This advanced undergraduate- and graduate-level text by the 1988 Nobel Prize winner establishes the subject's mathematical background, reviews the principles of electrostatics, then introduces Einstein's special theory of relativity and applies it throughout the book in topics ranging from Gauss' theorem and Coulomb's law to electric and magnetic susceptibility.
Author(s): Melvin Schwartz, Physics
Series: Dover Books on Physics
Publisher: Dover Publications
Year: 1987
Language: English
Pages: 368
Tags: Физика;Электродинамика / Электричество и магнетизм;
Front Matter......Page 1
Preface......Page 3
Table of Contents......Page 5
1. Mathematical Review and Survey of Some New Mathematical Ideas......Page 9
1.1 Vectors in Three Dimensions; A Review of Elementary Notions......Page 10
1.2 The Transformation Properties of Vectors under Spatial Rotation......Page 11
1.3 Differentiation of Vectors with Respect to Time and Position; The "DEL" Operator nabla as a Vector......Page 20
1.4 The Notion of Flux; Divergence of a Vector Field; Gauss' Theorem......Page 22
1.5 The Curl of a Vector Function of Space; Stokes' Theorem......Page 26
1.6 Tensors of the Second Rank......Page 29
1.7 Diagonalizing a Second-Rank Symmetric Tensor......Page 32
Problems......Page 34
2.1 Introduction; Coulomb's Law......Page 36
2.2 The Divergence of E; Gauss' Law......Page 38
2.3 A Few Words about Materials; Conductors......Page 41
2.4 The Conservative Nature of Electrostatics; Potential......Page 44
2.5 Some Important Theorems about Potential Functions; Boundary Conditions and Uniqueness......Page 50
2.6 Electric Dipole Moment; Polarization; Displacement Field......Page 53
2.7 The Energy of a Charge Distribution......Page 59
2.8 The General Theory of Capacitance......Page 62
2.9 Cylindrical and Spherical Coordinates......Page 70
2.10 Solving Laplace's Equation in Cartesian Coordinates......Page 77
2.11 Solving Laplace's Equation in Cylindrical Coordinates......Page 81
2.12 The Solution to Laplace's Equation in Spherical Coordinates......Page 86
2.13 Solving Boundary-Value Problems in Spherical Coordinates with Azimuthal Symmetry......Page 91
2.14 The Multipole Expansion of an Azimuthally Symmetrical Charge Distribution......Page 98
2.15 The Interaction Energy of Two Nonoverlapping Azimuthally Symmetric Charge Distributions; Determination of Nuclear Shape......Page 102
2.16 The Electrostatic Stress Tensor......Page 105
Problems......Page 108
3.1 Introduction; The Michelson-Morley Experiment......Page 113
3.2 The Lorentz Transformation......Page 118
3.3 Charge Density and Current Density as Components of a Four-Vector......Page 129
3.4 There Must Be a "Magnetic Field"! the Requirement of Lorentz Invariance Implies a Vector Potential......Page 131
3.5 The Electric and Magnetic Fields as Elements of a Second-Rank Tensor......Page 134
3.6 Maxwell's Equations......Page 139
Problems......Page 145
4. Time-Independent Current Distributions; Magnetostatics......Page 147
4.1 An Elementary Derivation of OHM'S Law......Page 148
4.2 Finding the Magnetic Field through the Vector Potential......Page 149
4.3 The Biot-Savart Law......Page 153
4.4 Ampere's Law......Page 156
4.5 B as the Gradient of a Potential Function......Page 157
4.6 Magnetization M and the H Field......Page 161
4.7 The Energy of a Static Current Distribution; Force and Torque on a Magnetic Dipole......Page 170
4.8 The Motion of a Charged Particle in a Constant Magnetic Field......Page 176
4.9 The Motion of a Charged Particle in Crossed Electric and Magnetic Fields......Page 178
4.10 Larmor Precession in a Magnetic Field......Page 180
4.11 A Method of Measuring g - 2......Page 182
4.12 The Magnetic Stress Tensor......Page 187
Problems......Page 190
5. The Variation of the Electromagnetic Field with Time: Faraday's Law, Displacement Currents, the Retarded Potential......Page 194
5.1 Faraday's Law......Page 195
5.2 The Conservation of Energy; The Poynting Vector......Page 203
5.3 Momentum Conservation in Electromagnetism......Page 205
5.4 Electromagnetic Mass......Page 208
5.5 The Displacement Current......Page 211
5.6 The Four-Vector Potential and How it is Modified Now That Currents and Charges are Changing with Time......Page 213
Problems......Page 216
6. Let There Be Light!......Page 220
6.1 A New Way of Calculating Retarded Potentials in an Intuitively Appealing Manner......Page 221
6.2 The Potentials of a Small Moving Charge Lienard-Wiechert Potentials......Page 222
