Chapter 1 Vector analysis 1.1 Vector and vector operations 1.1.1 Scalar and vector 1.1.2 Vector operations 1.2 Scalar and vector fields 1.2.1 Classification of fields 1.2.2 Representation of field 1.3 Orthogonal coordinate systems and differential elements 1.3.1 Rectangular coordinate system 1.3.2 Cylindrical coordinate system 1.3.3 Spherical coordinate system 1.4 Directional derivative and the gradient of a scalar field 1.4.1 Directional derivative 1.4.2 The gradient of a scalar field 1.5 Flux and divergence of a vector field 1.5.1 Flux and flux source 1.5.2 Divergence of a vector field 1.5.3 Divergence theorem 1.6 Circulation and the curl of a vector field 1.6.1 Circulation and vortex source 1.6.2 The curl of a vector field 1.6.3 Stokes』 theorem 1.7 Helmholtz theorem 1.7.1 Non-divergence field and irrotational field 1.7.2 Helmholtz theorem Summary Exercise Chapter 2 Electrostatic field 2.1 Coulomb』s law and electric field intensity 2.1.1 Coulomb』s law 2.1.2 Electric field intensity 2.2 Electrostatic field in vacuum 2.2.1 Flux and divergence 2.2.2 Circulation and curl 2.2.3 Basic equations of electrostatic field in vacuum 2.3 The electric potential 2.3.1 Definition of the electric potential 2.3.2 Calculation of the electric potential 2.3.3 Electric dipole 2.4 Electrostatic field in media 2.4.1 Polarization of a dielectric 2.4.2 Gauss』s law in a dielectric 2.5 Boundary conditions 2.5.1 Boundary conditions on the interface between two dielectrics 2.5.2 Boundary conditions on the interface between a dielectric and a conductor 2.6 Poisson』s equation and Lace』s equation 2.7 Basic theorems of static fields 2.7.1 Green』s theorem 2.7.2 The uniqueness theorem 2.8 Method of images
2.8.1 Method of images for conducting nes 2.8.2 Method of images for a conducting sphere 2.8.3 Method of images for a conducting cylinder 2.9 Multi-conductor system and partial capacitance 2.9.1 The concept of capacitance 2.9.2 Partial capacitance in a multi-conductor system 2.10 Electrostatic field energy and electrostatic force 2.10.1 Electrostatic energy 2.10.2 Electrostatic force 2.11 Applications of electrostatic fields Summary Exercises Chapter 3 Steady electric field 3.1 Current density 3.1.1 Current and current density 3.1.2 Current density and charge density 3.1.3 Ohm』s law 3.1.4 Joule』s law 3.2 Basic equations and the electromotive force 3.2.1 The equation of current continuity 3.2.2 Basic equations of a steady electric field 3.2.3 The electromotive force 3.3 Boundary conditions 3.4 Analogy between a steady electric field and an electrostatic field 3.5 Applications of steady electric fields Summary Exercise Chapter 4 Steady magnetic field 4.1 Ampere』s force law and magnetic flux density 4.1.1 Ampere』s force law 4.1.2 The Biot-Savart law 4.1.3 Lorentz Force 4.2 Fundamental equations of steady magnetic field in vacuum 4.2.1 The equation of magnetic flux continuity 4.2.2 Ampere』s circuital law 4.3 Magnetic vector potential 4.3.1 Magnetic vector potential 4.3.2 Magnetic dipole 4.4 Fundamental equations of steady magnetic field in magnetic medium 4.4.1 Magnetization 4.4.2 Ampere』s circuital law for magnetic media 4.5 Boundary conditions for magnetic fields 4.5.1 Boundary conditions at the interface between two magnetic media 4.5.2 Boundary conditions for the surface of magnetic materials 4.5.3 Boundary conditions expressed by magnetic vector potentials 4.6 Magnetic scalar potential 4.6.1 Magnetic scalar potential and its equations 4.6.2 Multi valuedness of magnetic scalar potential 4.7 Inductance 4.7.1 Self-inductance and mutual inductance
4.7.2 Calculations of self - inductance and mutual inductance 4.8 Magnetic energy stored in a magnetic field and magnetic force 4.8.1 Magnetic energy stored in a magnetic field 4.8.2 Magnetic force 4.9 Applications of steady magnetic fields Summary Exercise Chapter 5 Time-varying electromagnetic fields 5.1 Faraday』s law of electromagnetic induction 5.2 Discement current 5.3 Maxwell』s equations 5.3.1 Maxwell』s equations 5.3.2 The constitutive equations 5.3.3 Maxwell』s equations in a source-free medium 5.3.4 Wave equation in a source-free medium 5.4 Boundary conditions for time-varying electromagnetic fields 5.4.1 Boundary conditions on the interface between two media 5.4.2 Boundary conditions for the surface of a perfect conductor 5.5 The phasor representation of sinusoidal electromagnetic fields 5.5.1 The phasor representation of a sinusoidal field 5.5.2 Maxwell』s equations in phasor form 5.5.3 Wave equations in phasor form 5.5.4 Complex permittivity, complex permeability 5.6 Poynting』s theorem and Poynting vector 5.6.1 The energy and power of a time-varying electromagnetic field 5.6.2 Poynting』s theorem in time domain 5.6.3 Poynting』s theorem in phasor form 5.7 The dynamic potential of time-varying electromagnetic fields 5.7.1 Wave equations in terms of dynamic potential functions 5.7.2 The solutions of D』Alembert』s equations 5.8 Applications of electromagnetic fields Summary Exercise Chapter 6 Plane wave 6.1 Uniform ne wave in an ideal dielectric 6.1.1 Equations and solutions of a uniform ne wave 6.1.2 Propagation characteristics of a uniform ne wave 6.2 Polarization of an electromagnetic wave 6.2.1 Linear polarization 6.2.2 Circular polarization 6.2.3 Elliptical polarization 6.3 Uniform ne wave in a conducting medium 6.3.1 Wave equations and solutions 6.3.2 Propagation characteristics of a uniform ne wave 6.4 Normal incidence of a uniform ne wave 6.4.1 Conductor-conductor interface 6.4.2 Dielectric-perfect conductor interface 6.4.3 Dielectric-dielectric interface 6.4.4 Dielectric-conductor interface 6.5 Oblique incidence of a uniform ne wave
6.5.1 Dielectric-dielectric interface 6.5.2 Total reflection and total refraction 6.5.3 Dielectric-perfect conductor interface 6.6 Group velocity 6.7 Applications of electromagnetic waves Summary Exercises Appendix A Answers to exercises
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