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Part I Electrodynamics: Phenomenological Approach |
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3 | (74) |
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1.1 Electrostatic Field in Vacuum |
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3 | (23) |
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3 | (1) |
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4 | (1) |
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1.1.3 Electrostatic Field Strength |
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5 | (1) |
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6 | (1) |
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1.1.5 Flux of the Electrostatic Field |
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7 | (2) |
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1.1.6 Electrostatic Field Potential |
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9 | (2) |
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1.1.7 Equipotential Surfaces |
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11 | (1) |
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1.1.8 Equations of the Electrostatic Potential |
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12 | (5) |
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1.1.9 Electrostatic Field Energy |
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17 | (2) |
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1.1.10 Electrostatic Dipole |
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19 | (3) |
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1.1.11 Electrostatic Multipoles |
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22 | (4) |
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1.2 Electrostatic Field in Polarized Media |
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26 | (7) |
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1.2.1 Dielectric Polarization |
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26 | (1) |
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1.2.2 Gauss's Law for Dielectric Media |
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27 | (1) |
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1.2.3 Types of Dielectrics |
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28 | (2) |
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1.2.4 Jump Conditions for the Components of the Fields E and D |
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30 | (3) |
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1.3 Special Methods of Solving Problems in Electrostatics |
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33 | (20) |
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1.3.1 Method of Electric Images |
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34 | (7) |
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1.3.2 Integration of the Laplace Equation by the Method of Separation of Variables |
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41 | (6) |
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1.3.3 Two-Dimensional Electrostatic Problems and Conformal Mapping |
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47 | (6) |
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1.4 Mechanical Action of the Electrostatic Field on Dielectric Media. Electrostriction |
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53 | (5) |
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58 | (16) |
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74 | (3) |
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2 Fields of Stationary Currents |
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77 | (38) |
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2.1 Magnetostatic Field in Vacuum |
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77 | (20) |
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2.1.1 Stationary Electric Current |
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77 | (1) |
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78 | (6) |
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2.1.3 Magnetic Field of a Stationary Electric Current |
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84 | (2) |
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86 | (3) |
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2.1.5 Ampere's Circuital Law |
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89 | (2) |
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2.1.6 Vector Potential of the Field of a Stationary Current |
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91 | (1) |
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2.1.7 Energy of the Magnetic Field of Stationary Currents |
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92 | (2) |
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2.1.8 Magnetic Multipoles |
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94 | (3) |
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2.2 Magnetostatic Field in Magnetized Media |
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97 | (7) |
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2.2.1 Polarized Magnetic Media |
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97 | (2) |
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2.2.2 Types of Magnetizable Media |
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99 | (3) |
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2.2.3 Jump Conditions for the Components of the Fields H and B |
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102 | (2) |
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104 | (9) |
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113 | (2) |
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3 The Electromagnetic Field |
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115 | (54) |
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3.1 Maxwell's Equations in Vacuum |
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115 | (5) |
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3.1.1 Maxwell--Ampere Equation |
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115 | (2) |
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3.1.2 Maxwell--Faraday Equation |
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117 | (3) |
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3.2 Maxwell's Equations for Polarizable Media |
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120 | (9) |
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3.2.1 Source-free Equations |
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123 | (1) |
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3.2.2 Equations with Sources |
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123 | (6) |
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129 | (1) |
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3.4 Electromagnetic Field Energy. Poynting's Theorem |
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130 | (2) |
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3.5 Uniqueness of the Solutions of Maxwell's Equations |
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132 | (2) |
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3.6 Electromagnetic Momentum. Momentum Theorem |
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134 | (2) |
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3.7 Electromagnetic Angular Momentum. Angular Momentum Theorem |
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136 | (1) |
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3.8 Electrodynamic Potentials |
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137 | (1) |
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3.9 Differential Equations for the Electrodynamic Potentials |
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138 | (5) |
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3.9.1 Gauge Transformations |
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141 | (2) |
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3.10 Different Types of Electrodynamic Potentials |
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143 | (3) |
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143 | (1) |
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3.10.2 Hertz's Vector Potential |
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144 | (2) |
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3.11 Electrodynamic Potentials and the Analytical Derivation of Some Fundamental Equations |
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146 | (5) |
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3.11.1 Analytical Derivation of the Equation of Motion of a Point Charge in an External Electromagnetic Field |
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147 | (1) |
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3.11.2 Analytical Derivation of Maxwell's Equations |
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148 | (3) |
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3.12 Electromagnetic Field Equations for Moving Media |
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151 | (8) |
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3.12.1 Source-free Equations |
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151 | (5) |
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156 | (3) |
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159 | (8) |
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167 | (2) |
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169 | (130) |
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4.1 Conductors, Semiconductors, Dielectrics |