6.3 Differentiating the Lienard-Wiechert Potentials; The Radiation Field......Page 224
6.4 Energy Radiation: Nonrelativistic Treatment......Page 228
6.5 Polarization......Page 230
6.6 The Scattering of Radiation by a Free Electron......Page 231
6.7 Mathematical Supplement: Completeness and Orthogonality......Page 232
6.8 Mathematical Supplement: Fourier Series and Fourier Integral......Page 233
6.9 The Interaction of Radiation with a Charge in a Harmonic Potential......Page 237
Problems......Page 239
7. The Interaction of Radiation with Matter......Page 242
7.1 The Absorption and Reflection of Radiation by an Idealized Conducting Sheet with No Magnetization......Page 243
7.2 We Allow the Conductor to Have Magnetic Permeability mu......Page 256
7.3 The Physical Origin of the Refractive Index......Page 258
7.4 What Happens When n < 1? Phase Velocity and Group Velocity......Page 261
7.5 The Index of Refraction in Terms of the Forward-Scattering Amplitude......Page 264
7.6 The Faraday Effect......Page 266
7.7 We Remove the Requirement of Normal Incidence; Fresnel's Equations; Total Internal Reflection......Page 273
Problems......Page 278
8.1 A General Statement of the Problem......Page 281
8.2 Electric Dipole Radiation......Page 284
8.3 Magnetic Dipole and Electric Quadrupole Radiation......Page 288
8.4 We Reexamine the Passage of Radiation through Matter......Page 295
8.5 Interference Phenomena from an Array of Discrete Dipoles; The Notion of Coherence......Page 297
8.6 Frauenhofer Diffraction by a Slit; Scattering by a Disk; The Diffraction Grating......Page 301
Problems......Page 309
9. Waveguides and Cavities......Page 312
9.1 The Perfectly Conducting, Rectangular Waveguide......Page 313
9.2 Ideal Rectangular Cavities......Page 320
9.3 Loss in the Cavity Walls; The Notion of Q in General and as Applied to Our Cavity......Page 323
Problems......Page 327
10. Electric and Magnetic Susceptibility......Page 329
10.1 The Electric Polarizability of Nonpolar Molecules Having Spherical Symmetry......Page 330
10.2 The Relation between Atomic Polarizability and Electric Susceptibility......Page 332
10.3 Polarizability as a Second-Rank Tensor......Page 333
10.4 The Polarizability of a Polar Molecule......Page 335
10.5 Diamagnetism......Page 338
10.6 Paramagnetism and Ferromagnetism......Page 341
Problem......Page 345
Tables......Page 346
C......Page 348
D......Page 349
E......Page 350
F......Page 351
I......Page 352
L......Page 353
M......Page 354
O......Page 355
Q......Page 356
S......Page 357
V......Page 358
W......Page 359
Preface......Page 3
Table of Contents......Page 5
1. Mathematical Review and Survey of Some New Mathematical Ideas......Page 9
1.1 Vectors in Three Dimensions; A Review of Elementary Notions......Page 10
1.2 The Transformation Properties of Vectors under Spatial Rotation......Page 11
1.3 Differentiation of Vectors with Respect to Time and Position; The "DEL" Operator nabla as a Vector......Page 20
1.4 The Notion of Flux; Divergence of a Vector Field; Gauss' Theorem......Page 22
1.5 The Curl of a Vector Function of Space; Stokes' Theorem......Page 26
1.6 Tensors of the Second Rank......Page 29
1.7 Diagonalizing a Second-Rank Symmetric Tensor......Page 32
Problems......Page 34
2.1 Introduction; Coulomb's Law......Page 36
2.2 The Divergence of E; Gauss' Law......Page 38
2.3 A Few Words about Materials; Conductors......Page 41
2.4 The Conservative Nature of Electrostatics; Potential......Page 44
2.5 Some Important Theorems about Potential Functions; Boundary Conditions and Uniqueness......Page 50
2.6 Electric Dipole Moment; Polarization; Displacement Field......Page 53
2.7 The Energy of a Charge Distribution......Page 59
2.8 The General Theory of Capacitance......Page 62
2.9 Cylindrical and Spherical Coordinates......Page 70
2.10 Solving Laplace's Equation in Cartesian Coordinates......Page 77
2.11 Solving Laplace's Equation in Cylindrical Coordinates......Page 81
2.12 The Solution to Laplace's Equation in Spherical Coordinates......Page 86
2.13 Solving Boundary-Value Problems in Spherical Coordinates with Azimuthal Symmetry......Page 91
2.14 The Multipole Expansion of an Azimuthally Symmetrical Charge Distribution......Page 98
2.15 The Interaction Energy of Two Nonoverlapping Azimuthally Symmetric Charge Distributions; Determination of Nuclear Shape......Page 102
2.16 The Electrostatic Stress Tensor......Page 105
Problems......Page 108
3.1 Introduction; The Michelson-Morley Experiment......Page 113
3.2 The Lorentz Transformation......Page 118
