The Magnetic Circuit in Theory and Practice

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Longmans, 1896 - Electromagnetic theory - 362 pages
 

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Contents

Magnetically Indifferent Toroid
10
Ferromagnetic Toroid Magnetic Induction
12
Saturation Magnetisation
13
Summary
15
Curves of Magnetisation Curves of Induction
16
Susceptibility Permeability Beductivity
19
Perfect and Imperfect Magnetic Circuits
21
ELEMENTARY THEORY OF IMPERFECT MAGNETIC CIRCUITS 16 Action of a Narrow Transverse Cut
23
Shearing Backward Shearing
25
Action at a Distance of a Single End
26
General Remarks about the Law of Action between Points
28
Attraction or Repulsion between the Ends
29
Action at a Distance of a Pair of Ends
30
Mechanical Action of External Fields on Pairs of Ends
31
Demagnetising Action of a Bar
32
Demagnetising Factors of Circular Cylinders
34
The End Elements as Centres of Action at a Distance Hy pothesis of two Fluids
36
Uniform Field Ellipsoid
37
Ellipsoid of Revolution Ovoid Spheroid
38
Further Special Cases Solid Sphere and Solid Cylinder
39
Tabular Summary
40
Graphical Eepresentation
41
Hyperbolic Curves of Magnetisation
42
CHAPTER III
44
Surface Integrals and their Properties
45
Complex Solenoidal Distribution
48
Complex Lamellar Distribution
50
Lamellar Distribution
51
LineIntegrals and their Properties
53
LamellarSolenoidal Distribution
54
Complex LamellarSolenoidal Distribution
55
General Law
56
4A Solenoidal Character of the Electromagnetic Field
57
Magnetic Potential in the Field outside Conductors
58
Action of a Permanent Magnet at External Points
60
Distribution of Magnetic Intensity
62
Potential of a Permanent Magnet
64
Analogy with Gravitation Potential
66
Local Variations of Magnetic Strength as Centres of Magnetic Force
67
Magnetic Intensity and Magnetic Induction within Ferro magnetic Media
69
Magnetic Induction is Distributed Solenoidally
70
CHAPTER IV
73
Kirchhofif s Assumptions
74
ARTICLE PAGE 55 LineIntegral of the Demagnetising Intensity
76
Properties of the Resultant Magnetic Intensity
79
Properties of the Magnetisation
80
Properties of the Resultant Magnetic Induction
82
Practical Approximation
83
Ferromagnetic Body conveying a Current
84
Conservation of the Flow of Induction
85
Refraction of the Lines of Induction
86
Representation of the Field hy means of Unit Tubes
89
Induced Electromotive Force
91
Faradays Lines of Force
92
Statement of the Problem of Magnetisation
95
Similar Systems Lord Kelvins Rules
96
Uniform Magnetisation
98
Magnetisation of an Ellipsoid
99
Further Special Cases
101
Solution by Successive Superposition
103
CHAPTER V
105
Kirchhoff s Theory
106
Rings of Rectangular and of Circular Section
108
Fundamental Equation of a Radially Divided Toroid
109
First Approximation Limiting Case
111
Divergence of the Lines of Induction
114
Leakage Coefficient
116
Magnetic EndElements on the Boundary Surface
117
Second Approximation
118
Toroid with several Radial Slits
119
The Functions v and n are approximately Reciprocal
121
B Experimental 83 The Iron Toroid Examined
123
Standardisation of the Ballistic Galvanometer
124
Tracing the Normal Curve of Magnetisation
125
Arrangement of the Slit
127
The Curves of Magnetisation
129
Discussion of the Principal Results
130
Comparison of Theory and Experiment
134
Empirical Formula for the Leakage
137
GENERAL PROPERTIES OF MAGNETIC CIRCUITS A NonTJniformly Magnetised Rings ARTICLE PAGE 91 General Remarks
141
Experiments of Oberbeck with Local Coils
142
Further Experiments by Von Ettingshausen and Mues
143
Theoretical Explanation of the Experiments
145
SelfCompensating Effect of Leakage
146
Principles of the Method
148
Application to Radially Divided Toroids
150
Graphical Representation Transformation of Curves
151
Second Approximation Correction for Leakage
152
Generalisation of the Method
154
Electromagnetic Stress 101 Specification of the state of Stress
155
Resultant Tension in the Gap
156
Theoretical Lifting Force of a Diametrically Divided Toroid
158
Resolution and Interpretation of Maxwells Equation
160
Magnetic Lifting Force 105 Older Investigations
161
Wassmuths Experiments
162
Bidwells Experiments Sources of Error
163
Bosanquets Experiments
164
Conclusions from Maxwells Law
167
