Electrodynamics: An Introduction Including Quantum Effects

by Muller-Kirsten, Harald J. W.

• ISBN13: 9789812388087
• ISBN10: 9812388087
• Format: Paperback
• Copyright: 2004-09-30
• Publisher: Textstream

Summary

An extensive text on electrodynamics with detailed explanations and calculations. One hundred worked examples have been incorporated, making the book suitable also for self-instruction. Apart from all traditional topics of Maxwell theory, the book includes the special theory of relativity and the Lagrangian formalism and applications; the text also contains introductions to quantum effects related to electrodynamics, such as the Aharonov-Bohm and the Casimir effects. Numerous modern applications in diverse directions are treated in the examples.

Table of Contents

Preface	xiii
Introduction	1	(8)
What is Electrodynamics?	1	(1)
Presentation of Macroscopic Electrodynamics	1	(5)
On the Choice of Units	6	(3)
Electrostatics -- Basic Aspects	9	(38)
Introductory Remarks	9	(1)
The Coulomb Law	9	(3)
The Electrostatic Potential	12	(2)
The Equations of Electrostatics	14	(3)
Dirac's Delta Distribution	17	(6)
Potential Energy of Charges in Electric Fields	23	(1)
The Electric Field at Charged Surfaces	24	(3)
Examples	27	(6)
Conductors and Electrical Screening	33	(8)
Energy of Charge Distributions	41	(6)
Applications of Electrostatics	47	(38)
Introductory Remarks	47	(1)
Method I: The Gauss Law	47	(1)
Method II: Poisson and Laplace Equations	47	(2)
Method III: Direct Integration	49	(1)
Method IV: Kelvin's Method of Image Charges	50	(3)
Theoretical Aspects of Image Charges	53	(13)
The Induced Charge	53	(4)
Green's Theorems	57	(3)
Green's Function and Image Potential	60	(2)
The Image Potential in an Example	62	(4)
Method V: Conjugate Functions	66	(6)
Orthogonal Functions	72	(6)
Orthogonal Functions in General	72	(2)
Fourier Series, Fourier Expansions	74	(2)
Spherical Functions (Legendre, Associated Legendre, Hyperspherical Functions)	76	(2)
The Multipole Expansion	78	(7)
Macroscopic Electrostatics	85	(24)
Introductory Remarks	85	(1)
Dielectrics and Dielectric Displacement	85	(8)
The Behaviour of D at an Interface	93	(1)
Examples	94	(3)
Polarisation of a Sphere in an Electric Field E0	97	(5)
Energy of the Electric Field	102	(4)
The Energy Density Formula	102	(2)
Polarisation Energy	104	(2)
Summary of Formulae of Electrostatics	106	(3)
Magnetostatics	109	(26)
Introductory Remarks	109	(1)
Continuity Equation and Stationary Current	109	(4)
Ampere's Experiments and the Law of Biot and Savart	113	(6)
Examples	119	(4)
The Electromagnetic Vector Potential A	123	(3)
Integral Form of Ampere's Law	126	(1)
Further Examples	127	(8)
Macroscopic Magnetostatics	135	(16)
Introductory Remarks	135	(1)
Macroscopic Magnetisation	136	(5)
Magnetic Properties of Matter	141	(1)
Energy of the Magnetic Field	142	(1)
Behaviour of B and H at Boundary Surfaces	142	(2)
Current Circuits Compared with Flux Circuits	144	(1)
Examples	145	(5)
Summary of Formulae of Magnetostatics	150	(1)
The Maxwell Equations	151	(22)
Preliminary Remarks	151	(1)
Time-Dependent Fields and Faraday's Law of Induction	151	(5)
Energy of the Magnetic Field	156	(1)
The Generalised Ohm's Law	157	(1)
E and B with Time-Dependent Potentials	158	(1)
Displacement Current and Maxwell Equations	158	(4)
Poynting Vector and Conservation of Energy	162	(5)
Application: The Conduction Wire	164	(1)
The Field Momentum Density	165	(2)
Further Examples	167	(6)
Applications to Coils and Circuits	173	(22)
Introductory Remarks	173	(1)
Inductances Lij	173	(2)
Examples	175	(3)
The Vector Potential of a Long Solenoid	178	(5)
Energy of a Self-Inductance	183	(6)
Simple Current Circuits	189	(3)
Current Circuits with R and L	189	(2)
Circuits with L, C and R	191	(1)
Self-Inductances: Conjugate Function Method	192	(3)
Electromagnetic Waves	195	(14)
Introductory Remarks	195	(1)
Electromagnetic Waves in Vacuum	195	(5)
Electromagnetic Waves in Media	200	(1)
Frequency Dependence of ε and σ	201	(6)
The Generalised Dielectric Constant	201	(1)
Frequency Dependence of σ	202	(5)
The (Normal) Skin Effect	207	(2)
Moving Charges in Vacuum	209	(34)
Introductory Remarks	209	(1)
Maxwell's Equations for Moving Charges	209	(6)
The Lienard--Wiechert Potentials of a Moving Point Charge	215	(3)
The Fields E, B of a Moving Point Charge	218	(10)
The Hertz Dipole	228	(5)
The Potentials	228	(3)
The Field Strengths	231	(2)
Current Element Ids and Dipole Radiation	233	(4)
The Power of an Oscillating Dipole	234	(2)
Radiation Resistance	236	(1)
Further Examples	237	(6)
The Laws of Optics	243	(24)
