A Treatise on Electricity and Magnetism, Volume 2

Front Cover
Clarendon, 1937 - Electricity - 23 pages
0 Reviews

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

MAGNETISM CHAPTER I
1
Action of magnets on one another Law of magnetic force
2
Definition of magnetic units and their dimensions
3
Nature of the evidence for the law of magnetic force
4
Effects of breaking a magnet
5
Theory of magneticmatter
6
Magnetization is of the nature of a vector
7
Meaning of the term Magnetic Polarization
8
Electric potential
287
Magnetic action of a currentsheet with closed currents
288
Magnetic potential due to a currentsheet
289
Induction of currents in a sheet of infinite conductivity
290
Theory of a plane currentsheet
291
Action of a variable magnetic system on the sheet
293
When there is no external action the currents decay and their magnetic action diminishes as if the sheet had moved off with constant velocity R
294
The currents excited by the instantaneous introduction of a magnetic system produce an effect equivalent to an image of that system
295

Properties of a magnetic particle
9
Potential of a magnet of finite size Two expressions for this potential corresponding respectively to the theory of polariza tion and to that of magnetic...
10
Investigation of the action of one magnetic particle on another
11
Particular cases
13
Potential energy of a magnet in any field of force
15
On the magnetic moment and axis of a magnet
17
Magnetic force in a cylindric cavity in a magnet uniformly
23
Vectorpotential of magnetic induction
29
tends at the point
35
The potential at a point on the positive side of a shell of strength t exceeds that on the nearest point on the negative side by 4 w
36
Complex lamellar distribution
37
Vectorpotential of a lamellar magnet
38
On the solid angle subtended at a given point by a closed curve
39
The solid angle expressed by the length of a curve on the sphere
40
FI expressed as a determinant
41
The solid angle is a cyclic function
42
Theory of the vectorpotential of a closed curve
43
Potential energy of a magnetic shell placed in a magnetic field
45
CHAPTER IV
47
Magnetic induction in different substances
49
Definition of the coefficient of induced magnetization
50
Faradays method
53
Case of a body surrounded by a magnetic medium
55
Poissons physical theory of the cause of induced magnetism
57
CHAPTER V
59
Case when is large
61
Corresponding case in two dimensions Fig XV
62
Case of a solid sphere the coefficients of magnetization being different in different directions
63
Theory of an ellipsoid acted on by a uniform magnetic force
66
Cases of very flat and of very long ellipsoids
68
Statement of problems solved by Neumann Kirchhoff and Green
72
Method of approximation to a solution of the general problem when K is very small Magnetic bodies tend towards places of most intense magnetic f...
73
On ships magnetism
74
A plane electric circuit A spherical shell An ellipsoidal
75
CHAPTER VI
79
Webers mathematical theory of temporary magnetization
81
Modification of the theory to account for residual magnetization
85
Explanation of phenomena by the modified theory
87
Magnetization demagnetization and remagnetization
90
Effects of magnetization on the dimensions of the magnet
92
Experiments of Joule
93
MAGNETIC MEASUREMENTS 449 Suspension of the magnet
95
Methods of observation by mirror and scale Photographic method
96
Principle of collimation employed in the Kew magnetometer
101
Measurement of the moment of a magnet and of the intensity of the horizontal component of magnetic force
104
Rotation produced by quartz turpentine c independently
105
Observations of deflexion
108
Method of tangents and method of sines
109
Observation of vibrations
110
Elimination of the effects of magnetic induction
112
Statical method of measuring the horizontal force
114
Bifilar suspension
115
System of observations in an observatory
119
Observation of the dipcircle
120
Art Page
123
CHAPTER VIII
129
The solar and lunar variations
135
The action of this current compared with that of a magnetic
141
Reaction on the circuit
147
The wire is urged from the side on which its magnetic action
153
His method of experimenting
159
tralize each other
160
Kinematics analysis of the phenomena 454
163
Final expressions for electromagnetic force between two ele
173
ON THE INDUCTION OF ELECTRIC CURRENTS Art Fane 528 Faradays discovery Nature of his methods
175
The method of this treatise founded on that of Faraday
176
Phenomena of magnetoelectric induction
178
General law of induction of currents
179
Induction by the motion of the earth
180
The electromotive force due to induction does not depend on the material of the conductor
181
It has no tendency to move the conductor
182
Use of the galvanometer to determine the timeintegral of the electromotive force
184
Conjugate positions of two coils
