation in Spherical Coordinates	95	(1)
3.2 Legendre Equation and Legendre Polynomials	96	(5)
3.3 Boundary-Value Problems with Azimuthal Symmetry	101	(3)
3.4 Behavior of Fields in a Conical Hole or Near a Sharp Point	104	(3)
3.5 Associated Legendre Functions and the Spherical Harmonics Y(lm) (Theta. Phi)	107	(3)
3.6 Addition Theorem for Spherical Harmonics	110	(1)
3.7 Laplace Equation in Cylindrical Coordinates: Bessel Functions	111	(6)
3.8 Boundary-Value Problems in Cylindrical Coordinates	117	(2)
3.9 Expansion of Green Functions in Spherical Coordinates	119
3.10 Solution of Potential Problems with the Spherical Green Function Expansion	112
3.11 Expansion of Green Functions in Cylindrical Coordinates	125	(2)
3.12 Eigenfunction Expansions for Green Functions	127	(2)
3.13 Mixed Boundary Conditions. Conducting Plane with a Circular Hole	129	(6)
References and Suggested Reading	135	(1)
Problems	135	(10)
Chapter 4 Multipoles, Electrostatics of Macroscopic Media, Dielectrics	145	(29)
4.1 Multipole Expansion	145	(5)
4.2 Multipole Expansion of the Energy of a Charge Distribution in an External Field	150	(1)
4.3 Elementary Treatment of Electrostatics with Ponderable Media	151	(3)
4.4 Boundary-Value Problems with Dielectrics	154	(5)
4.5 Molecular Polarizability and Electric Susceptibility	159	(3)
4.6 Models for Electric Polarizability	162	(3)
4.7 Electrostatic Energy in Dielectric Media	165	(4)
References and Suggested Reading	169	(1)
Problems	169	(5)
Chapter 5 Magnetostatics, Faraday's Law, Quasi-Static Fields	174	(63)
5.1 Introduction and Definitions	174	(1)
5.2 Biot and Savart Law	175	(3)
5.3 Differential Equations of Magnetostatics and Ampere's Law	178	(2)
5.4 Vector Potential	180	(1)
5.5 Vector Potential and Magnetic Induction for a Circular Current Loop	181	(3)
5.6 Magnetic Fields of a Localized Current Distribution, Magnetic Moment	184	(4)
5.7 Force and Torque on and Energy of a Localized Current Distribution in an External Magnetic Induction	188	(3)
5.8 Macroscopic Equations, Boundary Conditions on B and H	191	(3)
5.9 Methods of Solving Boundary-Value Problems in Magnetostatics	194	(4)
5.10 Uniformly Magetized Sphere	198	(1)
5.11 Magnetized Sphere in an External Field: Permanent Magnets	199	(2)
5.12 Magnetic Shielding, Spherical Shell of Permeable Material in a Uniform Field	201	(2)
5.13 Effect of a Circular Hole in a Perfectly Conducting Plane with an Asymptotically Uniform Tangential Magnetic Fields on One Side	203	(3)
5.14 Numerical Methods for Two-Dimensional Magnetic Fields	206	(2)
5.15 Faraday's Law of Induction	208	(4)
5.16 Energy in the Magnetic Field	212	(3)
5.17 Energy and Self-and Mutual Inductances	215	(3)
5.18 Quasi-Static Magnetic Fields in Conductors; Eddy Currents: Magnetic Diffusion	218	(5)
References and Suggested Reading	223	(2)
Problems	225	(12)
Chapter 6 Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws	237	(58)
6.1 Maxwell's Displacement Current; Maxwell Equations	237	(2)
6.2 Vector and Scalar Potentials	239	(1)
6.3 Gauge Transformations, Lorentz Gauge, Coulomb Gauge	240	(3)
6.4 Green Functions for the Wave Equation	243	(3)
6.5 Retarded Solutions for the Fields: Jefimenko's Generalizations of the Coulomb and Biot-Savart Laws; Heaviside-Feynman Expressions for Fields of Point Charge	246	(2)
6.6 Derivation for the Equations of Macroscopic Electromagnetism	248	(10)
6.7 Poynting's Theorem and Conservation of Energy and Momentum for a System of Charged Particles and Electromagnetic Fields	258	(4)
6.8 Poynting's Theorem in Linear Dissipative Media with Losses	262	(2)
6.9 Poynting's Theorem for Harmonic Fields; Fields Definitions of Impedance and Admittance	264	(3)
6.10 Transformation Properties for Electromagnetic Fields and Sources Under Rotations, Spatial Reflections, and Time Reversal	267	(6)
6.11 On the Question of Magnetic Monopoles	273	(2)
6.12 Discussion of the Dirac Quantization Condition	275	(5)
6.13 Polarization Potentials (Hertz Vectors)	280	(2)
References and Suggested Reading	282	(1)
Problems	283	(12)
Chapter 7 Plane Electromagnetic Waves and Wave Propagation	295	(57)
7.1 Plane Waves in a Nonconducting Medium	295	(4)
