THE DEGREE ENGINEERING SERIES: ELECTROSTATICS
Part 1 ELECTROSTATICS: BASIC PRINCIPLES 1 1 VECTOR ANALYSIS 3 11 Introduction 3 12 Vector Notation 4 13 Vector Algebra 5 14 Coordinate Systems 8 15 Differential Volume, Surface, and Line Elements 11 16 Vector Fields 13 17 Transformations Between Coordinate Systems 14 18 Problems and Solutions: Vector Analysis 15 References 22 2 COULOMB FORCES AND ELECTRIC FIELD INTENSITY 23 21 Coulomb’s Law 24 22 Electric Field Intensity 27 23 Charge Distributions 28 24 Standard Charge Configurations 32 25 Problems: Coulomb Force and E-Field Intensity 33 References 36 3 ELECTRIC FLUX AND GAUSS’ LAW 37 31 Net Charge in a Region 37 32 Electric Flux and Flux Density 38 33 Gauss’ Law 40 34 Relation Between Flux Density and Electric Field Intensity 41 35 Special Gaussian Surfaces 42 36 Problems and Solutions: Electric Flux and Gauss’ Law 44 References 47 4 DIVERGENCE AND THE DIVERGENCE THEOREM 49 41 Divergence 49 42 Divergence in Cartesian Coordinates 50 43 Divergence of D 52 44 The Del Operator 53 45 Divergence Theorem 54 46 Problems and Solutions: Divergence and the Divergence Theorem 55 References 56 5 ENERGY AND ELECTRIC POTENTIAL OF CHARGE SYSTEMS 57 51 Work Done in Moving a Point Charge 57 52 Electric Potential Between Two Points 59 53 Potential of a Point Charge 60 54 Potential of a Charge Distribution 61 55 Gradient 63 56 Relationship Between E and ? 65 57 Energy in Static Electric Fields 66 58 Problems and Solutions : Energy and Electric Potential of Charge Systems 68 References 71 6 CURRENT, CURRENT DENSITY, AND CONDUCTORS 73 61 Introduction 73 62 Charges in Motion 74 63 Convection Current Density, J 75 64 Conduction Current Density, J 76 65 Conductivity, ? 77 66 Current, I 78 67 Resistance, R 79 68 Current Sheet Density, K 80 69 Continuity of Current 81 610 Conductor: Dielectric Boundary Conditions 84 611 Problems and Solutions: Current, Current Density, and Conductors 87 References 91 7 CAPACITANCE AND DIELECTRIC MATERIALS 93 71 Polarization P and Relative Permittivity 93 72 Fixed Voltage D and E 95 73 Fixed Charge D and E 96 74 Boundary Conditions at the Interface of Two Dielectrics 97 75 Capacitance 98 76 Multiple-Dielectric Capacitors 99 77 Energy Stored in a Capacitor 100 78 Problems and Solutions: Capacitance and Dielectric Materials 101 References 111 8 LAPLACE’S EQUATION 113 81 Introduction 113 82 Poisson’s Equation and Laplace’s Equation 114 83 Explicit Forms of Laplace’s Equation 114 84 Uniqueness Theorem 116 85 Mean Value and Maximum Value Theorems 117 86 Cartesian Solution in One Variable 117 87 Cartesian Product Solution 119 88 Cylindrical Product Solution 121 89 Spherical Product Solution 124 810 Problems and Solutions: Laplace’s Equation 125 References 127 Part 2 MAGNETOSTATICS: BASIC PRINCIPLES 129 9 AMPERE’S LAW AND THE MAGNETIC FIELD 131 91 Magnetostatics 131 92 Biot-Savart Law 131 93 Ampere’s Law 134 94 Curl 134 95 Current Density J and ? × H 138 96 Magnetic Flux Density B 138 97 Vector Magnetic Potential A 140 98 Stokes’ Theorem 143 99 Problems and Solutions 144 References 151 10 FORCES AND TORQUES IN MAGNETIC FIELDS 153 101 Magnetic Force on Particles 153 102 Electric and Magnetic Fields Combined 155 103 Magnetic Force on a Current Element 157 104 Work and Power 158 105 Torque 161 106 Magnetic Moment of a Planar Coil 162 107 Problems and Solutions 164 References 169 11 INDUCTANCE AND MAGNETIC CIRCUITS 171 111 Voltage of Self-Induction 171 112 Inductors and Inductance 172 113 Standard Forms 173 114 Internal Inductance 175 115 Magnetic Circuits 177 116 Nonlinearity of the B-H Curve 178 117 Ampere’s Law for Magnetic Circuits 180 118 Cores with Air Gaps 182 119 Multiple Coils 183 1110 Parallel Magnetic Circuits 183 1111 Problems and Solutions 185 References 190 12 DISPLACEMENT CURRENT AND INDUCED EMF 191 121 Displacement Current 191 122 Ratio of JC to JD 193 123 Faraday’s Law 194 124 Conductors in Motion Through Time-Independent Fields 197 125 Conductors in Motion Through Time-Dependent Fields 198 126 Problems and Solutions 198 References 205