Engineering Field Theory (eBook)

Front Cover 1
Engineering Field Theory 4
Copyright Page 5
Table of Contents 6
Preface 14
Part I: 
16 
CHAPTER 1. INTRODUCTION 18
1.1. Inverse square law 18
1.2. Force at a distance 19
1.3. Field theory 19
1.4. Flux theory 20
1.5. Systems of units and dimensions 20
1.6. Vector quantities 23
1.7. Mathematical basis 26
1.8. Summary 27
Problems 27
Part II: 
28 
CHAPTER 2. ELECTRIC FLUX 30
2.1. An imaginary fluid 30
2.2. Coulomb's law 30
2.3. Electric flux 32
2.4. Permittivity 32
2.5. Flux density 33
2.6. Field intensity 
34 
2.7. Principle of superposition 35
2.8. Gauss's law 36
2.9. Field of a line charge 40
2.10. Field of a surface charge 43
2.11. Two parallel surface charges 45
2.12. Summary 46
Problems 47
CHAPTER 3. FLUX FUNCTION 48
3.1. Introduction 48
3.2. Flux tube and flux line 49
3.3. Flux function 50
3.4. Differential relationships 53
3.5. Uniform field 54
3.6. Line charge 55
3.7. Line sink 56
3.8. Line source and line sink 56
3.9. Doublet 59
3.10. Line source and uniform field 61
3.11. Doublet and uniform field 63
3.12. Summary 64
Problems 66
CHAPTER 4. ELECTRICAL MATERIALS 67
4.1. Atomic properties 67
4.2. A conducting medium in a uniform electric field 68
4.3. Charge distribution on a conductor 69
4.4. Field intensity at the surface of a conductor 71
4.5. Force on a charged surface 72
4.6. An insulating medium in a uniform electric field 74
4.7. Relative permittivity 76
4.8. Summary 77
Problems 78
CHAPTER 5. GRAVITATION AND FLUID FLOW 79
5.1. Gravitational flux 79
5.2. Gravitational constant 80
5.3. Gravitational field intensity 80
5.4. Uniform sphere 81
5.5. Fluid field 83
5.6. Bernoulli's equation 84
5.7. Ideal fluid 85
5.8. Gauss's law 87
5.9. Stream function 89
5.10. Velocity 91
5.11. Pressure 93
5.12. Summary 96
Problems 97
CHAPTER 6. MAGNETIC FLUX 99
6.1. Coulomb's law 99
6.2. Flux density 100
6.3. Gauss's law 101
6.4. Magnetic field of an electric current 101
6.5. Force on an electric current 103
6.6. Direction of magnetic forces 104
6.7. Current loop and magnetic dipole 107
6.8. Field intensity 109
6.9. Magnetic materials 109
6.10. Permeability 110
6.11. Magnetization 113
6.12. Summary 113
Problems 114
Part III: 
116 
CHAPTER 7. ELECTRIC POTENTIAL 118
7.1. Electric intensity 118
7.2. Potential function 120
7.3. Absolute potential 122
7.4. Differential relationships 123
7.5. Capacitance 126
7.6. Boundary along an equipotential 127
7.7. Capacitance with mixed dielectric 129
7.8. Boundary along a flux line 131
7.9. Energy 133
7.10. Summary 136
Problems 137
CHAPTER 8. POTENTIAL FUNCTION 138
8.1. Potential function calculations 138
8.2. Point charge 138
8.3. Dipole 140
8.4. Line charge 141
8.5. Line source and line sink 143
8.6. Method of images 145
8.7. Doublet 147
8.8. Doublet and uniform field 150
8.9. Dual 152
8.10. Summary 153
Problems 154
CHAPTER 9. 
156 
9.1. GRAVITATIONAL POTENTIAL 156
9.2. POTENTIAL ENERGY 157
9.3. ELECTRIC CONDUCTION 157
9.4. RESISTANCE 159
9.5. POWER DISSIPATED 159
9.6. CONDUCTIVE HEAT TRANSFER 160
9.7. SURFACE HEAT TRANSFER 162
9.8. FLUID FLOW THROUGH PERMEABLE MEDIA 165
9.9. PERMEABILITY 167
9.10. SUMMARY 169
PROBLEMS 170
CHAPTER 10. FLUID FLOW 172
10.1. Velocity potential 172
10.2. Circulation 173
10.3. Forced vortex 176
10.4. Free vortex 177
10.5. Potential function of a line vortex 179
10.6. Flux function of a line vortex 181
10.7. Doublet 182
10.8. Cylinder rotating in a uniform stream, flux function 183
10.9. Velocity 185
10.10. Rotating cylinder, potential function 186
10.11. Lift 188
10.12. Summary 189
Problems 191
CHAPTER 11. MAGNETIC POTENTIAL 192
11.1. Toroidal coil 192
11.2. Magnetic potential 194
11.3. Circulation 195
11.4. Magnetomotive force 196
11.5. Magnetic circuit calculations 197
11.6. Biot-Savart law 200
11.7. Permanent magnets 202
11.8. Magnet design 204
11.9. Magnet stability 206
11.10. Summary 207
Problems 208
CHAPTER 12. ELECTROMAGNETIC INDUCTION 210
12.1. Faraday's law 
210 
12.2. Inductance 213
12.3. Electric and magnetic forces 214
12.4. Hall effect 215
12.5. Magnetic energy 216
12.6. Force on the pole piece of a magnet 219
12.7. Electromagnetic energy 220
12.8. Analogous electromagnetic relationships 220
12.9. Flux function and potential function 221
12.10. Summary 222
Problems 223
Part IV: 
224 
CHAPTER 13. FREE-HAND SKETCHING 226
13.1. Introduction 226
13.2. Uniform field 226
13.3. Non-uniform field 228
13.4. Field intensity 231
13.5. Mixed media 232
13.6. Corners 233
13.7. Method of construction 235
13.8. Summary 236
Problems 236
CHAPTER 14. NUMERICAL METHODS 238
14.1. Introduction 238
14.2. Laplace's equation 238
14.3. Numerical solution 239
14.4. Finite differences 240
14.5. Matrix formulation 242
14.6. Iterative techniques 243
14.7. Relaxation 245
14.8. Space diagram 246
14.9. Computer techniques 249
14.10. Summary 250
Problem 251
CHAPTER 15. EXPERIMENTAL TECHNIQUES 252
15.1. Introduction 252
15.2. Resistive film 252
15.3. Electrolytic tank 254
15.4. Viscous fluid flow 255
15.5. Real fluid flow 256
15.6. Seepage flow 257
15.7. Membrane analogy 258
15.8. Summary 259
Problem 259
Bibliography 260
FURTHER READING 260
Appendix 1. Physical Constants 261
Appendix 2. Comparative Summary of Relevant Formulae 262
Appendix 3. Notation 264
Index 268