A Treatise on Electricity and Magnetism, Volume 2

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Clarendon Press, 1873 - Electricity - 459 pages

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Contents

The solid angle expressed by the length of a curve on the sphere 419 Solid angle found by two lineintegrations 420 II expressed as a determinant
39
The solid angle is a cyclic function 422 Theory of the vectorpotential of a closed curve 423 Potential energy of a magnetic shell placed in a magnetic...
42
INDUCED MAGNETIZATION 424 When a body under the action of magnetic force becomes itself magnetized the phenomenon is called magnetic ...
44
Magnetic induction in different substances
45
Definition of the coefficient of induced magnetization
47
1
48
Mathematical theory of magnetic induction Poissons method 428 Faradays method
49
MAGNETIC PROBLEMS
54
Theory of a hollow spherical shell
56
Case when x is large
58
Corresponding case in two dimensions Fig XV
60
CHAPTER
74
CHAPTER VII
88
Properties of a magnet when acted on by the earth 372 Definition of the axis of the magnet and of the direction
94
magnetic force
95
CONTENTS xxi
97
Balance vertical force magnetometer
118
Gauss calculation of the 24 coefficients of the first four
124
Electromagnetic measure of the current
130
Reaction on the circuit
137
Generality of these laws
143
His method of experimenting
146
The geometrical quantities which determine their relative posi
152
Complete expression for the action between two finite currents
158
INDUCTION OF ELECTRIC CURRENTS Art Page 528 Faradays discovery Nature of his methods
162
The method of this treatise founded on that of Faraday
163
Phenomena of magnetoelectric induction
164
General law of induction of currents
166
Induction by the motion of the earth
167
The electromotive force due to induction does not depend on the material of the conductor
168
Use of the galvanometer to determine the timeintegral of the electromotive force
170
Conjugate positions of two coils
171
Mathematical expression for the total current of induction 540 Faradays conception of an electrotonic state
174
His method of stating the laws of induction with reference to the lines of magnetic force
175
The law of Lenz and Neumanns theory of induction
176
Thomsons application of the same principle
178
CHAPTER IV
180
Difference between this case and that of a tube containing a current of water
181
An electric current has energy which may be called electro kinetic energy
182
Lagranges method furnishes appropriate ideas for the study
184
Hamiltons equations of motion
189
CHAPTER VI
195
Another experimental test
202
Case of two circuits
208
Theory of induced currents
209
Mechanical action between the circuits
210
CHAPTER VIII
211
Any system of contiguous circuits is equivalent to the circuit formed by their exterior boundary
212
A crooked portion of a circuit equivalent to a straight portion
213
Electrokinetic momentum at a point expressed as a vector A
214
Justification of these names
215
Conventions with respect to the signs of translations and rot tions
216
Theory of a sliding piece
217
Electromotive force due to the motion of a conductor
218
Electromagnetic force on the sliding piece 597 Four definitions of a line of magnetic induction
219
Analysis of the electromotive force
222
The general equations referred to moving axes 601 The motion of the axes changes nothing but the apparent value of the electric potential
224
Electromagnetic force on an element of a conducting body Equations C
226
CHAPTER IX
227
Mathematical expression for the effect of the induced currents
269
The vectorpotential
276
A pair of induction coils
282
Kinetic energy of the current
288
Geometrical mean distance of two figures in a plane
294
The electrokinetic energy of a system of linear circuits
300
Potential energy of two circular currents
302
Potential due to a spherical bowl
305
Approximation when the circles are very near one another
310
Sensitive galvanometers
322
Thomsons suspended coil and galvanometer combined
328
Art Page
331
Observation of vibrations
338
Best angle of deflexion of a tangent galvanometer
350
Determination of the mutual induction of two coils
357
CHAPTER XIX
368
Action of magnets on one another Law of magnetic force
373
Definition of magnetic units and their dimensions
374
Nature of the evidence for the law of magnetic force
375
Magnetism as a mathematical quantity
376
The quantities of the opposite kinds of magnetism in a magnet are always exactly equal
377
Effects of breaking a magnet
378
A magnet is built up of particles each of which is a magnet
379
Theory of magnetic matter
380
Magnetization is of the nature of a vector
381
Meaning of the term Magnetic Polarization
382
Properties of a magnetic particle
383
Definitions of Magnetic Moment Intensity of Magnetization and Components of Magnetization
384
Potential of a magnetized element of volume
385
Potential of a magnet of finite size Two expressions for this potential corresponding respectively to the theory of polari zation and to that of magnetic...
386
Investigation of the action of one magnetic particle on another
387
Particular cases
388
Potential energy of a magnet in any field of force
389
On the magnetic moment and axis of a magnet 00 00 ver er er
390
Energy and stress during radiation
391
Equations of motion in a crystallized medium
392
9
394
Comparison with facts
395
Solution of the equations when the medium is a conductor 802 Case of an infinite medium the initial state being given
396
Characteristics of diffusion
397
Rapid approximation to an ultimate state
398
CHAPTER XXI
399
The rotation of the plane of polarization by magnetic action
400
Rotation produced by quartz turpentine c independently of magnetism
401
Kinematical analysis of the phenomena
402
Right and lefthanded rays
403
In media acted on by magnetism the velocity is different for opposite directions of rotation
404
Kinematic equations of circularlypolarized light
405
Kinetic and potential energy of the medium
406
Definition of a magnetic solenoid
407
The magnetic rotation
413
The phenomena of magnetic molecules may be imitated
419
Theory of a molecule with a primitive current
425
Segregating force in a conductor
435
Quantities which enter into Ampères formula
439
Definition of resistance
441
Principle of collimation employed in the Kew magnetometer
451
Elimination of the effects of magnetic induction
457

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Page 432 - Principle!, 2nd edition. something is transmitted from one particle to another at a distance, what is its condition after it has left the one particle and before it has reached the other...
Page 260 - If we differentiate the first of these equations with respect to x, and the second with respect to -y, and add the results, we obtain £f + ».0.
Page 180 - Returning to the phenomena in question, the first thought that arises in the mind is, that the electricity circulates with something like momentum or inertia in the wire, and that thus a long wire produces effects at the instant the current is stopped, which a short wire cannot produce. Such an explanation is, however, at once set aside by the fact, that the same length of wire produces the effects in very different degrees, according as it is simply extended, or made...
Page 432 - In fact, whenever energy is transmitted from one body to another in time, there must be a medium or substance in which the energy exists after it leaves one body and before it reaches the other, for energy, as Torricelli remarked, 'is a quintessence of so subtile a nature that it cannot be contained in any vessel except the inmost substance of material things'.
Page 144 - If the conductor be a rotating disk or a fluid it will move in obedience to this force, and this motion may or may not be accompanied with a change of position of the electric current which it carries. But if the current itself be free to choose any path through a fixed solid conductor or a network of wires, then, when a constant magnetic force is made to act on the system, the path of the current through the conductors is not permanently altered, but after certain transient phenomena, called induction...
Page 402 - This angular velocity cannot be that of any portion of the medium of sensible dimensions rotating as a whole. We must therefore conceive the rotation to be that of very small portions of the medium, each rotating on its own axis.
Page 162 - The experimental investigation by which Ampere established the laws of the mechanical action between electric currents is one of the most brilliant achievements in science. The whole, theory and experiment, seems as if it had leaped, full grown and full armed, from the brain of the

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