3.3 Charge Density and Current Density as Components of a Four-Vector......Page 129
3.4 There Must Be a "Magnetic Field"! the Requirement of Lorentz Invariance Implies a Vector Potential......Page 131
3.5 The Electric and Magnetic Fields as Elements of a Second-Rank Tensor......Page 134
3.6 Maxwell's Equations......Page 139
Problems......Page 145
4. Time-Independent Current Distributions; Magnetostatics......Page 147
4.1 An Elementary Derivation of OHM'S Law......Page 148
4.2 Finding the Magnetic Field through the Vector Potential......Page 149
4.3 The Biot-Savart Law......Page 153
4.4 Ampere's Law......Page 156
4.5 B as the Gradient of a Potential Function......Page 157
4.6 Magnetization M and the H Field......Page 161
4.7 The Energy of a Static Current Distribution; Force and Torque on a Magnetic Dipole......Page 170
4.8 The Motion of a Charged Particle in a Constant Magnetic Field......Page 176
4.9 The Motion of a Charged Particle in Crossed Electric and Magnetic Fields......Page 178
4.10 Larmor Precession in a Magnetic Field......Page 180
4.11 A Method of Measuring g - 2......Page 182
4.12 The Magnetic Stress Tensor......Page 187
Problems......Page 190
5. The Variation of the Electromagnetic Field with Time: Faraday's Law, Displacement Currents, the Retarded Potential......Page 194
5.1 Faraday's Law......Page 195
5.2 The Conservation of Energy; The Poynting Vector......Page 203
5.3 Momentum Conservation in Electromagnetism......Page 205
5.4 Electromagnetic Mass......Page 208
5.5 The Displacement Current......Page 211
5.6 The Four-Vector Potential and How it is Modified Now That Currents and Charges are Changing with Time......Page 213
Problems......Page 216
6. Let There Be Light!......Page 220
6.1 A New Way of Calculating Retarded Potentials in an Intuitively Appealing Manner......Page 221
6.2 The Potentials of a Small Moving Charge Lienard-Wiechert Potentials......Page 222
6.3 Differentiating the Lienard-Wiechert Potentials; The Radiation Field......Page 224
6.4 Energy Radiation: Nonrelativistic Treatment......Page 228
6.5 Polarization......Page 230
6.6 The Scattering of Radiation by a Free Electron......Page 231
6.7 Mathematical Supplement: Completeness and Orthogonality......Page 232
6.8 Mathematical Supplement: Fourier Series and Fourier Integral......Page 233
6.9 The Interaction of Radiation with a Charge in a Harmonic Potential......Page 237
Problems......Page 239
7. The Interaction of Radiation with Matter......Page 242
7.1 The Absorption and Reflection of Radiation by an Idealized Conducting Sheet with No Magnetization......Page 243
7.2 We Allow the Conductor to Have Magnetic Permeability mu......Page 256
7.3 The Physical Origin of the Refractive Index......Page 258
7.4 What Happens When n < 1? Phase Velocity and Group Velocity......Page 261
7.5 The Index of Refraction in Terms of the Forward-Scattering Amplitude......Page 264
7.6 The Faraday Effect......Page 266
7.7 We Remove the Requirement of Normal Incidence; Fresnel's Equations; Total Internal Reflection......Page 273
Problems......Page 278
8.1 A General Statement of the Problem......Page 281
8.2 Electric Dipole Radiation......Page 284
8.3 Magnetic Dipole and Electric Quadrupole Radiation......Page 288
8.4 We Reexamine the Passage of Radiation through Matter......Page 295
8.5 Interference Phenomena from an Array of Discrete Dipoles; The Notion of Coherence......Page 297
8.6 Frauenhofer Diffraction by a Slit; Scattering by a Disk; The Diffraction Grating......Page 301
Problems......Page 309
9. Waveguides and Cavities......Page 312
9.1 The Perfectly Conducting, Rectangular Waveguide......Page 313
9.2 Ideal Rectangular Cavities......Page 320
9.3 Loss in the Cavity Walls; The Notion of Q in General and as Applied to Our Cavity......Page 323
Problems......Page 327
10. Electric and Magnetic Susceptibility......Page 329
10.1 The Electric Polarizability of Nonpolar Molecules Having Spherical Symmetry......Page 330
10.2 The Relation between Atomic Polarizability and Electric Susceptibility......Page 332
10.3 Polarizability as a Second-Rank Tensor......Page 333
10.4 The Polarizability of a Polar Molecule......Page 335
10.5 Diamagnetism......Page 338
10.6 Paramagnetism and Ferromagnetism......Page 341
Problem......Page 345
Tables......Page 346
C......Page 348
D......Page 349
E......Page 350
F......Page 351
I......Page 352
L......Page 353
M......Page 354
O......Page 355
Q......Page 356
S......Page 357
V......Page 358
W......Page 359