Electricity and Magnetism: An Introduction to the Mathematical Theory (Cambridge Library Collection - Mathematics)

A. S. Ramsey (1867–1954) was a distinguished Cambridge mathematician and President of Magdalene College. He wrote several textbooks 'for the use of higher divisions in schools and for first-year students at university'. This book on electricity and magnetism, first published in 1937, and based upon his lectures over many years, was 'adapted more particularly to the needs of candidates for Part I of the Mathematical Tripos'. It covers electrostatics, conductors and condensers, dielectrics, electrical images, currents, magnetism and electromagnetism, and magnetic induction. The book is interspersed with examples for solution, for some of which answers are provided. Cover......Page 1 Electricity and Magnetism......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 A textbook on electricity and magnetism first published in 1937, based upon lectures by the distinguished twentieth-century Cambridge mathematician, interspersed with examples for solution, for some of which answers are provided. It covers electrostatics, conductors and condensers, dielectrics, electrical images, currents, magnetism and electromagnetism, and magnetic induction.