Nathaniel H. Frank (1904-84) played an active role in shaping physics education. He was the head of MIT's physics department, specializing in theoretical physics and metallic conduction.
Klappentext
Clearly developed from first principles, this introductory study supplies basic material on electrostatics and magnetostatics, then concentrates on electromagnetic theory ? the authors are both leading men in the field. The book ranges freely over many areas of electromagnetic theory with some concern for electrical engineering. It covers the field theory of electromagnetism, electrostatics and the equations and theorems of Gauss, Poisson, Laplace and Green, solutions of Laplace's equation, dielectrics, magnetic fields of linear and circular currents, electromagnetic induction and Maxwell's equations, electromagnetic waves, electron theory, wave guides and cavity resonators, spherical electromagnetic waves, Huygen's principle and Green's theorem, and Fresnel and Fraunhofer diffraction. Practice problems are supplied at chapter ends.
Physicists and engineers will find this presentation particularly useful; but mathematicians have also used the book not only as an introduction to electromagnetism, but also as a means to an increased knowledge of the aims and tools of theoretical physics. The only background required to follow the development is a knowledge of the calculus and differential equations. More advanced mathematics is developed in appendixes.
Inhalt
PREFACE
CHAPTER I THE FIELD THEORY OF ELECTROMAGNETISM
Introduction
1. The Force on a Charge
2. The Field of a Distribution of Static Point Charges
3. The Potentials
4. Electric Images
Problems
CHAPTER II ELECTROSTATICS
Introduction
1. Gauss's Theorem
2. Capacity of Condensers
3. Poisson's Equation and Laplace's Equation
4. "Green's Theorem, and the Solution of Poisson's Equation in an Unbounded Region"
5. Direct Solution of Poisson's Equation
Problems
CHAPTER III SOLUTIONS OF LAPLACE'S EQUATION
Introduction
1. Solution of Laplace's Equation in Rectangular Coordinates by Separation of variables
2. Laplace's Equation in Spherical Coordinates
3. Spherical Harmonics
4. Simple Solutions of Laplace's Equation in Spherical Coordinates
5. The Dipole and the Double Layer
6. Green's Solution for a Bounded Region
Problems
CHAPTER IV DIELECTRICS
Introduction
1. The Polarization and the Displacement
2. The Dielectric Constant
3. Boundary Conditions at the Surface of a Dielectric
4. "Electrostatic Problems Involving Dielectrics, and the Condenser"
5. A Charge outside a Semi-infinite Dielectric Slab
6. Dielectric Sphere in a Uniform Field
7. Field in Flat and Needle-shaped Cavities
Problems
CHAPTER V MAGNETIC FIELDS OF CURRENTS
Introduction
1. The Biot-Savart Law
2. The Magnetic Field of a Linear and a Circular Current
3. "The Divergence of B, and the Scalar Potential"
4. The Magentic Dipole
5. Ampère's Law
6. The Vector Potential
Problems
CHAPTER VI MAGNETIC MATERIALS
Introduction
1. The Magnetization Vector
2. The Magnetic Field
3. Magnetostatic Problems Involving Magnetic Media
4. Uniformly Magnetized Sphere in an External Field
5. Magnetomotive Force
Problems
CHAPTER VII ELECTROMAGNETIC INDUCTION AND MAXWELL'S EQUATIONS
Introduction
1. The Law of Electromagnetic Induction
2. Self- and Mutual Induction
3. The Displacement Current
4. Maxwell's Equations
5. The Vector and Scalar Potentials
Problems
CHAPTER VIII ELETROMAGNETIC WAVES AND ENERGY FLOW
Introduction
1. Plane Waves and Maxwell's Equations
2. The Relation between E and H in a Plane Wave
3. Electric and Magnetic Energy Density
4. Poynting's Theorem and Poynting's Vector
5. Power Flow and Sinusoidal Time Variation
6. Power Flow and Energy Density in a Plane Wave
Problems
CHAPTER IX ELECTRON THEORY AND DISPERSION
Introduction
1. Dispersion in Gases
2. Dispersion in Liquids and Solids
3. Dispersion in Metals
4. The Quantum Theory and Dispersion
Problems
CHAPTER X REFLECTION AND REFRACTION OF ELECTROMAGNETIC WAVES
Introduction
1. Boundary Conditions at a Surface of Discontinuity
2. The Laws of Reflection and Refraction
3. Reflection Coefficient at Normal Incidence
4. Fresnel's Equation
5. Total Reflection
6. "Damped Plane Waves, Normal Incidence"
7. "Damped Plane Waves, Oblique Incidence"
Problems
CHAPTER XI WAVE GUIDES AND CAVITY RESONATORS
Introduction
1. Propagation between Two Parallel Mirrors
2. Electromagnetic Field in the Wave Guide
3. Examples of Wave Guides
4. Standing Waves in Wave Guides
5. Resonant Cavities
Problems
CHAPTER XII SPHERICAL ELECTROMAGNETIC WAVES
Introduction
1. Maxwell's Equations in Spherical Coordinates
2. Solutions of Maxwell's Equations in Spherical Coordinates
3. The Field of an Oscillating Dipole
4. The Field of a Dipole at Large Distances
5. Scattering of Light
6. Coherence and Incoherence of Light
Problems
CHAPTER XIII HUYGENS' PRINCIPLE AND GREEN'S THEOREM
Introduction
1. The Retarded Potentials
2. Mathematical Formulation of Huygens' Principle
3. Integration for a Spherical Surface by Fresnel's Zones
4. Huygens' Principle for Diffraction Problems
Problems
CHAPTER XIV FRESNEL AND FRAUNHOFER DIFFRACTION
Introduction
1. Comparison of Fresnel and Fraunhofer Diffraction
2. Fresnel Diffraction from a Slit
3. Fraunhofer Diffraction from a Slit
4. "The Circular Aperture, and the Resolving Power of a Lens"
5. Diffraction from Several Slits; the Diffraction Grating
Problems
APPENDIX I
Vectors
Vectors and Their Components
Scalar and Vector Products of Two Vectors
The Differentiation of Vectors
The Divergence Theorem and Stoke's Theorem
Problems
APPENDIX II
Units
APPENDIX III
Fourier Series
Problems
APPENDIX IV
Vector Operations in Curvilinear Coordinates
Gradient
Divergence
Laplacian
Curl
APPENDIX V
Spherical Harmonics
APPENDIX VI
Multipoles
APPENDIX VII
Bessel's Functions
SUGGESTED REFERENCES
INDEX