185
Mathematical expression for the total current of induction
186
Faradays conception of an electrotonic state
188
The law of Lenz and Neumanns theory of induction
189
Helmholtzs deduction of induction from the mechanical action of currents by the principle of conservation of energy
190
Thomsons application of the same principle
191
Webers contributions to electrical science
193
CHAPTER IV
195
Difference between this case and that of a tube containing a current of water
196
An electric current has energy which may be called electro kinetic energy
197
Lagranges method furnishes appropriate ideas for the study of the higher dynamical sciences
199
Degrees of freedom of a connected system
200
Generalized meaning of velocity
201
Work done by a small impulse
203
Hamiltons equations of motion
205
Kinetic energy in terms of the velocities and momenta 7
206
Relations between Tf and Tp and q
207
Moments and products of inertia and mobility
208
Necessary conditions which these coefficients must satisfy
209
CHAPTER VI
211
Work done by electromotive force
212
The most general expression for the kinetic energy of a system including electric currents
213
The electrical variables do not appear in this expression
214
Mechanical force acting on a conductor
215
The part depending on products of ordinary velocities and strengths of currents does not exist
216
Another experimental test
218
Discussion of the electromotive force
221
Art Page 578 The electrokinetic energy of a system of linear circuits
223
Electromotive force in each circuit
224
Electromagnetic force
225
Case of two circuits
226
Mechanical action between the circuits
227
All the phenomena of the mutual action of two circuits depend on a single quantity the potential of the two circuits
228
The electrokinetic momentum of the secondary circuit
229
Expressed as a lineintegral
230
A crooked portion of a circuit equivalent to a straight portion
231
Electrokinetic momentum at a point expressed as a vector 51
232
Its relation to the magnetic induction SB Equations A
233
Justification of these names
234
Theory of a sliding piece
235
Electromotive force due to the motion of a conductor
236
Electromagnetic force on the sliding piece
237
General equations of electromotive force B
238
Analysis of the electromotive force
240
The general equations referred to moving axes
241
The motion of the axes changes nothing but the apparent value of the electric potential
243
Electromagnetic force on an element of a conducting body Equations C
244
CHAPTER IX
247
Equations of magnetization D
249
Equations of electric currents E
250
Equations of electric displacement F
252
Equations of electric conductivity G
253
Volumedensity of free electricity J
254
Electric currents in terms of electrokinetic momentum
255
Vectorpotential of electric currents
256
Quaternion expressions for electromagnetic quantities
257
Quaternion equations of the electromagnetic field
258
Appendix to Chapter IX
259
CHAPTER X
263
Fifieen relations among these quantities
264
Dimensions in terms of and m
265
Reciprocal properties of the two systems
266
Dimensions of the twelve quantities in the two systems
267
Practical system of electric units Table of practical units
268
Art Pg
270
The force acting on a particle of a substance due to its magnet
276
Force acting on a conductor carrying a current
282
Definition of a currentsheet
286
Trail of images formed by a magnetic system in continuous motion
296
Mathematical expression for the effect of the induced currents
297
Value of the force acting on the magnetic pole 29S 666 Case of curvilinear motion
299
Theory of Aragos rotating disk
300
Trail of images in the form of a helix
303
Spherical currentsheets
304
The vectorpotential
305
To produce a field of constant magnetic force within a spherical shell
306
Currents parallel to a plane
307
Bhell
308
A solenoid
310
A pair of induction coils
311
Proper thickness of wire
312
An endless solenoid
313
CHAPTER XIII
315
fi83 The external magnetic action of a cylindric wire depends only on the whole current through it
316
The vectorpotential
317
Repulsion between the direct and the return current
318
Selfinduction of a wire doubled on itself
320
Relation between the electromotive force and the total current
322
Geometrical mean distance of two figures in a plane
324
Particular cases
326
Application of the method to a coil of insulated wires
328
CHAPTER XIV
331
Solid angle subtended by a circle at any point
333
Potential energy of two circular currents
334
Moment of the couple acting between two coils
335
Values of P
336
Calculation of the coefficients for a coil of finite section
337
Potential of two parallel circles expressed by elliptic integrals
338
Alt Page 702 Lines of force round a circular current Fig XVIII
340
Differential equation of the potential of two circles
341
