Physics of Classical Electromagnetism (eBook)

Minoru Fujimoto is retired Professor of Physics at the University of Guelph, Ontario, Canada.

Contents 5
Preface 10
Steady Electric Currents 12
1.1. Introduction 12
1.2. Standards for Electric Voltages and Current 13
1.3. Ohm Law's and Heat Energy 15
1.4. The Kirchhoff Theorem 19
Electrostatics 24
Electrostatic Fields 25
2.1. Static Charges and Their Interactions 25
2.2. A Transient Current and Static Charges 26
2.3. Uniform Electric Field in a Parallel-Plate Condenser 29
2.4. Parallel and Series Connections of Capacitors 35
2.5. Insulating Materials 36
Exercises 39
The Gauss Theorem 40
3.1. A Spherical Capacitor 40
3.2. A Cylindrical Capacitor 43
3.3. The Gauss Theorem 44
3.4. Boundary Conditions 49
The Laplace-Poisson Equations 53
4.1. The Electrostatic Potential 53
4.2. The Gauss Theorem in Differential Form 54
4.3. Curvilinear Coordinates (1) 56
4.4. The Laplace-Poisson Equations 59
4.5. Simple Examples 63
4.6. The Coulomb Potential 65
4.7. Point Charges and the Superposition Principle 68
The Legendre Expansion of Potentials 74
5.1. The Laplace Equation in Spherical Coordinates 74
5.2. Series Expansion of the Coulomb Potential 76
5.3. LegendreÌs Polynomials 78
5.4. A Conducting Sphere in a Uniform Field 79
5.5. A Dielectric Sphere in a Uniform Field 81
5.6. A Point Charge Near a Grounded Conducting Sphere 82
5.7. A Simple Quadrupole 85
5.8. Associated Legendre Polynomials 86
5.9. Multipole Potentials 89
Electromagnetism 93
The Amp`ere Law 94
6.1. Introduction 94
6.2. The Amp`ere Law 95
6.3. A Long Solenoid 98
6.4. Stokes' Theorem 100
6.5. Curvilinear Coordinates (2) 103
6.6. The Amp`ere Law in Differential Form 105
6.7. The Rowland Experiment 107
Magnetic Induction 110
7.1. Laws of Magnetic Induction 110
7.2. Differential Law of Induction and the Dynamic Electric Field 113
7.3. Magnetic Moments 117
Scalar and Vector Potentials 121
8.1. Magnets 121
8.2. Pohl's Magnetic Potentiometer 123
8.3. Scalar Potentials of Magnets 125
8.4. Vector Potentials 128
8.5. Examples of Steady Magnetic Fields 130
8.6. Vector and Scalar Potentials of a Magnetic Moment 135
8.7. Magnetism of a Bohr's Atom 137
Inductances and Magnetic Energies 141
9.1. Inductances 141
9.2. Self- and Mutual Inductances 144
9.3. Mutual Interaction Force Between Currents 147
9.4. Examples of Mutual Induction 148
Time-Dependent Currents 151
10.1. Continuity of Charge and Current 151
10.2. Alternating Currents 152
10.3. Impedances 154
10.4. Complex Vector Diagrams 156
10.5. Resonances 158
10.6. Four-Terminal Networks 161
Electromagnetic Waves 168
Transmission Lines 169
11.1. Self-Sustained Oscillators 169
11.2. Transmission Lines 171
11.3. Fourier Transforms 173
11.4. Reflection and Standing Waves 175
11.5. The Smith Chart 178
The Maxwell Equations 180
12.1. The Maxwell Equations 180
12.2. Electromagnetic Energy and the Poynting Theorem 183
12.3. Vector and Scalar Potentials 184
12.4. Retarded Potentials 185
12.5. Multipole Expansion 188
Electromagnetic Radiation 192
13.1. Dipole Antenna 192
13.2. Electric Dipole Radiation 192
13.3. The Hertz Vector 196
13.4. A Half-Wave Antenna 200
13.5. A Loop Antenna 201
13.6. Plane Waves in Free Space 203
The Special Theory of Relativity 207
14.1. Newton's Laws of Mechanics 207
14.2. The Michelson-Morley Experiment 208
14.3. The Lorentz Transformation 210
14.4. Velocity and Acceleration in Four-Dimensional Space 212
14.5. Relativistic Equation of Motion 214
14.6. The Electromagnetic Field in Four-Dimensional Space 216
Waves and Boundary Problems 222
15.1. Skin Depths 222
15.2. Plane Electromagnetic Waves in a Conducting Medium 224
15.3. Boundary Conditions for Propagating Waves 226
15.4. Reflection from a Conducting Boundary 227
15.5. Dielectric Boundaries 229
15.6. The Fresnel Formula 231
Guided Waves 234
16.1. Propagation Between Parallel Conducting Plates 234
16.2. Uniform Waveguides 237
16.3. Examples of Waveguides 241
Coherent Waves and Radiation Quanta 248
Waveguide Transmission 249
17.1. Orthogonality Relations of Waveguide Modes 249
17.2. Impedances 251
17.3. Power Transmission Through a Waveguide 255
17.4. Multiple Reflections in a Waveguide 256
Resonant Cavities 259
18.1. SlaterÌs Theory of Normal Modes 259
18.2. The Maxwell Equations in a Cavity 262
18.3. Free and Damped Oscillations 264
18.4. Input Impedance of a Cavity 266
18.5. Example of a Resonant Cavity 269
18.6. Measurements of a Cavity Resonance 271
Electronic Excitation of Cavity Oscillations 274
19.1. Electronic Admittance 274
19.2. A Klystron Cavity 276
19.3. Velocity Modulation 280
19.4. A Reflex Oscillator 282
Dielectric and Magnetic Responses in Resonant Electromagnetic Fields 286
20.1. Introduction 286
20.2. The Kramers-Krönig Formula 287
20.3. Dielectric Relaxation 289
20.4. Magnetic Resonance 294
20.5. The Bloch Theory 296
20.6. Magnetic Susceptibility Measured by Resonance Experiments 298
Laser Oscillations, Phase Coherence, and Photons 300
21.1. Optical Resonators 300
21.2. Quantum Transitions 302
21.3. Inverted Population and the Negative Temperature 305
21.4. Ammonium Maser 306
21.5. Coherent Light Emission from a Gas Laser 307
21.6. Phase Coherence and Radiation Quanta 308
Appendix 310
Mathematical Notes 311
A.1. Orthogonal Vector Space 311
A.2. Orthogonality of Legendre's Polynomials 312
A.3. Associated Legendre Polynomials 314
A.4. Fourier Expansion and Wave Equations 316
A.5. Bessel's Functions 318
References 321
Index 322