Introductory Remarks	243	(1)
Continuity Conditions and Definition of the Surface Current	243	(4)
Electromagnetic Waves in Media	247	(3)
Kinematical Aspects of Reflection and Refraction: Snell's Law	250	(3)
Preliminary Remarks	250	(2)
Kinematical Aspects of Reflection and Refraction	252	(1)
Dynamical Aspects of Reflection and Refraction: The Fresnel Formulae	253	(11)
The Conditions	253	(1)
Two Cases of Linear Polarisation	254	(6)
The Brewster Angle and the Case without Reflection	260	(1)
The General Case	260	(1)
Total Reflection	261	(3)
Useful Formulation of the Fresnel Formulae	264	(3)
Metals	267	(10)
Introductory Remarks	267	(1)
Reflection and Absorption of Plane Waves by Metals	267	(3)
The Theory of Drude	270	(7)
Propagation of Radio Waves in the Ionosphere	277	(12)
Introductory Remarks	277	(1)
Condition for Return of Waves	278	(4)
Effect of Terrestrial Magnetic Field	282	(7)
Wave Guides and Resonators	289	(56)
What are Wave Guides?	289	(2)
Transverse Fields Derived from Longitudinal Fields	291	(3)
Boundary Conditions	294	(2)
Wave Guides and their TEM Fields	296	(4)
TEM Fields	296	(3)
The Coaxial Transmission Cable	299	(1)
Fundamental Equations for the Coaxial Cable	300	(4)
TM and TE Waves in Wave Guides	304	(12)
General Considerations	304	(1)
Wave Guides with Rectangular Cross Section	305	(9)
Wave Guides with Circular Cross Section	314	(2)
Alternative Treatment using Scalar and Vector Potentials	316	(3)
Wave Velocities	319	(1)
Energy Transport in Wave Guides	320	(12)
The Complex Poynting Vector	320	(2)
Application of the Complex Poynting Vector	322	(2)
Attenuation of Wave Guides (σ ≠ 0)	324	(5)
Optimal Use of a Wave Guide	329	(3)
Resonators (Closed Wave Guides)	332	(7)
Examples	339	(6)
Propagation of Waves in Media	345	(16)
Introductory Remarks	345	(1)
Dispersion Relation: Normal and Anomalous Dispersion	345	(3)
Absorption, Causality and Analyticity	348	(8)
Properties of A(w)	349	(3)
Properties of n(w)	352	(4)
No Wave Packet with a Velocity > c	356	(1)
Explanation of the Anomalous Dispersion	357	(4)
Causality and Dispersion Relations	361	(20)
Introductory Remarks	361	(1)
Cause U and Effect E	361	(1)
(U, E)-Linearity and Green's Functions	362	(2)
Causality	364	(2)
Causality and Analyticity	366	(2)
Principal Value Integrals and Dispersion Relations	368	(4)
Absorption: Special Cases	372	(2)
Comments on Principal Values	374	(4)
Subtracted Dispersion Relations	378	(3)
Covariant Formulation of Electrodynamics	381	(42)
Introductory Remarks	381	(1)
The Special Theory of Relativity	381	(7)
Introduction	381	(6)
Einstein's Interpretation of Lorentz Transformations	387	(1)
Minkowski Space	388	(4)
The 10-Parametric Poincare Group	392	(5)
Covariant and Contravariant Derivatives	396	(1)
Construction of the Field Tensor Fμν	397	(7)
Transformation from Rest Frame to Inertial Frame	404	(7)
Covariant Form of Maxwell's Equations	411	(2)
Covariantised Newton Equation of a Charged Particle	413	(4)
Examples	417	(6)
The Lagrange Formalism for the Electromagnetic Field	423	(24)
Introductory Remarks	423	(1)
Euler-Lagrange Equation	423	(2)
Symmetries and Energy-Momentum Tensor	425	(3)
The Lagrangian of the Electromagnetic Field	428	(4)
Gauge Invariance and Charge Conservation	432	(1)
Lorentz Transformations and Associated Conservation Laws	433	(1)
Masslessness of the Electromagnetic Field	434	(2)
Transversality of the Electromagnetic Field	436	(1)
The Spin of the Photon	437	(3)
Examples	440	(7)
The Gauge Covariant Schrodinger Equation and the Aharonov--Bohm Effect	447	(14)
Introductory Remarks	447	(1)
Schrodinger Equation of a Charged Particle in an Electromagnetic Field	448	(5)
Hamiltonian of a Charge in an Electromagnetic Field	448	(2)
The Gauge Covariant Schrodinger Equation	450	(3)
The Aharonov-Bohm Effect	453	(8)
Quantisation of the Electromagnetic Field and the Casimir Effect	461	(18)
Introductory Remarks	461	(1)
Quantisation of the n-Dimensional Harmonic Oscillator	462	(2)
Hamiltonian of the Gauge Field	464	(1)
Quantisation of the Electromagnetic Field	465	(5)
One-dimensional Illustration of the Casimir Effect	470	(4)
The Three-Dimensional Case	474	(5)
Duality and Magnetic Monopoles	479	(16)
Symmetrisation of the Maxwell Equations	479	(4)
Quantisation of Electric Charge	483	(3)
The Field of the Monopole	486	(1)
Uniqueness of the Wave Function	487	(3)
Regularisation of the Monopole Field	490	(3)
Concluding Remarks	493	(2)
A The Delta Distribution	495	(10)
B Units and Physical Constants	505	(8)
C Formulae	513	(2)
C.1 Vector Products	513	(1)
C.2 Integral Theorems	514	(1)
Bibliography	515	(2)
Index	517