Chapter 1 Vector analysis 11.1 Vector and vector operations 11.1.1 Scalar and vector 11.1.2 Vector operations 11.2 Scalar and vector fields 41.2.1 Classification of fields 41.2.2 Representation of field 51.3 Orthogonal coordinate systems and differential elements 61.3.1 Rectangular coordinate system 61.3.2 Cylindrical coordinate system 81.3.3 Spherical coordinate system 111.4 Directional derivative and the gradient of a scalar field 141.4.1 Directional derivative 141.4.2 The gradient of a scalar field 141.5 Flux and divergence of a vector field 181.5.1 Flux and flux source 181.5.2 Divergence of a vector field 201.5.3 Divergence theorem 231.6 Circulation and the curl of a vector field 241.6.1 Circulation and vortex source 241.6.2 The curl of a vector field 251.6.3 Stokes’ theorem 281.7 Helmholtz theorem 291.7.1 Non-divergence field and irrotational field 291.7.2 Helmholtz theorem 30Summary 31Exercise 33Chapter 2 Electrostatic field 352.1 Coulomb’s law and electric field intensity 352.1.1 Coulomb’s law 362.1.2 Electric field intensity 362.2 Electrostatic field in vacuum 392.2.1 Flux and divergence 392.2.2 Circulation and curl 412.2.3 Basic equations of electrostatic field in vacuum 412.3 The electric potential 432.3.1 Definition of the electric potential 432.3.2 Calculation of the electric potential 442.3.3 Electric dipole 452.4 Electrostatic field in media 472.4.1 Polarization of a dielectric 482.4.2 Gauss’s law in a dielectric 492.5 Boundary conditions 512.5.1 Boundary conditions on the interface between two dielectrics 522.5.2 Boundary conditions on the interface between a dielectric and a conductor 532.6 Poisson’s equation and Laplace’s equation 552.7 Basic theorems of static fields 572.7.1 Green’s theorem 572.7.2 The uniqueness theorem 572.8 Method of images 592.8.1 Method of images for conducting planes 602.8.2 Method of images for a conducting sphere 622.8.3 Method of images for a conducting cylinder 632.9 Multi-conductor system and partial capacitance 662.9.1 The concept of capacitance 662.9.2 Partial capacitance in a multi-conductor system 672.10 Electrostatic field energy and electrostatic force 682.10.1 Electrostatic energy 692.10.2 Electrostatic force 702.11 Applications of electrostatic fields 72Summary 74Exercises 76Chapter 3 Steady electric field 833.1 Current density 833.1.1 Current and current density 833.1.2 Current density and charge density 843.1.3 Ohm’s law 853.1.4 Joule’s law 853.2 Basic equations and the electromotive force 863.2.1 The equation of current continuity 863.2.2 Basic equations of a steady electric field 873.2.3 The electromotive force 893.3 Boundary conditions 903.4 Analogy between a steady electric field and an electrostatic field 923.5 Applications of steady electric fields 94Summary 95Exercise 96Chapter 4 Steady magnetic field 994.1 Ampere’s force law and magnetic flux density 994.1.1 Ampere’s force law 994.1.2 The Biot-Savart law 1004.1.3 Lorentz Force 1014.2 Fundamental equations of steady magnetic field in vacuum 1034.2.1 The equation of magnetic flux continuity 1034.2.2 Ampere’s circuital law 1044.3 Magnetic vector potential 1084.3.1 Magnetic vector potential 1084.3.2 Magnetic dipole 1104.4 Fundamental equations of steady magnetic field in magnetic medium 1114.4.1 Magnetization 1114.4.2 Ampere’s circuital law for magnetic media 1144.5 Boundary conditions for magnetic fields 1164.5.1 Boundary conditions at the interface between two magnetic media 1164.5.2 Boundary conditions for the surface of magnetic materials 1184.5.3 Boundary conditions expressed by magnetic vector potentials 1194.6 Magnetic scalar potential 1204.6.1 Magnetic scalar potential and its equations 1204.6.2 Multi valuedness of magnetic scalar potential 1214.7 Inductance 1224.7.1 Self-inductance and mutual inductance 1224.7.2 Calculations of self - inductance and mutual inductance 1234.8 Magnetic energy stored in a magnetic field and magnetic force 1264.8.1 Magnetic energy stored in a magnetic field 1264.8.2 Magnetic force 1304.9 Applications of steady magnetic fields 132Summary 133Exercise 135Chapter 5 Time-varying electromagnetic fields 1405.1 Faraday’s law of electromagnetic induction 1405.2 Displacement current 1435.3 Maxwell’s equations 1465.3.1 Maxwell’s equations 1475.3.2 The constitutive equations 1475.3.3 Maxwell’s equations in a source-free medium 1485.3.4 Wave equation in a source-free medium 1485.4 Boundary conditions for time-varying electromagnetic fields 1495.4.1 Boundary conditions on the interface between two media 1495.4.2 Boundary conditions for the surface of a perfect conductor 1495.5 The phasor representation of sinusoidal electromagnetic fields 1515.5.1 The phasor representation of a sinusoidal field 1525.5.2 Maxwell’s equations in phasor form 1545.5.3 Wave equations in phasor form 1545.5.4 Complex permittivity， complex permeability 1555.6 Poynting’s theorem and Poynting vector 1575.6.1 The energy and power of a time-varying electromagnetic field 1575.6.2 Poynting’s theorem in time domain 1585.6.3 Poynting’s theorem in phasor form 1625.7 The dynamic potential of time-varying electromagnetic fields 1645.7.1 Wave equations in terms of dynamic potential functions 1645.7.2 The solutions of D’Alembert’s equations 1665.8 Applications of electromagnetic fields 169Summary 170Exercise 172Chapter 6 Plane wave 1766.1 Uniform plane wave in an ideal dielectric 1766.1.1 Equations and solutions of a uniform plane wave 1766.1.2 Propagation characteristics of a uniform plane wave 1786.2 Polarization of an electromagnetic wave 1836.2.1 Linear polarization 1836.2.2 Circular polarization 1846.2.3 Elliptical polarization 1856.3 Uniform plane wave in a conducting medium 1896.3.1 Wave equations and solutions 1896.3.2 Propagation characteristics of a uniform plane wave 1906.4 Normal incidence of a uniform plane wave 1956.4.1 Conductor-conductor interface 1956.4.2 Dielectric-perfect conductor interface 1976.4.3 Dielectric-dielectric interface 1996.4.4 Dielectric-conductor interface 2036.5 Oblique incidence of a uniform plane wave 2066.5.1 Dielectric-dielectric interface 2066.5.2 Total reflection and total refraction 2096.5.3 Dielectric-perfect conductor interface 2156.6 Group velocity 2186.7 Applications of electromagnetic waves 220Summary 222Exercises 225Appendix A Answers to exercises 230
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