LoadRatio of a Magnet
168
CHAPTER VII
170
Continuation Faraday Maxwell
171
Continuation Lord Kelvin
172
Summary
174
ARTICLE PAGE 115 More Recent Developments Rowland
175
Continuation Bosanquet
176
Armature yielding a Current External Characteristic
192
Investigations of Dr Hopkinson
194
Graphical Construction
195
Experimental Determination of the Leakage
197
Introduction of Magnetic Reluctance
199
Calculation of Air Reluctances
201
Other Determinations of Air Reluctances
203
Influence of the Position of the Brushes
204
Calculation of the Armature Reaction
206
Experiments on Reactions of the Armature
208
Empirical Formulae
209
Frolichs Formula
210
Relation of Frolichs to other Formulae
211
General Arrangement of the Magnetic Circuit
213
Arrangement of the Field Magnets
214
Continuation PolePieces Material
215
Arrangement of the Armature
217
Arrangement of the Interspace
218
Machines with Multiple Magnetic Circuit
219
Diagrams of Various Magnetic Circuits
220
CHAPTER IX
224
Dissipation of Energy by Hysteresis
226
ARTICLE PAGB 149 Influence of Shape Retentivity Coercive Intensity
228
Permanent Magnets
230
Magnetic Reluctance in Joints
232
Influence of Applied Longitudinal Pressure
235
Time Variations of the Magnetic Conditions
236
Discussion of the Function dd
237
Simplification with Constant Selfinduction
239
Influence of Variable SelfInductors
241
Sinusoidal Electromotive Forces
244
Principle of Least Reluctance
245
Mechanisms depending on Electromagnetism
246
Small Iron Sphere in a Magnetic Field
248
Attractive Action of Circular Conductors on Sphere
249
Attractive Action of Coils on Spheres
250
Attractive Action of Coils on Iron Cores
252
Polarised Mechanisms
253
Electromagnets with Large Lifting Power
255
Description of some Types of Electromagnets
256
Electromagnets for producing Strong Fields 167 Review of the Usual Types
258
Principles of Design
261
Description of the Electromagnet
262
Coils of the Electromagnet
263
Method of Investigation
265
Confirmation of the Theory
267
Influence of Leakage
268
Theory of Conical PolePieces
269
Experiments with Truncated Cones
271
Inductors and Transformers 176 Discussion of Mutually Inducing Coils
272
Mutual Induction
273
Action of Induction Coils
275
Magnetic Circuit of Induction Coils
276
Simultaneous Differential Equations of Transformers
277
Action of an Ideal Transformer
279
Influence of Saturation and of Hysteresis
281
Influence of Leakage
282
Transformer Diagrams
283
Core and Shell Transformers
285
Magnetic Circuit of Transformers
286
Eddy Currents Screening Action
287
EXPERIMENTAL DETERMINATION OF FIELD INTENSITY ARTICLE PAGE 188 General Introduction
289
Distribution of Magnetic Fields
290
A Magnetometric Methods 190 Plan of Gausss Method
292
Observations of Deflection
294
Measurement of a Dynamical Force
296
Measurement of a Torque
297
Measurement of a Hydrostatic Pressure
298
Methods of Induction 195 Arrangement of the Exploring Coil
300
Ballistic Galvanometer
301
Standard Flux of Induction
303
Measurement of a Field by Damping
306
Magnetooptical Methods 199 Rotation of the Plane of Polarisation
307
Standard Glass Plates
308
E Halls Phenomenon MagnetoElectrical Alteration of Resistance 201 Halls Phenomenon
310
Measurement of a Field by Bismuth Spirals
311
F MagnetoHydrostatic Method 203 Principle of the Method
314
Practical Execution
315
EXPERIMENTAL DETERMINATION OF MAGNETISATION OR OF INDUCTION 205 General Eemarks
317
Discussion of the Shape of the TestPiece
318
Details of the Method
319
Determination of Distribution
320
A Magnetometric Methods 209 Plan of the Experiments
321
ARTICLK PAGE 211 Heliuholtzs Method Compensating Coil
324
Searles Curve Tracer
325
Eickemeyers Differential Magnetometer
327
Virtual Length of the Magnet
328
Apparatus of Koepsel and of Kennelly
331
Induction Methods 216 The Ballistic Method
332
Isthmus Method
333
Yoke Method
335
Various Forms of Closed Yoke
336
Case of great SelfInduction
337
Methods of J and B Hopkinson and of T Gray
339
Kerrs Phenomenon
340
Kundts Phenomenon
342
Halls Phenomenon Bismuth Spiral
343
F Traction Methods
344
Thompsons Permeameter
345
Magnetic Balance
346
Use of the Balance
349
Magnetohydrostatic Methods
350
Index of Names
353
Index of Subjects
356
Nomenclature
361

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