7.2 Linear and Circular Polarization; Stockes Parameters	299	(3)
7.3 Reflection and Refraction of Electromagnetic Waves at a Plane Interface Between Two Dielectrics	302	(4)
7.4 Polarization by Reflection, Total Internal Reflection: Goos-Hanchen Effect	306	(3)
7.5 Frequency Dispersion Characteristics of Dielectrics, Conductors, and Plasmas	309	(7)
7.6 Simplified Model of Propagation in the Ionosphere and Magnetosphere	316	(3)
7.7 Magnetohydrodynamic Waves	319	(3)
7.8 Superposition of the Waves in One Dimension; Group Velocity	322	(4)
7.9 Illustration of the Spreading of a Pulse As It Propagates in a Dispersive Medium	326	(4)
7.10 Causality in the Connection Between D and E: Kramers-Kroning Relations	330	(5)
7.11 Arrival of a Signal After Propagation Through a Dispersive Medium	335	(4)
References and Suggested Reading	339	(1)
Problems	340	(12)
Chapter 8 Waveguides, Resonant Cavities, and Optical Fibers	352	(55)
8.1 Fields at the Surface of and Within a Conductor	352	(4)
8.2 Cylindrical Cavities and Waveguides	356	(3)
8.3 Waveguides	359	(2)
8.4 Modes in a Rectangular Waveguides	361	(2)
8.5 Energy Flow and Attenuation in Waveguides	363	(3)
8.6 Perturbation of Boundary Conditions	366	(2)
8.7 Resonant Cavities	368	(3)
8.8 Power Losses in a Cavity; Q of a Cavity	371	(3)
8.9 Earth and Ionosphere as a Resonant Cavity: Schumann Resonances	374	(4)
8.10 Multimode Propagation in Optical Fibers	378	(7)
8.11 Modes in Dielectric Waveguides	385	(4)
8.12 Expansion in Normal Modes; Fields Generated by a Localized Source in a Hollow Metallic Guide	389	(6)
References and Suggested Reading	395	(1)
Problems	396	(11)
Chapter 9 Radiating Systems, Multipole Fields and Radiation	407	(49)
9.1 Fields and Radiation of a Localized Oscillating Source	407	(3)
9.2 Electric Dipole Fields and Radiation	410	(3)
9.3 Magnetic Dipole and Electric Quadrupole Fields	413	(3)
9.4 Center-Fed Linear Antenna	416	(3)
9.5 Multipole Expansion for Localized Source or Aperture in Waveguide	419	(6)
9.6 Spherical Wave Solutions of the Scalar Wave Equation	425	(4)
9.7 Multipole Expansion of the Electromagnetic Fields	429	(3)
9.8 Properties of Multipole Fields, Energy and Angular Momentum of Multipole Radiation	432	(5)
9.9 Angular Distribution of Multipole Radiation	437	(2)
9.10 Sources of Multipole Radiation; Multipole Moments	439	(3)
9.11 Multipole Radiation in Atoms and Nuclei	442	(2)
9.12 Multipole Radiation from a Linear, Center-Fed Antenna	444	(4)
References and Suggested Reading	448	(1)
Problems	449	(7)
Chapter 10 Scattering and Diffraction	456	(58)
10.1 Scattering at Long Wavelengths	456	(6)
10.2 Perturbation Theory of Scattering, Rayleigh's Explanation of the Blue Sky, Scattering by Gases and Liquids, Attenuation in Optical Fibers	462	(9)
10.3 Spherical Wave Expansion of a Vector Plane Wave	471	(2)
10.4 Scattering of Electromagnetic Waves by a Sphere	473	(5)
10.5 Scalar Diffraction Theory	478	(4)
10.6 Vector Equivalents of the Kirchhoff Integral	482	(3)
10.7 Vectorial Diffraction Theory	485	(3)
10.8 Babinet's Principle of Complementary Screens	488	(2)
10.9 Diffraction by a Circular Aperture; Remarks on Small Apertures	490	(5)
10.10 Scattering in the Short-Wavelength Limit	495	(5)
10.11 Optical Theorem and Related Matters	500	(6)
References and Suggested Reading	506	(1)
Problems	507	(7)
Chapter 11 / Special Theory of Relativity	514	(65)
11.1 The Situation Before 1900, Einstein's Two Postulates	515	(3)
11.2 Some Recent Experiments	518	(6)
11.3 Lorentz Transformations and Basic Kinematic Results of Special Relativity	524	(6)
11.4 Addition of Velocities; 4-Velocity	530	(3)
11.5 Relativistic Momentum and Energy of a Particle	533	(6)
11.6 Mathematical Properties of the Space-Time of Special Relativity	539	(4)
11.7 Matrix Representation of Lorentz Transformations, Infinitesimal Generators	543	(5)
11.8 Thomas Precession	548	(5)
11.9 Invariance of Electric Charge; Covariance of Electrodynamics	553	(5)
11.10 Transformation of Electromagnetic Fields	558	(3)
11.11 Relativistic Equation of Motion for Spin in Uniform or Slowly Varying External Fields	561	(4)
