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Classical Theory of Electric and Magnetic Fields
- 1st Edition - January 1, 1971
- Authors: Roland H. Good, Terence J. Nelson
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 3 9 5 9 - 0
- Hardback ISBN:9 7 8 - 0 - 1 2 - 2 9 0 0 5 0 - 1
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 2 0 3 - 0
Classical Theory of Electric and Magnetic Fields is a textbook on the principles of electricity and magnetism. This book discusses mathematical techniques, calculations, with… Read more
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Request a sales quoteClassical Theory of Electric and Magnetic Fields is a textbook on the principles of electricity and magnetism. This book discusses mathematical techniques, calculations, with examples of physical reasoning, that are generally applied in theoretical physics. This text reviews the classical theory of electric and magnetic fields, Maxwell's Equations, Lorentz Force, and Faraday's Law of Induction. The book also focuses on electrostatics and the general methods for solving electrostatic problems concerning images, inversion, complex variable, or separation of variables. The text also explains magnetostatics and compares the calculation methods of electrostatics with those of magnetostatics. The book also discusses electromagnetic wave phenomena concerning wave equations with a source term and the Maxwell equations which are linear and homogenous. The book also explains Einstein's the Special Theory of Relativity which is applicable' only to inertial coordinate systems. The text also discusses the particle aspects of electromagnetic field equations such as those concerning wave equations for particles with spin. This textbook is intended for graduate or advanced students and academicians in the field of physics.
Preface
Acknowledgments
I. Introduction
Phenomena Governed by Maxwell'S Equations and the Lorentz Force
Importance Of E & M in Understanding Modern Physics
References
II. Development of Maxwell's Equations
1. Electrostatics
Review of Vector Notation
Coulomb's Law
Distributions
Dipole Field
The Continuity Equation
Spherical Symmetry
Electrostatic Potential
Problems
2. Magnetostatics
Ampere's Law
Magnetic Field of a Long Straight Wire
Curl and Divergence of the Magnetic Field
The Case When the Curl Vanishes
Determination of a Field by Its Divergence and Curl
The Vector Potential
Cylindrical Symmetry
Problems
3. Faraday's Law of Induction
4. Maxwell'S Displacement Current
Final Form of Maxwell's Equations
The Speed of Light
Problem
References
III. Cartesian Vector and Tensor Analysis
5. Notation
Sum Convention
Kronecker Delta Symbol
The Levi-Civita Symbol
Problems
6. Orthogonal Transformations
Direction Cosines
Transformation of Coordinates
Rotations and Reflections
Problem
7. Definition of Tensors
Rank and Transformation Properties
Importance of Tensors in Physics
Problems
8. Co Variant Operations
Covariance Distinguished from Invariance
Examples of Covariant Operations
Pseudotensors
Differentiation
Problems
9. Reduction of Tensors
Simplification by Contraction and Symmetrization
Irreducible Tensors
Problem
Reference
IV. Electrostatics
10. Fields near Singular Sources
Expansion of Potential Outside Charges
The Quadrupole Moment Tensor
Energy of Singular Sources in an External Electrostatic Field
Surface Singularities
Problems
11. The General Electrostatic Boundary Value Problem
Uniqueness of Solution
Green's Function
Problems
12. Solution by Images
Conducting Planes
Conducting Spheres
Dirichlet Green's Function for a Sphere
Problems
13. Inversion of Solutions
Basic Theorem
Geometry of Inversion
Surface Charges
Example of Inversion
Problems
14. Solution by Complex Variable Technique
Differentiation of a Function of a Complex Variable
Integration on Closed Paths in the Complex Plane
Analytic Functions as Solutions of Laplace's Equation
Application to Electrostatics
Problems
15. Method of Separation of Variables
Separation of Laplace's Equation in Spherical Coordinates
Summary of Properties of the Spherical Harmonics
Multipole Expansion of the Potential of a Distribution of Charges
The Quadrupole Moment in Nuclear Physics
