This classic introduction to electromagnetic fields, thoroughly revised in 1964 and available here in a one-volume edition, includes a self-contained section on quantum theory. Problems with solutions. 148 illustrations.
The definitive translation of a scientific classic, this volume includes a valuable self-contained section on quantum theory. Based on research by science historian Gerald Holton, the text explains Maxwell's and Dirac's field equations and contains a profound discussion and elegant use of the Helmholtz theorem on vector fields. Problems with solutions. 148 illustrations. 1964 edition.
Richard Becker (1887-1955) was a German theoretical physicist who made contributions to the fields of thermodynamics, statistical mechanics, superconductivity, and quantum electrodynamics. A student of Max Born and Albert Einstein, he received his PhD under the tutelage of Max Planck.
PART A. Introduction to vector and tensor calculus
Chapter AI. Vectors
1 Definition of a vector
2 Addition and subtraction of vectors
3 "Unit vectors, base vectors, components"
4 The inner or scalar product
5 The outer or vector product
6 Products of three and four vectors
7 Differentiation of vectors with respect to a parameter
Chapter AII. Vector fields
8 Definition of a vector field
9 The space derivative of a field quantity. The gradient
10 The strength of a source field and its divergence. Gauss's theorem and Green's theorem
11 The line integral and the curl. Stokes's theorem
12 Calculation of a vector field from its sources and vortices
13 Orthogonal curvillinear coordinates
Chapter AIII. Tensors
14 Definition of a tensor. The anti-symmetric tensor
15 The symmetric tensor and its invariants. The deviator
PART B. The Electrostatic field
Chapter BI. Electric charge and the electrostatic field in vacuum
16 Electric charge
17 The elementary electrical quantum
18 Electric field strength and the electric potential
19 Coulomb's law. The flux of electric force
20 The distribution of electricity on conductors
21 The capacitance of spherical and parallel-plate capacitors
22 The prolate ellipsoid of revolution
23 Induced charges
24 The electric field at a great distance from field-producing charges. The dipole and quadrupole field
Chapter BII. Electrostatics of dielectrics
25 The parallel-plate capacitor with dielectric insulation
26 Dielectric polarization
27 The fundamental equations of electrostatics for insulators. The Maxwell displacement vector
28 Point charge opposite a semi-infinite dielectric
29 Dielectric sphere in a uniform field
30 The homogeneously polarized ellipsoid
Chapter BIII. Force effects and energy relations in the electrostatic field
31 Systems of point charges in free space
32 Field energy when conductors and insulators are present. Thomson's theorem
33 Thermodynamical considerations of the field energy
34 Force effects in the electrostatic field calculated by means of the field energy; several simple examples
35 General calculation of the force on an insulator in an electric field
36 The Maxwell stresses
37 Electric force effects in homogeneous liquids and gases
PART C. Electric current and the magnetic field
Chapter CI. The law of the electric current
38 Current strength and currrent density
39 Ohm's law
40 Joule heating
41 Impressed forces. The galvanic chain
42 Inertia effects of electrons in metals
Chapter CII. Force effects in the magnetic field
43 The magnetic field vectors
44 The force on a current-carrying conductor. The Lorentz force
45 The Faraday law of induction
Chapter CIII. Magnetic fields of currents and permanent magnets
46 The magnetic field of steady currents. Oersted's law
47 The ring current as a magnetic dipole
48 Magnetization and magnetic susceptibility
Chapter CIV. Electrodynamics of quasi-stationary currents
49 Self-induction and mutual induction
50 Circuit with resistance and self-inductance. The vector diagram
51 "Circuit with resistance, self-inductance and capacitance"
52 The energy theorem for a system of linear currents
PART D. The general fundamental equations of the electromagnetic field
Chapter DI. Maxwell's theory for stationary media
53 Completing the Maxwell equations
54 The energy theorem in Maxwell's theory. The Poynting vector
55 Magnetic field energy. Forces in the magnetic field
56 The momentum theorem in Maxwell's theory. The momentum density of the radiation field
Chapter DII. Electromagnetic waves
57 Electromagnetic waves in a vacuum
58 Plane waves in stationary homogeneous media
59 The reflection of electromagnetic waves at boundary surfaces
60 Current displacement or the skin effect
61 Electromagnetic waves along ideal conductors
62 Waves along wires of finite resistance
63 Waves in hollow conductors
Chapter DIII. The electromagnetic field of a given distribution of charge and current
64 The field of uniformly moving charged particle
65 Energy and momentum for a uniformly moving charged particle
66 The electromagnetic potential of an arbitrary distribution of charge and current
67 The Hertz solution for the oscillating dipole
68 The radiation of electromagnetic waves by an emitter
69 The field of an arbitrarily moving point charge
Chapter DIV. The field equations in slowly moving non-magnetic media
70 Derivation of the field equations
71 Experimental confirmation of the basic equations
72 Fizeau's investigation
73 The Michelson experiment
74 Search for an explanation of the negative result of the Michaelson experiment
PART E. The theory of relativity
Chapter EI. The physical basis of relativity theory and its mathematical aids
75 Revision of the space-time concept
76 The Lorentz transformation
77 Consequences of the Lorentz transformation
78 Programme of the special theory of relativity
79 The general Lorentz group
80 Four-vectors and four-tensors
Chapter EII. The relativistic electrodynamics of empty space
81 The field equations
82 The force density
83 The energy-momentum tensor of the electromagnetic field
84 The plan light-wave
85 The radiation field of a moving electron
Chapter EIII. The relativistic electrodynamics of material bodies
86 The field equation
87 The moments tensor
88 Unipolar induction
Chapter EIV. Relativistic mechanics
89 The mechanics of mass points
90 The inertia of energy
91 Mechanical stresses
PART F. Exercise problems and solutions
Chapter FI. Exercises
A. Vector and tensor calculus
B. The electrostatic field
C. The electric current and the magnetic field
D. The fundamental equations of the electromagnetic field
E. Relativity theory
Chapter FII. Solutions
A. Vector and tensor calculus
B. The electrostatic field
C. The electric current and the magnetic field
D. The fundamental equations of the electromagnetic field
E. Relativity theory
PART G. List of formulae
Chapter GI. Vector and tensor calculus
1 Vector algebra
2 Vector analysis
3 Tensor algebra
Chapter GII. Electrodynamics
1 The field equations and the constitutive equations
2 The material constants
3 Energy and force expressions
4 Wave propagation
5 Electrotechnical concepts
6 Conversion table from MKSA units to the Gaussian system
Chapter GIII. Relativity theory
Index