Classical electrodynamics

Preface to the Second Edition
Preface to the First Edition
Contents
1 Classical Electrodynamics: A Short Review
	1.1 Coulomb's Law and the First Maxwell Equation
	1.2 Charge Conservation and Continuity Equation
	1.3 Absence of Magnetic Charges in Nature and the Second Maxwell Equation
	1.4 Laplace's Laws, Biot and Savart Law and the Steady Fourth Maxwell Equation
	1.5 Faraday's Law and the Third Maxwell Equation
	1.6 Displacement Current and the Fourth Maxwell Equation
	1.7 Maxwell Equations in Vacuum
	1.8 Maxwell Equations in Matter
	1.9 Electrodynamic Potentials and Gauge Transformations
	1.10 Electromagnetic Waves
	References
2 Multipole Expansion of the Electrostatic Potential
	2.1 The Potential of the Electric Dipole
	2.2 Interaction of the Dipole with an Electric Field
	2.3 Multipole Expansion for the Potential of a Distribution of Point Charges
	2.4 Properties of the Electric Dipole Moment
	2.5 The Quadrupole Tensor
	2.6 A Bidimensional Quadrupole
	Problems
	Solutions
	References
3 The Method of Image Charges
	3.1 The Method of Image Charges
	3.2 Point Charge and Conductive Plane
	3.3 Point Charge and Conducting Sphere
		3.3.1 Force on a Point Charge Near a Charged Conducting Sphere
	3.4 Conducting Sphere in a Uniform Electric Field
	3.5 A Charged Wire Near a Cylindrical Conductor
	Problems
	Solutions
	References
4 Image Charges in Dielectrics
	4.1 Electrostatics in Dielectric Media
	4.2 Point Charge Near the Plane Separating Two Dielectric Media
	4.3 Dielectric Sphere in an External Uniform Electric Field
	Problems
	Solutions
	References
5 Series of Image Charges
	5.1 Point Charge Between Two Grounded Plates
	5.2 Two Separated Charged Conductive Spheres
	5.3 Force Between Two Charged Spherical Conductors
	5.4 A Charged Conductive Sphere and a Conductive Plate at Ground
	5.5 Dielectric Sphere and Point Charge
	Problems
	Solutions
	References
6 Functions of Complex Variables and Electrostatics
	6.1 Analytic Functions of Complex Variable
	6.2 Electrostatics and Analytic Functions
	6.3 The Function f left parenthesis z right parenthesis equals z Superscript muf(z)=zµ
		6.3.1 The Quadrupole: f left parenthesis z right parenthesis equals z squaredf(z)=z2
		6.3.2 The Conductive Wedge at Fixed Potential
		6.3.3 Edge of a Thin Plate
	6.4 The Charged Wire: f left parenthesis z right parenthesis equals log zf(z)= logz
	Problems
	Solutions
	References
7 Conformal Mapping in Electrostatics
	7.1 Conformal Mapping
	7.2 Conformal Mapping and Harmonic Functions
	7.3 Conformal Mapping and Bilinear Electrostatic Problems
		7.3.1 Charged Wire Between Two Grounded Plates
	7.4 The Linear-Fractional Function
		7.4.1 The Split Cylinder: Two Opposite Half Cylinders at Different Potentials
	7.5 The Schwarz-Christoffel Transformation
		7.5.1 Conformal Transformation for a Single Corner
		7.5.2 The Field Near the Edge of a Parallel-Plate Capacitor
	Problems
	Solutions
	References
8 Separation of Variables in Laplace Equation
	8.1 The Method of Separation of Variables
	8.2 Orthogonal and Complete Sets of Functions
	8.3 Separation of Variables in the Laplace Equation
	8.4 Separation of Variables in Cartesian Coordinates
		8.4.1 Box with a Side at Given Potential and Five Conductive Grounded Sides
	8.5 Separation of Variables in Spherical Coordinates with Azimuthal Symmetry
		8.5.1 A Dielectric Sphere in a Uniform Electric Field
		8.5.2 Potential for a Charged Ring
		8.5.3 Conducting/Dielectric Sphere and Point Charge
	8.6 Separation of Variables in Spherical Coordinates
	8.7 Separation of Variables in Polar (Cylindrical) Coordinates
		8.7.1 Wire and Cylindrical Capacitor
		8.7.2 Conducting Wedge (Corner)
		8.7.3 Split Cylinder
		8.7.4 Cylinder in a Uniform Electric Field
	Problems
	Solutions
	References
9 Relativistic Transformation of E and B Fields
	9.1 From Charge Invariance to the 4-Current Density
	9.2 Electric Current in a Wire and a Charged Particle in Motion
	9.3 Transformation of the E and B Fields
