78 ELECTRICITY LELEUTKOMAGNETIC INDUCTION. which they have rightly dwelt as being in a sense the reverse of the electromagnetic rotations. The following theory of the phenomenon will make this clearer : Referring back to figure 40, let AB be part of a conducting cir cuit arranged as there described, and let it be caused to move in the direction Pp. Then if E be the electromotive force in the circuit in the direction AB, N the number of lines of force passing through the circuit, q> the angle through which AB moves (from X to Y) about OZ, we have, by our general law, dt ~ d<t> dt idN Now, by Ampere s theory, K = -r- > hence (p. 73) If _ K U:^ i di -= - m (cos j8j - cos oj - cos j8 2 -1- cos a.,) . (27). Hence, if the conductor AB be caused to move with given angular velocity about the magnet SN, in that direction which it would take under the action of the magnet if it carried a current i, then there will be an electromotive force of induction along the circuit of which AB forms part, whose direction is opposite to that of i, and whose magni tude is found by dividing the couple acting on AB (when traversed by i) by i, and multiplying it by the given angu lar velocity. This result is a beautiful instance of the law of Lenz. A great variety of experimental arrangements may be imagined to realize the case thus described. Every appa ratus devised to produce an electromagnetic rotation may be used to illustrate it. The following case may be taken as typical. SN (fig. 49) is a bar magnet whose action may be represented by two poles, N and S. At the middle point of its axis is fixed a disc BA, against which presses the terminal of a wire CA in metallic connection with the axis through the pivot at S. If CA be caused to rotate in the direction of the arrow p, the disc standing still, there will be an induced current in CABC in the direction of the arrow q. If CA and the disc revolve together, there will be no current. If CA stand still, and the disc rotate in the direction of the arrow, there will be a current in the opposite direction; for this is clearly the same as if the disc stood still, and CA rotated in the opposite direction. 1 The electromotive force in each case is indepen dent of the form of CA, and is given by i!?)i(l ~coset)a>, where m is the strength of the pole N, a the angle ANB, and u> the angular velocity. It is well to remind the reader that the lines of force are closed curves, every one of which passes up the axis of the magnet from S to N, and back through the outside medium to S. If this be for gotten, and an attempt be made to determine the electromotive force of induction by considering the motion of the disc, an error will easily be made. If we take the simpler course above, and consider the motion of the conductor, there is then no danger of mistake. In most of the experiments we have hitherto been de- with iron scribing, the object has been to obtain indications of the core. direction of the currents of induction, or to measure the electromotive force of induction under definite circum stances ; if, however, we desire to exhibit the effects of induction in a striking manner, in order to convey belief to the spectator, or to serve some practical purpose, recourse is had to a different kind of apparatus. We may wind our primary and secondary coils on bobbins, and insert the former within the latter, so as to get the greatest possible Fig. 49. 1 If the reader wish for a proximate rule for the direction of the electromotive force of induction, the following will serve. Stand with the body in the line of magnetic force with the head pointing in the positive direction, look in the direction in which the part of the circuit on which the feet are is moving ; the E. M. F. along the circuit is towards the right hand. number of turns of wire into proximity. The number of turns on the primary is usually made small, in order that the current in it may not be weakened by a large resist ance, and that its coefficient of self-induction (see below) may be small. Mention has already been made of the effect of soft iron in increasing the number of lines of force that pass through a circuit. It is easy to see that it will produce a corresponding effect in strengthening induction. The precise amount of it is very hard to calculate, owing to the irregularities in the magnetization arid demagnetiza tion that arise from residual magnetism. The question belongs, however, to magnetism. The effect can be de monstrated practically by observing the alteration in the inductive action produced by inserting a bundle of iron wires 2 into our primary coil. The physiological effects of induced currents are very striking; indeed, the nerve and muscle preparation of the physiologist affords a very delicate method for detecting them. If the human body form part of the circuit of the secondary coil of such an induction apparatus as we have just indicated, and the primary current be stopped and started in rapid succession, say by stripping one terminal of the circuit on a toothed wheel attached to the other, a sensation is experienced which, with a moderately powerful apparatus furnished with a core, is so painful and peculiar that the patient is not likely to forget either it or its cause. The tetanic muscular contractions produced in this way have formed the subject of much physiological investiga tion, of which an account will be found in the proper place (see article PHYSIOLOGY). The flat spirals of Henry, formed of flat bands of copper insulated from each other with silk ribbon, are also very convenient for demonstrating the existence of induced currents. The most powerful inductive apparatus for furnishing large quantities of electricity are the various magneto- electric machines which have now been brought to great perfection (see Historical Sketch). By means of these and similar appliances, all the effects of the electric current and the electric discharge may be shown in the greatest perfection. Induction by Discharge of Statical Electricity. The phenomena of induction can be exhibited with the tran- sient current of electricity in the discharge of a Leyden jar or other accumulator of statical electricity. There is a difficulty in exhibiting the effect, owing to the great differ ences of potential between different parts of the circuit, which render the application of a coil of silk-covered wire useless. A common way of getting over the difficulty consists in cutting two spiral grooves in two flat ebonite discs. Wires are embedded in these, and they are then put together with a thin plate of glass between, so that the spirals are opposite each other. When a jar is discharged through one spiral, an induction current passes in the other, and may be indicated by a galvanometer, or. better still, by a frog preparation. The induced current is, however, in general a complicated phenomenon, owing to the oscillatory nature of the discharge (see above, p. G5). It would lead us too far to go into these and kindred subjects : the reader who desires to pursue the matter will find excellent accounts in Mascart, t. ii. 611-825, and Riess, Bd. ii. 780-906. Particularly interesting are the researches of Verdet, an account of which will be found in his works, along with many indications of vjiat others have done in the same field. Induced Currents of Higher Orders, Induced currents may in their turn induce other currents, and these again 2 The iron is broken up into wires to prevent the formation of in duced currents in the body of the metal. These currents retard the rise of the induced currents. Physio logical effects. Indue- statical
charge.