Table of Contents

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

About the Author

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.