Electricity and Magnetism: An Introduction to the Mathematical Theory

Cover......Page 1
Frontmatter......Page 6
PREFACE......Page 10
Contents......Page 12
Table of Units......Page 16
1·2. Surface and volume integrals......Page 18
1·3. Solid angles......Page 19
1·4. Scalar functions of position and their gradients......Page 21
1·5. A vector field......Page 23
2·1. The electric field......Page 27
2·2. The electric vector......Page 33
2·3. Gauss\'s theorem and its consequences......Page 36
2·4. The potential function......Page 45
2·5. Special fields---point charges......Page 51
2·6. Cavendish\'s experiment......Page 58
Examples......Page 60
3·1. Mechanical force on a charged surface......Page 65
3·3. Condensers......Page 66
3·4. Spherical condenser......Page 68
3·5. Use of Laplace\'s equation......Page 72
3·6. Sets of condensers......Page 74
3·7. Energy of a charged conductor......Page 76
3·8. Approximate expression for capacity......Page 77
3·9. Electrostatic units......Page 78
Examples......Page 83
4·2. Principle of superposition......Page 90
4·3. Coefficients of potential, capacity and induction......Page 92
4·4. Energy of a system of charged conductors......Page 95
4·5. Energy as a quadratic function of charges or potentials......Page 99
4·6. Mechanical forces......Page 100
4·7. Electric screens......Page 103
4·8. Quadrant electrometer......Page 104
4·9. Worked examples......Page 105
Examples......Page 107
5·1. Specific inductive capacity......Page 114
5·2. Electric displacement......Page 115
5·3. The potential......Page 120
5·4. Comparisons......Page 121
Examples......Page 127
6·1. Theorem of the equivalent layer......Page 131
6·2. Images---definition......Page 132
6·3. Sphere and point charge......Page 134
6·4. Evaluation of induced charge......Page 140
6·5. Orthogonal spheres......Page 145
6·6. Field due to an electric doublet......Page 148
6·7. Dielectric problems......Page 151
6·8. Two--dimensional images......Page 155
Examples......Page 158
7·1. Current strength......Page 165
7·2. Electrolysis......Page 167
7·3. Ohm\'s Law......Page 169
7·5. Kirchhoff\'s Laws......Page 173
7·6. Wheatstone\'s bridge......Page 177
7·7. Currents in a network. Reciprocal theorems......Page 180
7·8. Telegraph wire with a `fault\'......Page 183
7·9. Worked examples......Page 185
Examples......Page 188
8·1. Earth\'s magnetic field......Page 197
8·2. Field of a magnetic bipole......Page 199
8·3. Potential energy of a magnetic bipole......Page 203
8·4. Gauss\'s verification of the law of inverse squares......Page 210
8·6. Finite magnets. Intensity of magnetization......Page 214
8·7. Magnetic shells......Page 217
Examples......Page 220
9·11. Magnetic field of a straight current......Page 226
9·2. Comparison with magnetic shell......Page 230
9·3. Parallel straight currents......Page 232
9·4. Field due to a circular current......Page 234
9·5. Potential energy of uniform shell......Page 239
9·6. Mechanical force on a circuit......Page 240
9·8. Tangent galvanometer......Page 245
Examples......Page 250
10·1. Magnetic induction......Page 256
10·2. Continuity of normal induction......Page 259
10·3. Induced magnetism......Page 260
10·4. Equations for the potential......Page 261
10·5. Examples of induced magnetism......Page 263
Examples......Page 267
11·1. Faraday\'s experiments......Page 269
11·2. Law of electromagnetic induction......Page 270
11·3. Self-induction and mutual induction......Page 271
11·4. Single circuit with self-induction......Page 273
11·5. Periodic electromotive force......Page 274
11·6. Circuit containing a condenser......Page 277
11·7. Examples of circuits with inductance......Page 279
Examples......Page 282