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169 | (2) |
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4.2 Propagation of Electromagnetic Waves in Dielectric Media |
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171 | (7) |
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173 | (2) |
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4.2.2 Transversality of Electromagnetic Waves |
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175 | (2) |
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4.2.3 Electromagnetic Theory of Light |
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177 | (1) |
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4.3 Polarization of the Electromagnetic Waves |
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178 | (5) |
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4.4 Reflection and Refraction of Plane Electromagnetic Waves |
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183 | (8) |
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4.4.1 Laws of Reflection and Refraction |
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185 | (1) |
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186 | (5) |
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4.5 Propagation of Electromagnetic Waves in Massive Conductors. Skin Effect |
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191 | (4) |
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4.6 Propagation of Electromagnetic Waves in Semiconductors |
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195 | (2) |
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4.7 Propagation of Electromagnetic Waves in Anisotropic Media |
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197 | (9) |
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4.7.1 Fresnel's Ellipsoid |
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198 | (1) |
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4.7.2 Fresnel's Law of Velocities for Electromagnetic Waves |
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199 | (7) |
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4.8 Dispersion of Electromagnetic Waves |
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206 | (20) |
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4.8.1 Phase Velocity and Group Velocity |
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208 | (6) |
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4.8.2 Classical Theory of Dispersion |
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214 | (5) |
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4.8.3 Kramers--Kronig Dispersion Relations |
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219 | (4) |
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4.8.4 Dispersion in Crystals |
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223 | (3) |
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4.9 Propagation of Electromagnetic Waves in Waveguides |
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226 | (13) |
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4.9.1 Rectangular Waveguides |
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227 | (7) |
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4.9.2 Circular Waveguides |
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234 | (3) |
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237 | (2) |
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4.10 Electromagnetic Radiation |
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239 | (12) |
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4.10.1 Solutions of the Electrodynamic Potential Equations |
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239 | (10) |
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4.10.2 Wiechert--Lienard Potentials |
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249 | (2) |
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4.11 Potentials of a Time-Variable Continuous Charge Distribution |
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251 | (31) |
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4.11.1 Electric Dipole Radiation |
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257 | (6) |
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4.11.2 The Centre-Fed Thin Linear Antenna |
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263 | (19) |
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282 | (14) |
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296 | (3) |
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5 Elements of Magnetofluid Dynamics |
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299 | (36) |
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5.1 Basic Equations of Magnetofluid Dynamics |
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300 | (3) |
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5.2 Freezing-In of Magnetic Field Lines |
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303 | (1) |
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5.3 Magnetohydrodynamic Waves |
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304 | (5) |
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5.4 Some Problems of Magnetohydrostatics |
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309 | (6) |
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5.4.1 Magnetic Thermal Insulation. The Pinch Effect |
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310 | (3) |
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313 | (2) |
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315 | (15) |
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330 | (5) |
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Part II Relativistic Formulation of Electrodynamics |
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6 Special Theory of Relativity |
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335 | (42) |
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6.1 Experimental Basis of Special Relativity |
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335 | (9) |
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6.1.1 Aberration of Light |
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337 | (1) |
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338 | (2) |
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6.1.3 Fizeau's Experiment |
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340 | (1) |
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6.1.4 Michelson--Morley Experiment |
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341 | (3) |
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6.2 Principles of Special Relativity |
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344 | (9) |
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6.2.1 Einstein's Postulates |
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344 | (3) |
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347 | (6) |
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6.3 Some Consequences of the Lorentz Transformations |
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353 | (13) |
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6.3.1 Relativity of Simultaneity |
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353 | (3) |
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356 | (2) |
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358 | (2) |
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6.3.4 Relativistic Doppler Effect |
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360 | (4) |
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6.3.5 Composition of Velocities and Accelerations |
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364 | (2) |
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366 | (9) |
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375 | (2) |
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377 | (60) |
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7.1 Time-Like and Space-Like Intervals |
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379 | (2) |
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7.2 Various Representations of Minkowski Space |
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381 | (6) |
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7.2.1 Euclidean-Complex Representation |
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381 | (3) |
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7.2.2 Hyperbolic Representation |
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384 | (3) |
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387 | (10) |
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7.3.1 Euclidean-Complex Representation |
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387 | (2) |
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7.3.2 Hyperbolic Representation |
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389 | (2) |
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391 | (6) |
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7.4 Relativistic Kinematics |
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397 | (2) |
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7.5 Relativistic Dynamics in Three-Dimensional Approach |
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399 | (6) |
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7.5.1 Notions, Quantities, and Fundamental Relations |
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399 | (3) |
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7.5.2 Variation of Mass with Velocity |
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402 | (2) |
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7.5.3 Relationship Between Mass and Energy |
