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Table of Contents:
Preface i  
1  Introduction 1  
2  Mathematical Toolkit 9  
2.1  Scalars, Vectors and Tensors 9  
2.2  Scalar, Vector, and Tensor Fields 16  
2.3  Vector Fields and Integral Theorems 26  
2.3.1  Vector Field of a Conservative Force 31  
2.3.2  Sources and Vortices of Vector Fields I 32  
2.4  The Delta Function 33  
2.4.1  Sources and Vortices of Vector Fields II 37  
3  Fundamentals of Electrostatics 43  
3.1  Fundamental Equations of Electrostatics 44  
3.1.1  The Electrostatic Field 44  
3.1.2  The Electrostatic Potential 49  
3.1.3  Electrostatic Field Energy 53  
3.2  Fields of Bound Charge Distributions 57  
3.2.1  The Electric Dipole 59  
3.2.2  The Multipole Expansion of the Potential 67  
4  Electrostatic Fields 77  
4.1  Uniformly Charged Solid or Hollow Sphere 78  
4.2  The Classical Electron Radius 84  
4.3  Charge Carrying Wire and Coaxial Cable 85  
4.4  Infinitely Extended, Planar Surface Charge 89  
4.5  Uniformly Charged Ring 93  
4.6  Uniformly Charged Disk 101  
5  Conductors in Electrostatic Fields 111  
5.1  Direct Solution of the Poisson Equation 111  
5.1.1  The Radially Symmetric Charge Distribution 112  
5.2  The Ideal Conductor in an Electrostatic Field 115  
5.2.1  Uniqueness of Solutions to the Poisson Equation 118  
5.2.2  Separation of Induction Charges 119  
5.2.3  The Faraday Cage 121  
5.3  The Principle of Image Charges 122  
5.3.1  Point Charge Near a Grounded Metal Plate 122  
5.3.2  Point Charge Near a Grounded Metal Sphere 124  
5.3.3  Metal Sphere in a Homogeneous Electrostatic Field 128  
5.4  Green’s Functions 134  
5.4.1  Point Charge in Front of a Grounded Metal Plate 137  
5.4.2  Point Charge in Front of a Grounded Metal Sphere 140  
6  Electrostatic Fields in Matter 147  
6.1  Dielectric Polarization 148  
6.1.1  Dielectric Displacement 152  
6.1.2  Interfaces of and within Dielectrics 159  
6.2  Insulators in an Electrostatic Field 163  
6.2.1  The Field of a Point Charge in Dielectrics 163  
6.2.2  Insulating Sphere in a Homogeneous Electrostatic Field 169  
6.2.3  Polarized Dielectric Sphere 172  
7  Dielectric Matter 177  
7.1  Field Energy in Dielectric Materials 177  
7.1.1  Field Energy of the Insulator Sphere 179  
7.1.2  Force on Dielectric Materials in an Electrostatic Field 182  
7.2  Properties of Dielectric Matter 185  
7.2.1  Polarizable Gases 186  
7.2.2  Orientational Polarization 189  
7.2.3  Dielectric Behavior of Liquids 194  
7.2.4  Dielectric Behavior of Solids 199  
8  Direct Electric Current 207  
8.1  Charge Conservation and Electrical Circuits 208  
8.1.1  The Continuity Equation 210  
8.1.2  Ohm’s Law and Electrical Power 213  
8.1.3  Simple Electrical Circuits 216  
8.2  Charge Transport in Electrical Conductors 223  
8.2.1  The Drude Model of Conductivity in Metals 223  
8.2.2  Electron-Hole Conduction in Semiconductors 229  
8.2.3  Ionic Conduction in Electrolytes 232  
9  Fundamentals of Magnetostatics 237  
9.1  The Lorentz Force 237  
9.1.1  Force on a Current-Carrying Wire 239  
9.2  Ampère’s Law 240  
9.2.1  Magnetic Field Inside a Current-Carrying Conductor 244  
9.2.2  Magnetic Field of a Current-Carrying Coil 246  
9.3  The Biot-Savart Law 247  
9.3.1  Straight, Infinitely Long, Current-Carrying Wire 249  
9.3.2  Force Between Two Current-Carrying Wires 251  
9.3.3  Magnetic Field of a Current Loop 253  
9.4  Magnetic Fields and Special Relativity 256  
9.4.1  Moving Charges in a Conducting Wire 257  
9.4.2  The Moving Plate Capacitor 259  
9.4.3  Point Charge in Motion 263  
10  Magnetic Moment and Electromagnetic Induction 269  
10.1  Vector Potential and Magnetic Moment 269  
10.1.1  The Magnetic Dipole 275  
10.1.2  Force on a Magnetic Dipole 281  
10.2  Faraday’s Law of Induction 287  
10.2.1  The Hall Effect 288  
10.2.2  A Relativistic Perspective 290  
10.2.3  Lenz’s Law 295  
10.2.4  Self-induction 297  
11  Alternating Electric Current 303  
11.1  The Generation of Alternating Current 303  
11.2  Complex Resistances – Impedances 309  
11.3  Alternating Current Power 313  
11.4  Simple Circuits 320  
11.4.1  Four-Terminal Networks 320  
11.4.2  The Electrical Resonant Circuit 328  
11.5  Effective Resistance and Ampère’s Law 334  
11.5.1  The Frequency Dependence of Effective Resistance 334  
11.5.2  The Extension of Ampère’s Law 338  
12  Magnetism and Matter 341  
12.1  Magnetization 341  
12.1.1  Diamagnetism 347  
12.1.2  Paramagnetism 350  
12.1.3  Ferromagnetism 352  
12.2  Magnetic Fields in Matter 358  
12.2.1  Interfaces of and within Magnetic Materials 358  
12.2.2  The Homogeneously Magnetized Sphere 361  
12.2.3  Magnetic Sphere in a Homogeneous Magnetic Field 367  
13  Electromagnetic Waves I 371  
13.1  Maxwell’s Equations in a Vacuum 371  
13.1.1  Monochromatic Plane Waves 373  
13.1.2  Polarized Plane Waves 376  
13.1.3  Spherical Waves 380  
13.1.4  TE and TM Waves 384  
13.2  Field Energy and Field Momentum 388  
13.2.1  Electromagnetic Energy Density 388  
13.2.2  Electromagnetic Field Momentum 393  
14  Electromagnetic Waves II 397  
14.1  Electromagnetic Waves in Matter 397  
14.1.1  Reflection and Refraction of Light 399  
14.1.2  Electromagnetic Waves in Conductors 404  
14.2  Generation of Electromagnetic Waves 411  
14.2.1  The Oscillating Dipole 412  
14.2.2  Electromagnetic Radiation 423  
Appendix A 427  
Appendix B 443  

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