	9.4 The Total Charge in Different Frames
	9.5 Force Between Wires Carrying Currents
	9.6 Electromagnetic Induction and Relative Motion of Circuits
	Problems
	Solutions
	References
10 Relativistic Covariance  of Electrodynamics
	10.1 Electrodynamics and Special Theory of Relativity
	10.2 4-Vectors, Covariant and Contravariant Components
	10.3 Relativistic Covariance of the Electrodynamics
	10.4 4-Vector Potential and the Equations of Electrodynamics
	10.5 The Continuity Equation
	10.6 The Electromagnetic Tensor
	10.7 Lorentz Transformation for Electric and Magnetic Fields
	10.8 Maxwell Equations
		10.8.1 Inhomogeneous Equations
		10.8.2 Homogeneous Equations
	10.9 Potential Equations
	10.10 Gauge Transformations
	10.11 Phase of the Wave
	10.12 The Equations of Motion for a Charged Particle in the Electromagnetic Field
	References
11 Energy and Momentum of the Electromagnetic Field
	11.1 Poynting's Theorem
	11.2 Examples
		11.2.1 Resistor
		11.2.2 Solenoid
		11.2.3 Capacitor
	11.3 Energy Transfer in Electrical Circuits
	11.4 Momentum Conservation in a System of Charges  and Fields
	11.5 The Maxwell Stress Tensor
	11.6 Radiation Pressure on a Surface
	11.7 Angular Momentum
	11.8 The Covariant Maxwell Stress Tensor
	Problems
	Solutions
	References
12 The Feynman Paradox
	12.1 The Paradox
	12.2 A Charge and a Small Magnet
	12.3 Analysis of the Angular Momentum Present in the System
	12.4 Two Cylindrical Shells with Opposite Charge in a Vanishing Magnetic Field
	References
13 The Resonant Cavity
	13.1 The Capacitor at High Frequency
	13.2 The Resonant Cavity
	Problems
	Solutions
	References
14 Fields and Radiation
	14.1 Fields of a Point Charge in Uniform Motion
		14.1.1 Fields from the Lorentz Transformed Potentials for a Point Charge in Uniform Motion
	14.2 Potentials and Fields for a Point Charge in Arbitrary Motion
		14.2.1 The Retarded Potentials
		14.2.2 Liénard-Wiechert Potentials
		14.2.3 Comment to the Liénard-Wiechert Potentials
		14.2.4 Covariant Form of the Liénard-Wiechert Potentials
		14.2.5 Electric and Magnetic Fields
		14.2.6 Calculation of the Electric and Magnetic Fields
	14.3 Radiation by an Accelerated Charge
		14.3.1 Radiation by a Charged Particle with Velocity v llc
		14.3.2 Radiation by a Charged Particle with the Acceleration Parallel to the Velocity
		14.3.3 Power Radiated by a Charged Particle in Arbitrary Motion
		14.3.4 Radiation by a Charged Particle with the Acceleration Normal to the Velocity
	14.4 Radiation Reaction
	14.5 Electric Dipole Radiation
	Problems
	Solutions
	References
15 Test of the Coulomb's Law and Limits on the Mass of the Photon
	15.1 Gauss's Law
	15.2 First Tests of the Coulomb's Law
	15.3 Proca Equations
	15.4 The Williams, Faller and Hill Experiment
	15.5 Limits from Measurements of the Magnetic Field of the Earth and of Jupiter
	15.6 The Lakes Experiment
	15.7 Other Measurements
	15.8 Comments
	References
16 Magnetic Monopoles
	16.1 Generalized Maxwell Equations
	16.2 Generalized Duality Transformation
	16.3 Symmetry Properties for Electromagnetic Quantities
	16.4 The Dirac Monopole
	16.5 Magnetic Field and Potential of a Monopole
	16.6 Quantization Relation
	16.7 Quantization from Electric Charge-Magnetic Pole Scattering
	16.8 Properties of the Magnetic Monopoles
		16.8.1 Magnetic Charge and Coupling Constant
		16.8.2 Energy Losses for Monopoles in Matter
		16.8.3 Magnetic Monopoles in Magnetic Field
	16.9 Searches for Magnetic Monopoles
		16.9.1 Detection of Magnetic Monopoles
		16.9.2 Searches for Dirac Monopoles at Accelerators
		16.9.3 Search for Cosmic Monopoles
		16.9.4 Bounds on the Flux of Cosmic Magnetic Monopoles
		16.9.5 Direct Searches for Cosmic Massive Monopoles
	References
Appendix A Orthogonal Curvilinear Coordinates
A.1  Orthogonal curvilinear coordinates
A.2  Gradient
A.3  Divergence
A.4  Curl
A.5  Laplacian
A.6  Systems of Orthogonal Curvilinear Coordinates
A.7  Spherical Coordinates
A.8  Cylindrical Coordinates
	References
Index