Separation of Laplace's Equation in Cylindrical Coordinates
Expansions in Complete Sets of Functions
Eigenfunction Expansion of the Dirichlet Green's Function
Problems
16. Dielectrics
Polarization
The Problem of a Condenser Filled with a Dielectric
The Problem of a Charge near a Dielectric Boundary
The Clausius-Mossotti Relation
Problems
References
V. Magnetos tatics
17. The Magnetic Dipole
Field of a Magnetic Dipole
Force on a Dipole in an External Field
Singularities in the Dipole Field
The Gyromagnetic Ratio
Problem
18. Magnetization
Concept of Bound Currents
Field of a Uniformly Magnetized Sphere
Problems
19. Multipole Expansion
Expansion of the Vector Potential
Expansion of the Scalar Potential
Field of a Magnetized Object
Problems
VI. Dynamical Maxwell Equations
20. Final Form of Maxwell's Equations
21. Units and Dimensions
Gaussian Units
Heaviside-Lorentz Units
Electrostatic Units
Electromagnetic Units
MKS (Meter-Kilogram-Second) Units
Problem
22. Mechanical Properties of the Field
Momentum
Energy
Angular Momentum
Thermodynamics of Field and Material
Electrostatic Energy in Terms of Sources
Magnetostatic Energy in Terms of Sources
Inductance
Magnetostatic Assembly Work
Problems
23. Potentials
The Vector and Scalar Potentials
Lorentz Gauge
Hertz Potential
Coulomb Gauge
Problem
VII. Wave Phenomena
24. The Wave Equation
Special Cases
Initial Value Problem in One Dimension
Source Problem in One Dimension
Initial Value Problem in Three Dimensions
Source Problem in Three Dimensions (Green's Function Solution)
Problems
25. Plane Waves
Plane Waves in Linear Insulators
Reflection and Refraction at a Dielectric Interface
Phase and Group Velocity
Classical Model of a Dielectric with Dispersion, Resonance, and Absorption
Causality and Dispersion Relations
Problems
References
VIII. The Special Theory of Relativity
26. Before Einstein
27. Einstein's Theory
The Principle of Special Relativity
Properties of Lorentz Transformations
Problem
28. Relativistic Mechanics of Point Particles
Proper Time
Energy and Momentum in Relativistic Mechanics
Forces
Problems
29. Covariance of E & M
The Four-Dimensional Form of Maxwell1 s Equations
Lorentz Tensors with Zero Divergence
Stress-Energy-Momentum Tensor
Aberration and the Doppler Effect
Problems
30. Motion of a Particle with a Intrinsic Magnetic Moment
Intrinsic Properties of Elementary Particles
Lorentz Transformation from the Rest System to the Lab
Covariant Description of the Particle's Motion and Orientation
Generalization of the Equations of Motion from the Rest to the Lab Frame
Problems
References
IX. Radiation
31. The Long Wavelength Approximation
Distinction between the Near Field and the Far Field
Expansion far from Sources
Electric Dipole Radiation
Magnetic Dipole Radiation
Electric Quadrupole Radiation
Problems
32. Radiation from Source Distributions Comparable to a Wavelength in Extent
Radiation from a Center-Fed Linear Antenna
Electric and Magnetic Fields of a Moving Point Charge
Radiation from an Accelerated Charge
Spectral Distribution of Radiation from a Moving Charge
Cerenkov Radiation 534; Problems
References
X. Waves and Metallic Boundary Conditions
33. Waveguides and Resonant Cavities
Wave Propagation in Good Conductors
Zero-Order Surface Effects
First-Order Surface Effects
Propagation between Two Mirrors
General Theory for Propagation in a Guide of Uniform Cross Section
Modes in a Rectangular Guide
The Rectangular Resonant Cavity with Only TE10 above Cutoff
Problem
XI. Particle Aspects of Electromagnetic Field Equations
34. Introduction to Wave Equations for Particles with Spin
Particle States and Fields
Plane Wave Solutions
35. Particle Aspects of Electromagnetic Field Equations
Hamiltonian and Wave Function for the Photon
Transformation Properties of the Wave Function
Covariantly Defined Matrices
Manifestly Covariant Wave Equations
Invariant Inner Product
Energy, Momentum, and Angular Momentum Operators
Uncertainty Principle for Photons
Problems
References
Index
- No. of pages: 654
- Language: English
- Edition: 1
- Published: January 1, 1971
- Imprint: Academic Press
- Paperback ISBN: 9781483239590
- Hardback ISBN: 9780122900501
- eBook ISBN: 9781483272030
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