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404 | (1) |
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7.6 Relativistic Dynamics in Four-Dimensional Approach |
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405 | (6) |
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7.6.1 Hamilton--Jacobi Equation |
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407 | (1) |
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408 | (1) |
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7.6.3 Angular Momentum Four-Tensor |
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408 | (3) |
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7.7 Some Applications of Relativistic Mechanics |
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411 | (14) |
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7.7.1 Collision Between Two Particles |
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411 | (7) |
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418 | (2) |
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420 | (5) |
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425 | (8) |
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433 | (4) |
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8 Relativistic Formulation of Electrodynamics in Minkowski Space |
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437 | (74) |
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8.1 Point Charge in Electromagnetic Field |
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437 | (4) |
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8.1.1 Three-Dimensional Approach |
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437 | (1) |
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438 | (3) |
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8.2 Electromagnetic Field Tensor |
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441 | (9) |
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8.2.1 Gauge Invariance of Fμv |
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443 | (1) |
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8.2.2 Lorentz Transformations of the Electromagnetic Field |
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444 | (1) |
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8.2.3 Invariants of the Electromagnetic Field |
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445 | (5) |
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8.3 Covariant Form of the Equation of Continuity |
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450 | (3) |
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8.4 Covariant Form of Maxwell's Equations |
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453 | (5) |
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8.4.1 Maxwell's Equations for Vacuum |
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453 | (3) |
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8.4.2 Maxwell's Equations for Media |
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456 | (2) |
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8.5 Covariant Form of Constitutive Relations |
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458 | (5) |
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8.5.1 Relation Between Fμv and Gμv |
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459 | (2) |
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8.5.2 Covariant Form of Ohm's Law |
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461 | (2) |
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8.6 Four-Potential and Its Differential Equations |
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463 | (4) |
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8.7 Conservation Laws of Electrodynamics in Covariant Formulation |
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467 | (19) |
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469 | (3) |
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8.7.2 Energy-Momentum Tensor |
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472 | (4) |
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8.7.3 Angular Momentum Tensor |
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476 | (2) |
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8.7.4 Belinfante Energy-Momentum Tensor |
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478 | (1) |
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8.7.5 Energy-Momentum Tensor of the Electromagnetic Field |
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478 | (4) |
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8.7.6 Laws of Conservation of Electromagnetic Field in the Presence of Sources |
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482 | (4) |
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8.8 Elements of Relativistic Magnetofluid Dynamics |
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486 | (4) |
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8.8.1 Fundamental Equations |
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486 | (2) |
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8.8.2 Bernoulli's Equation in Relativistic Magnetofluid Dynamics |
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488 | (2) |
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490 | (16) |
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506 | (5) |
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Part III Introduction to General Relativity 9 General Theory of Relativity |
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511 | (80) |
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9.1 Classical Theory of Gravitation |
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512 | (3) |
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9.2 Principles of General Relativity |
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515 | (2) |
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517 | (3) |
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9.4 Covariant Derivatives |
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520 | (10) |
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9.4.1 Levi-Civita Connection |
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520 | (5) |
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9.4.2 Transformation Properties of the Connection Coefficients |
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525 | (2) |
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9.4.3 Other Connections and the Torsion Tensor |
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527 | (3) |
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9.5 Equations of Electrodynamics in the Presence of Gravitation |
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530 | (3) |
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9.5.1 Maxwell's Equations |
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530 | (2) |
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9.5.2 Equation of Continuity |
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532 | (1) |
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9.5.3 Equation of Motion of a Point Charge |
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532 | (1) |
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9.6 Riemann Curvature Tensor |
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533 | (4) |
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537 | (9) |
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9.8 Central Gravitational Field. Schwarzschild Metric |
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546 | (6) |
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9.9 Other Solutions of Einstein's Equations |
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552 | (8) |
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9.10 Tests of General Relativity |
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560 | (18) |
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9.10.1 Precession of the Perihelion of Planets |
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560 | (4) |
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9.10.2 Deflection of Light by the Sun |
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564 | (2) |
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9.10.3 Gravitational Redshift |
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566 | (2) |
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9.10.4 Gravitational Time Delay |
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568 | (3) |
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9.10.5 Gravitational Waves |
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571 | (7) |
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578 | (11) |
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589 | (2) |
Appendix A Vectors and Vector Analysis |
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591 | (12) |
Appendix B Tensors |
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603 | (14) |
Appendix C Representations of Minkowski Space |
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617 | (12) |
Appendix D Curvilinear Coordinates |
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629 | (8) |
Appendix E Dirac's δ-Function |
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637 | (8) |
Appendix F Green's Function |
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645 | (4) |
Bibliography |
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649 | (4) |
Author Index |
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653 | (4) |
Subject Index |
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657 | |