Approximation when the circles are very near one another
342
Further approximation
343
Coil of maximum selfinduction
345
Appendix I
347
Appendix II
350
CHAPTER XV
351
Construction of a standard coil
352
Mathematical theory of the galvanometer
353
Principle of the tangent galvanometer and the sine galvano meter
354
Gaugains eccentric suspension
356
Galvanometer with four coils
357
Galvanometer with three coils
358
Proper thickness of the wire of a galvanometer
359
Sensitive galvanometers
360
Law of thickness of the wire
361
Galvanometer with wire of uniform thickness
364
Thomsons sensitive coil
365
Determination of magnetic force by means of suspended coil and tangent galvanometer
366
Webers electrodynamometer
367
Joules currentweigher
371
Suction of solenoids
372
Electrodynamometer with torsionarm
373
CHAPTER XVI
374
Motion in a logarithmic spiral 375
375
Rectilinear oscillations in a resisting medium
376
Values of successive elongations
377
Determination of the logarithmic decrement
378
Determination of the time of vibration from three transits
379
Two series of observations
380
Dead beat galvanometer
381
To measure a constant current with the galvanometer
382
Best method of introducing the current
383
Measurement of a current by the first elongation
384
Method of multiplication for feeble currents
385
Measurement of a transient current by first elongation
386
Correction for damping
387
Series of observations Zuriickwerfungsmethode
388
If terms involving products of velocities and currents existed they would introduce electromotive forces which are not ob served 221
390
CHAPTER XVII
392
Determination of gl
393
Determination of the mutual induction of two coils
395
Determination of the selfinduction of a coil
397
Comparison of the selfinduction of two coils
398
Appendix to Chapter XVII
399
Definition of resistance
402
Webers method by transient currents
404
His method of observation
405
Thomsons method by a revolving coil
408
Mathematical theory of the revolving coil
409
Calculation of the resistance
410
Corrections
411
CHAPTER XIX
413
The ratio of the units is a velocity
414
Current by convection
415
Weber and Kohlrauschs method
416
Thomsons method by separate electrometer and electrodyna mometer
417
Maxwells method by combined electrometer and electrodyna mometer
418
Electromagnetic measurement of the capacity of a condenser Jenkins method
419
Method by an intermittent current
420
Condenser and Wippe as an arm of Wheatstones bridge
421
Correction when the action is too rapid
423
Capacity of a condenser compared with the selfinduction of a coil
425
Coil and condenser combined
427
Electrostatic measure of resistance compared with its electro magnetic measure
430
Comparison of the properties of the electromagnetic medium with those of the medium in the undulatory theory of light
431
Energy of light during HB propagation
432
Equation of propagation of an electromagnetic disturbance
433
Solution when the medium is a nonconductor
434
Characteristics of wavepropagation
435
Comparison of this velocity with that of light
436
The specific inductive capacity of a dielectric is the square of its index of refraction
437
Theory of plane waves
438
The electric displacement and the magnetic disturbance are in the plane of the wavefront and perpendicular to each other
439
Energy and stress during radiation
440
Pressure exerted by light
441
Equations of motion in a crystallized medium
442
Propagation of plane waves
444
The theory agrees with that of Fresnel
445
Comparison with facts
446
Solution of the equations when the medium is a conductor
447
Characteristics of diffusion
448
Rapid approximation to an ultimate state
449
CHAPTER XXI
451
The rotation of the plane of polarization by magnetic action
452
Verdets discovery of negative rotation in ferromagnetic media
453
The velocity of a circularlypolarized ray is different according
455
Hypothesis of molecular vortices
461
Note on a mechanical theory of molecular vortices
468
Theory of a current in a perfectly conducting circuit
474
Webers theory of diamaguetism
475
Theory of a perfect conductor
476
Mechanical action of magnetic force on the current which it excites
477
Modifications of Webers theory
478
Consequences of the theory
479
Potential function due to a straight current It is a function
480
Relative motion of four electric particles Fechners theory
481
Two new forms of Amperes formula
482
These are due to Gauss and to Weber respectively
483
Webers formula is consistent with this principle but that of Gauss is not
484
Potential of two currents
485
Webers theory of the induction of electric currents
486
Segregating force in a conductor
487
Case of moving conductors
488
The formula of Gauss leads to an erroneous result
489
Theory of Riemann
490
Theory of Betti
491
Repugnance to the idea of a medium
492

Other editions - View all

Bibliographic information