The sign + represents the case in which the current is in the direction of the electro-magnetic force.

The phenomenon is due to a modification of the lines of flow of the current under the influence of the magnetic field. Outside this field, if the plate is homogeneous, and has the same thickness throughout, the current at a small distance from the electrodes A and B is uniformly distributed; the lines of flow are parallel to AB, and the equipotential lines are perpendicular to them (Fig. 260).

FIG. 260.

But when the field is set up, the lines of flow and the equipotential lines are deformed in the case of antimony, as shown in

B

FIG. 261.

FIG. 262.

Figs. 261 and 262; the potential of the point a is higher than that of b in the former case, and lower in the latter.

Under the same circumstances the resistance of bismuth increases. This increase of resistance may serve to measure the intensity of the magnetic field.

CHAPTER XXV.

INDUCTION.

287. Induction Currents.-Whenever the flux of magnetic force through a closed circuit is changed, the circuit becomes the seat of a temporary current which lasts as long as the variation of the flux. Such a current is called an induction current or induced current. Induction currents were discovered by Faraday in 1831, and we shall here describe some of his fundamental experiments.

288. Induction by Currents.-A closed circuit, AB (Fig. 263), contains a galvanometer, G ; a second circuit, parallel to the first

for a great part of its length, is connected with a battery, and can be closed or broken, or the current can be reversed at pleasure. The former will be called the induced or secondary circuit, and the latter the inducing or primary circuit.

Every time the battery circuit is closed, the induced circuit AB is traversed by a momentary current in a contrary or inverse direction to that in the parallel portion CD of the inducing circuit. Every time the inducing circuit is broken, the secondary is traversed by a momentary current in the same direction as the inducing current, that is, by a direct current.

Nothing is observable in the induced circuit so long as a steady

current passes through the inducing circuit, and so long as it remains at the same distance. But when the wire CD is brought near AB, or when the current in CD is increased, an inverse induced current is produced in AB; while if the wire CD is moved away or the strength of its current is decreased, a direct induced current is produced.

In short, a current which begins to flow, or increases in strength, or is brought nearer, produces in an adjacent circuit an inverse induced current ; a current which ceases, or diminishes in strength, or is moved away, produces a direct induced current. These currents, which are produced by the influence of other currents, were spoken of by Faraday as currents due to volta-electric induction.

The effects are stronger the nearer are the two wires, and the greater the length of the parallel portions. The experiment is ordinarily made with two coils of insulated wire, one of which (Fig. 264) can be placed inside the other, like A and B.

289. Induction by Magnets. Suppose the coil B (Fig. 264) to be connected with a galvanometer: if a bar magnet is inserted in it, the effects are the same as though a second coil, A, carrying a current, had been put in in place of the magnet. In order to find the direction of the induced current, we may suppose the magnet replaced by the equivalent electro-magnetic cylinder (§ 256). In like manner any increase in the strength of the magnet produces an inverse current, and any diminution a direct current. This action Faraday called magneto-electric induction.

Both effects are obtained simultaneously and with far greater

§ 291.]

Self-Induction.

347

strength by placing a core of soft iron, D, in the inducing coil (Fig. 265). When the current is made, the cylinder of soft iron is magnetised, and the two actions, of the coil and of the magnet, which are evidently in the same direction, are added together. They are also added when the current is broken.

290. Induction by the Action of the Earth. If a closed circuit be displaced or deformed in the magnetic field of the earth so that the number of lines of force passing through it is altered, an induced current is produced, the direction of the current depending upon whether the change of the number of lines of force through the circuit is positive or negative. Thus if a coil, held with its axis in the line of dip, and connected by long wires with a galvanometer, is quickly turned through an angle of 180°, the galvanometer needle is deflected.

A

X

FIG. 265.

K

Y

B

G

E

291. Self-Induction-Extra Current.-Lastly, Faraday showed that any variation in the strength of a current produces in the circuit itself, in which the current passes, an induction current, which is superposed on the principal current, and always opposes the actual variation of strength, tending to weaken a current which is increasing, and to strengthen one that is decreasing. This phenomenon is called the induction of a current on itself, or, more briefly, self-induction, and the resulting current is called an extra current. The effect is especially marked in circuits which contain coils or electro-magnets. In this case the spark, on breaking the circuit, is much stronger and louder than the spark on closing the circuit, and if the body is interposed in the circuit, the extra current may produce strong physiological effects. Faraday used the following method for showing the extra current produced on making and breaking the circuit :

FIG. 266.

A coil, R (Fig. 266), is connected with a battery, E, and a key, K, by which the circuit can be closed or opened, and a galvanometer, G, is connected in multiple arc with the coil, so that the battery-current divides between it and the coil. Let a be the position of equilibrium of the needle under the influence of the current which passes through the galvanometer when the circuit is closed at K, and a stationary condition is established. The needle is kept at the angle a by means of a stop (Fig. 267), which prevents it from going back to zero when the circuit is interrupted. On again closing the circuit, the needle is deflected beyond a, because the "extra current" delays the growth of the current in R, and at first more than the normal proportion flows along AGB.

FIG. 267.

FIG. 268.

α

Next, the stop is placed at o (Fig. 268), so as to keep the needle at o3, while a steady current is again made to traverse the circuit; when the circuit is now broken at K, the needle is deflected in the opposite direction, because the current in the coil continues for an instant to flow after the battery-circuit has been broken. If the original directions were AXYB and AGB, the current continuing along XY, after K is open, causes a current through the galvanometer from B to A.

292. Characteristics of Induction Currents. -All the phenomenon of induction have the common characteristic that they correspond to a modification of the magnetic field enclosed by the induced circuit, whether this field be due to currents or to magnets, or to a current in the circuit itself. It remains to establish the numerical laws of these currents.

We will first consider currents due to a displacement of the circuit.

Almost immediately after the discovery of induced currents, Lenz gave a very simple rule for their direction, which is this: the direction of an induced current is always such that by its electro-magnetic action it tends to oppose the displacement.

In investigating the conditions which determine the strength of an induction current, we may remark, in the first place, that the existence of such a current implies the existence of an induced electromotive force, on which the strength of the current depends in the way expressed by Ohm's law. As the conditions deter