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Chapter 1��Vector analysis 1
1.1 Vector and vector operations 1
1.1.1 Scalar and vector 1
1.1.2 Vector operations 1
1.2 Scalar and vector fields 4
1.2.1 Classification of fields 4
1.2.2 Representation of field 5
1.3 Orthogonal coordinate systems and differential elements 6
1.3.1 Rectangular coordinate system 6
1.3.2 Cylindrical coordinate system 8
1.3.3 Spherical coordinate system 11
1.4 Directional derivative and the gradient of a scalar field 14
1.4.1 Directional derivative 14
1.4.2 The gradient of a scalar field 14
1.5 Flux and divergence of a vector field 18
1.5.1 Flux and flux source 18
1.5.2 Divergence of a vector field 20
1.5.3 Divergence theorem 23
1.6 Circulation and the curl of a vector field 24
1.6.1 Circulation and vortex source 24
1.6.2 The curl of a vector field 25
1.6.3 Stokes’ theorem 28
1.7 Helmholtz theorem 29
1.7.1 Non-divergence field and irrotational field 29
1.7.2 Helmholtz theorem 30
Summary 31
Exercise 33
Chapter 2 Electrostatic field 35
2.1 Coulomb’s law and electric field intensity 35
2.1.1 Coulomb’s law 36
2.1.2 Electric field intensity 36
2.2 Electrostatic field in vacuum 39
2.2.1 Flux and divergence 39
2.2.2 Circulation and curl 41
2.2.3 Basic equations of electrostatic field in vacuum 41
2.3 The electric potential 43
2.3.1 Definition of the electric potential 43
2.3.2 Calculation of the electric potential 44
2.3.3 Electric dipole 45
2.4 Electrostatic field in media 47
2.4.1 Polarization of a dielectric 48
2.4.2 Gauss’s law in a dielectric 49
2.5 Boundary conditions 51
2.5.1 Boundary conditions on the interface between two dielectrics 52
2.5.2 Boundary conditions on the interface between a dielectric and a conductor 53
2.6 Poisson’s equation and Laplace’s equation 55
2.7 Basic theorems of static fields 57
2.7.1 Green’s theorem 57
2.7.2 The uniqueness theorem 57
2.8 Method of images 59
2.8.1 Method of images for conducting planes 60
2.8.2 Method of images for a conducting sphere 62
2.8.3 Method of images for a conducting cylinder 63
2.9 Multi-conductor system and partial capacitance 66
2.9.1 The concept of capacitance 66
2.9.2 Partial capacitance in a multi-conductor system 67
2.10 Electrostatic field energy and electrostatic force 68
2.10.1 Electrostatic energy 69
2.10.2 Electrostatic force 70
2.11 Applications of electrostatic fields 72
Summary 74
Exercises 76
Chapter 3 Steady electric field 83
3.1 Current density 83
3.1.1 Current and current density 83
3.1.2 Current density and charge density 84
3.1.3 Ohm’s law 85
3.1.4 Joule’s law 85
3.2 Basic equations and the electromotive force 86
3.2.1 The equation of current continuity 86
3.2.2 Basic equations of a steady electric field 87
3.2.3 The electromotive force 89
3.3 Boundary conditions 90
3.4 Analogy between a steady electric field and an electrostatic field 92
3.5 Applications of steady electric fields 94
Summary 95
Exercise 96
Chapter 4 Steady magnetic field 99
4.1 Ampere’s force law and magnetic flux density 99
4.1.1 Ampere’s force law 99
4.1.2 The Biot-Savart law 100
4.1.3 Lorentz Force 101
4.2 Fundamental equations of steady magnetic field in vacuum 103
4.2.1 The equation of magnetic flux continuity 103
4.2.2 Ampere’s circuital law 104
4.3 Magnetic vector potential 108
4.3.1 Magnetic vector potential 108
4.3.2 Magnetic dipole 110
4.4 Fundamental equations of steady magnetic field in magnetic medium 111
4.4.1 Magnetization 111
4.4.2 Ampere’s circuital law for magnetic media 114
4.5 Boundary conditions for magnetic fields 116
4.5.1 Boundary conditions at the interface between two magnetic media 116
4.5.2 Boundary conditions for the surface of magnetic materials 118
4.5.3 Boundary conditions expressed by magnetic vector potentials 119
4.6 Magnetic scalar potential 120
4.6.1 Magnetic scalar potential and its equations 120
4.6.2 Multi valuedness of magnetic scalar potential 121
4.7 Inductance 122
4.7.1 Self-inductance and mutual inductance 122
4.7.2 Calculations of self - inductance and mutual inductance 123
4.8 Magnetic energy stored in a magnetic field and magnetic force 126
4.8.1 Magnetic energy stored in a magnetic field 126
4.8.2 Magnetic force 130
4.9 Applications of steady magnetic fields 132
Summary 133
Exercise 135
Chapter 5 Time-varying electromagnetic fields 140
5.1 Faraday’s law of electromagnetic induction 140
5.2 Displacement current 143
5.3 Maxwell’s equations 146
5.3.1 Maxwell’s equations 147
5.3.2 The constitutive equations 147
5.3.3 Maxwell’s equations in a source-free medium 148
5.3.4 Wave equation in a source-free medium 148
5.4 Boundary conditions for time-varying electromagnetic fields 149
5.4.1 Boundary conditions on the interface between two media 149
5.4.2 Boundary conditions for the surface of a perfect conductor 149
5.5 The phasor representation of sinusoidal electromagnetic fields 151
5.5.1 The phasor representation of a sinusoidal field 152
5.5.2 Maxwell’s equations in phasor form 154
5.5.3 Wave equations in phasor form 154
5.5.4 Complex permittivity, complex permeability 155
5.6 Poynting’s theorem and Poynting vector 157
5.6.1 The energy and power of a time-varying electromagnetic field 157
5.6.2 Poynting’s theorem in time domain 158
5.6.3 Poynting’s theorem in phasor form 162
5.7 The dynamic potential of time-varying electromagnetic fields 164
5.7.1 Wave equations in terms of dynamic potential functions 164
5.7.2 The solutions of D’Alembert’s equations 166
5.8 Applications of electromagnetic fields 169
Summary 170
Exercise 172
Chapter 6 Plane wave 176
6.1 Uniform plane wave in an ideal dielectric 176
6.1.1 Equations and solutions of a uniform plane wave 176
6.1.2 Propagation characteristics of a uniform plane wave 178
6.2 Polarization of an electromagnetic wave 183
6.2.1 Linear polarization 183
6.2.2 Circular polarization 184
6.2.3 Elliptical polarization 185
6.3 Uniform plane wave in a conducting medium 189
6.3.1 Wave equations and solutions 189
6.3.2 Propagation characteristics of a uniform plane wave 190
6.4 Normal incidence of a uniform plane wave 195
6.4.1 Conductor-conductor interface 195
6.4.2 Dielectric-perfect conductor interface 197
6.4.3 Dielectric-dielectric interface 199
6.4.4 Dielectric-conductor interface 203
6.5 Oblique incidence of a uniform plane wave 206
6.5.1 Dielectric-dielectric interface 206
6.5.2 Total reflection and total refraction 209
6.5.3 Dielectric-perfect conductor interface 215
6.6 Group velocity 218
6.7 Applications of electromagnetic waves 220
Summary 222
Exercises 225
Appendix A Answers to exercises 230