Introduction to Classical Electrodynamics, Volume 1

Preface ix

Chapter 1. Electrostatic Field in Vacuum 1

1.1. Electric charges 1

1.2. Electrostatic force 2

1.3. Electric field 12

1.4. Electric potential 28

1.5. Equipotential surfaces 35

1.6. Gauss' law 39

1.7. Electric field across a charged sheet 57

1.8. Model of the hydrogen atom 63

Chapter 2. Conductors in Electrostatic Equilibrium 67

2.1. Conductors 67

2.2. Electrostatic equilibrium 68

2.3. Electrostatic pressure 74

2.4. Influence between conductors at electrostatic equilibrium 77

2.5. Capacitors 88

2.6. Energy stored in a capacitor 106

2.7. Forces of attraction between the armatures of a capacitor 109

Chapter 3. Electrokinetics 117

3.1. Conduction in solids 117

3.2. Current density and intensity 118

3.3. Conservation of charge 124

3.4. Kirchhoff's first law and approximation of quasi-stationary regimes 126

3.5. Conduction model for charged gas 127

3.6. Resistance 136

3.7. Direct current circuits 143

3.8. Relaxation time 161

3.9. Earth atmosphere as a spherical capacitor 170

3.10. Space charge 172

Chapter 4. Magnetic Field in Vacuum 179

4.1. Force on a mobile charge 179

4.2. Magnetic field, Biot and Savart law 187

4.3. Conservation of magnetic flux 202

4.4. Laplace force 204

4.5. Ampère's theorem 212

4.6. Magnetic field continuity at a sheet interface 220

4.7. Potential vector 222

4.8. Magnetic scalar potential 235

Chapter 5. Electric and Magnetic Moments 239

5.1. Electric dipole 239

5.2. Electric multipole moments 245

5.3. Magnetic dipole moment 261

Chapter 6. Boundary Problems for Static Potentials in Vacuum 275

6.1. Introduction 275

6.2. 1D Laplace equation 277

6.3. 2D Laplace equation 278

6.4. 3D Laplace equation 351

References 371

Index 377