ELKCTUOMAGN Ei IC INDUCTION.] ELECTRICITY 77 current was the same, no matter what the material or thickness of the wire in each spiral. Since in this case the whole resistance of the circuit was always the same, the electromotive force of induction must have been the same. We conclude, therefore, that the electromotive force 1 of induction is independent of the material, and also of the thickness of the wire, so long as the latter is so small that we may consider the wire as a linear circuit. Lenz made quantitative determinations of the induced current by means of the above arrangement. The soft iron keeper, with a coil of n windings, was rapidly detached from the magnet, and the first swing a of a galvanometer in circuit with the coil was measured. The quantity of electricity which passes in the induced current is measured by sin a, provided the whole duration of the current is small compared with the time of oscillation of the galvanometer needle (see art. GALVANO METER). Again, when the keeper is attached to the magnet, very nearly all the lines of magnetic induction 2 pass through the keeper; hence the number of lines of induction which pass through the coil is very nearly proportional to the number of windings, and therefore, if the resistance of the circuit be kept the same, the whole amount of electricity which passes will be proportional to n. In the actual experiment the wire was wound and unwound from the keeper, so that the whole resistance did remain the same. The following is a set of Leuz s results : 3 No. of Windings. 2 4 8 12 16 20 sin 4 0-0491 0-1045 0-2156 0-3319 0-4470 0-5594 Sin a -r n 0-0245 0-0261 0-0270. 0-0276 0-0279 0-0280 The value of s m^a-rn is very nearly constant. It increases a little as the number of windings increases, as ought to be the case, for, although most of the lines of induction pass through the keeper, yet all do not, and a few more are included when the number of turns is increased.
- of Faraday made special investigations in search of the
au - effect of the medium across which induction is exerted. He found 1 that no effect on the integral current was pro duced by inserting shellac, sulphur, copper, &c. between the primary and secondary coils. The insertion of iron or any strongly magnetic body, of course, produces an effect, because the distribution of the lines of magnetic force is thereby altered, and therefore, by our general law, the electromotive force of induction will be correspondingly affected. We conclude, therefore, that the electromotive force of induction is independent of the medium across which it is exerted. 5 It must be remarked, however, that in the case of con ducting media, the statement is subject to a certain limita tion, the nature of which follows from the law of induction itself. For there will be induced currents in the interven ing medium if it be a conductor, and these currents will disturb the lines of force while they continue to flow. These currents are transient, however, so that their integral effect on the number of lines of force passing through the secondary is zero. It is obvious, therefore, that, if we replace " electromotive force" by " time integral of electru- tive force extended over the whole time that the induction currents last," the statement will still be true. The only effect, therefore, of interposed conducting media is on the lime which the induced currents take to rise and fall. er Weber 6 applied his electrodynamometer to test the laws r - of induction. 3. The suspended coil was caused to oscillate when there was no current either in it or in the fixed coil, and the logarithmic decre- 1 Of course, the same is not tnie of the current of induction, which depends on the resistance of the circuit. 4 Iu Maxwell s sense ; we might say "lines of magnetic force" iu Faraday s sense ; see art. MAGNKTISM.
- Wiedemann, Bd. ii. 706. 4 Exp. lies., 1709, &c., 1838.
5 Other investigators have sought for such effects, and some have affirmed their existence; but there is no body of concurrent testimony ou the point. 6 Maasbestimm., 10 and 11, 1816. merit 7 of its oscillations carefully determined. This decrement, due to the friction of the air, &c., was found to be constant for diii erent lengths of the arc of oscillation. The terminals of the suspended coil were next connected so that it formed a closed circuit, and a constant current was sent through the fixed coil. Induction cur rents were now generated in the suspended coil, whose electrody- namic action constantly opposed its motion. It was found that the logarithmic decrement was still constant, but greater than before. Weber therefore concluded that the induced current at each instant was proportional to the velocity of the coil. Since the resistance; does not vary, this is in accordance with the general law. Weber further showed that the induced current is the same whether it is produced by a current in the fixed coil or by a magnet, which exercises the same electromagnetic action as that current on the suspended coil, when the latter is traversed by a current of unit strength. The electrodynamometer may also be used to demonstrate the equality of the whole amounts of electricity which pass in the direct and inverse currents. If the induced currents from a secondary coil whose primary is being "made and broken" be passed through both coils of the instrument, there will be a deflec tion, since the action depends on the square of the current ; but if the induced current be sent through the suspended coil alone, and a constant current be sent through the fixed coil, there will be no deflection, which shows that the quantities of electricity passing ia the alternate currents of the secondary coil are equal and of opposite sign. Felici (1852 and 1859) made an extended series of Felici. experiments on the laws of induction. He used null methods, and his experiments bear a resemblance in some respects to the electrodynamical experiments of Ampere. Maxwell 8 has given a summary of Felici s results. It is found, for instance, that the electromotive force of induc tion of a circuit A on another B is independent of the material or section of the conductors, that it is proportional to the current iu A and to the number of windings in B. The induction of A on B is the same as that of B on A, when the inducing current i is the same in both cases. Any portion of A or B may be replaced by a zig-zag portion, which nowhere deviates far from it. In pairs of circuits geometrically similar, the electromotive force of induction is proportional to the linear dimensions, and so on. If B be so situated with respect to A that starting or stopping a current in A produces no induced current in B, B is said to be con jugate to A. There are an infinite numbei of such conjugate posi tions of B ; and Felici shows that, if B be moved from one of these P! into another P, very quickly, no effect ii produced on the gal vanometer. If B be moved from P t to any position P (not a con jugate position), the effect on the galvanometer is the same as if the current i were suddenly started in A, B being in the position P. All these results are direct consequences of our general law, and indeed might be used as a foundation for it. 9 In his later researches on electromagnetic induction Fara- (series xxvii. and xxix.), Faraday develops in consider- day s ex- able detail his ideas on the connection between the lines I )lonn o of magnetic force and the induced current, and gives iu- ^ l u creased precision to the experimental methods that flow therefrom. He points out the great value of methods, ^uch as the use of iron filings, for exhibiting in a visible form the course of the lines of magnetic force. He also insists on the great use of a small moving circuit, which can be used to explore the magnetic field under circumstances which render the application of other methods impossible. The direction of a line of force may be determined in various ways by mean* of the moving conductor. Maxwell 10 gives four such ways : (1) if a conductor be moved along a line of force parallel to itself, it will experience no electromotive force ; (2) if a conductor carrying a current be free to move along a line of force, it will show no tendency to do so ; (3) if a linear conductor coincide with a line of force and be moved parallel to itself iu any direction, it will experience no electromotive force in the direction of its length ; (4) if a linear conductor carrying an electric current coincide in direction with a line of magnetic induction, it will not experience any mechanical force. In these researches Faraday treats at considerable length Unipolar a case of the induction of electric currents, to which Conti- indue- uet-tal writers have given the somewhat mysterious name tion - of "unipolar induction." It belongs to a class of cases on 7 See art. . 8 Vol. ii. 536 ; see also Wiedem
- See Maxwell, I.e.
ann, Bd. ii. 709.
10 Vol. ii. 597.