11.12 Note on Notation and Units in Relativistic Kinematics	565	(1)
References and Suggested Reading	566	(2)
Problems	568	(11)
Chapter 12 Dynamics of Relativistic Particles and Electromagnetic Fields	579	(45)
12.1 Lagrangian and Hamiltonian for a Relativistic Charged Particle in External Electromagnetic Fields	579	(6)
12.2 Motion in a Uniform, Static Magnetic Field	585	(1)
12.3 Motion in Combined, Uniform, Static Electric and Magnetic Fields	586	(2)
12.4 Particle Drifts in Nonuniform, Static Magnetic Fields	588	(4)
12.5 Adiabatic Invariance of Flux Through Orbit of Particle	592	(4)
12.6 Lowest Order Relativistic Corrections to the Lagrangian for Interacting Charged Particles: The Darwin Lagrangian	596	(2)
12.7 Lagrangian for the Electromagnetic Field	598	(2)
12.8 Proca Lagrangian; Photon Mass Effects	600	(3)
12.9 Effective "Photon" Mass in Superconductivity; London Penetration Depth	603	(2)
12.10 Canonical and Symmetric Stress Tensors; Conservation Laws	605	(7)
12.11 Solution of the Wave Equation in Covariant Form; Invariant Green Functions	612	(3)
References and Suggested Reading	615	(2)
Problems	617	(7)
Chapter 13 Collisions, Energy Loss, and Scattering of Charged Particles, Cherenkov and Transition Radiation	624	(37)
13.1 Energy Transfer in Coulomb Collision Between Heavy Incident Particle and Free Electron; Energy Loss in Hard Collisions	625	(2)
13.2 Energy Loss form Soft Collisions; Total Energy Loss	627	(4)
13.3 Density Effect in Collisional Energy Loss	631	(6)
13.4 Cherenkov Radiation	637	(3)
13.5 Elastic Scattering of Fast Charged Particles by Atoms	640	(3)
13.6 Mean Square Angle of Scattering; Angular Distribution of Multiple Scattering	643	(3)
13.7 Transition Radiation	646	(8)
References and Suggested Reading	654	(1)
Problems	655	(6)
Chapter 14 Radiation by Moving Charges	661	(47)
14.1 Lienard-Wiechert Potentials and Fields for a Point Charge	661	(4)
14.2 Total Power Radiated by an Accelerated Charge: Larmor's Formula and Its Relativistic Generalization	665	(3)
14.3 Angular Distribution of Radiation Emitted by an Accelerated Charge	668	(3)
14.4 Radiation Emitted by a Charge in Arbitrary, Extremely Relativistic Motion	671	(2)
14.5 Distribution in Frequency and Angle of Energy Radiated by Accelerated Charges: Basic Results	673	(3)
14.6 Frequency Spectrum of Radiation Emitted by a Relativistic Charged Particle in Instantaneously Circular Motion	676	(7)
14.7 Undulators and Wigglers for Synchrotron Light Sources	683	(11)
14.8 Thomson Scattering of Radiation	694	(3)
References and Suggested Reading	697	(1)
Problems	698	(10)
Chapter 15 Bremsstrahlung, Method of Virtual Quanta, Radiative Beta Processes	708	(37)
15.1 Radiation Emitted During Collissions	709	(5)
15.2 Bremsstrahlung in Coulomb Collisions	714	(7)
15.3 Screening Effects; Relativistic Radiative Energy Loss	721	(3)
15.4 Weizsacker-Williams Method of Virtual Quanta	724	(5)
15.5 Bremsstrahlung as the Scattering of Virtual Quanta	729	(1)
15.6 Radiation Emitted During Beta Decay	730	(2)
15.7 Radiation Emitted During Orbital Electron Capture: Disappearance of Charge and Magnetic Moment	732	(5)
References and Suggested Reading	737	(1)
Problems	737	(8)
Chapter 16 Radiation Damping, Classical Models of Charged Particles	745	(30)
16.1 Introductory Considerations	745	(2)
16.2 Radiative Reaction Force from Conservation of Energy	747	(3)
16.3 Abraham-Lorentz Evaluation of the Self-Force	750	(5)
16.4 Relativistic Coveriance; Stability and Poincare Stresses	755	(2)
16.5 Covariant Definitions of Electromagnetic Energy and Momentum	757	(2)
16.6 Covariant Stable Charged Particle	759	(4)
16.7 Level Breadth and Level Shift of a Radiating Oscillator	763	(3)
16.8 Scattering and Absorption of Radiation by an Oscillator	766	(2)
References and Suggested Reading	768	(1)
Problems	769	(6)
Appendix on Units and Dimensions	775	(10)
1 Units and Dimensions, Basic Units and Derived Units and Derived Units	775	(2)
2 Electromagnetic Units and Equations	777	(2)
3 Various Systems of Electromagnetic Units	779	(3)
4 Conversion of Equations and Amounts Between SI Units and Gaussian Units	782	(3)
Bibliography	785	(6)
Index	791