ampere-turns proportional to their linear dimensions if they are to be raised to equal degree of saturation.

As the magnetism of the magnet depends on the number of ampere-turns, it should make no matter whether the coils are bigger than the core or whether they enwrap it quite closely. If there were no magnetic leakage this would be true in one sense; but for an equal number of turns large coils cost more and offer higher resistance. Hence the coils are wound as closely to the iron core as is consistent with good insulation. Also the iron is chosen as thick as possible, as permeable as possible, and forming as compact a magnetic circuit as possible, so that the magnetic resistance may be reduced to its utmost, giving the greatest amount of magnetism for the number of ampere-turns of excitation. This is why horse-shoeshaped electromagnets are more powerful than straight electromagnets of equal weight; and why also a horseshoe electromagnet will only lift about a quarter as much load if one pole only is used instead of both.

As the coils of electromagnets grow hot with the current, sufficient cooling surface must be allowed, or they may char their insulation. Each square centimetre of surface warmed 1° C. above the surrounding air can get rid of about 0-0029 watt. If 50°, above the surrounding air be taken as the safe limit of rise of temperature, and the electromagnet has resistance r and surface s sq. cms., the highest permissible current will be 0.38 √s/r amperes.

387. Polarized Mechanism. An electromagnet moves its armature one way, no matter which way the current flows. Reversing the current makes no difference. There are, however, two ways of making a mechanism that will cause an armature to move in either sense at will. (a) The armature's movement is controlled by an adjusted spring so as to be in an intermediate position when a weak current is flowing. Then sending a stronger current will move the armature one way, and weakening

or stopping the current will make it move the other way. (b) A polarized armature or tongue (i.e. one that is independently magnetized) is placed between the poles of the electromagnet instead of opposite them. The direction in which it tends to move will be reversed by reversing the current in the circuit of the electromagnet.

388. Growth of Magnetism.—It requires time to magnetize an iron core. This is mainly due to the fact that a current, when first switched on, does not instantly attain its full strength, being retarded by the self-induced counter-electromotive-force (Art. 458); it is partly due to the presence of transient reverse eddy-currents (Art. 457) induced in the iron itself. Faraday's large electromagnet at the Royal Institution takes about two seconds to attain its maximum strength. The electromagnets of large dynamo machines often take ten minutes or more to rise to their working stage of magnetization.

When electromagnets are used with rapidly alternating currents (Art. 470) there are various different phenomena, for which the student is referred to Art. 477.

LESSON XXXII.

389. Electrodynamics.

Electrodynamics

In 1821, almost immediately after Oersted's discovery of the action of a current on a magnet, Ampère discovered that a current acts upon another current, apparently attracting it* or repelling it according to certain definite laws. These actions he investigated by experiment, and from the experiments he built up a theory of the force exerted by one current on another. That part of the science which is concerned with the force which one current exerts upon another he termed Electrodynamics. It is now known that these

It would be more correct to speak of the force as acting on conductors carrying currents, than as acting on the currents themselves.

actions are purely magnetic, and are due to stresses in the intervening medium. The magnetic field around a single conductor consists of a magnetic whirl (Art. 202), and any other conductor carrying a current when brought into the field of the first is acted upon by it. Fig. 194 shows the field due to two parallel straight current con

ductors, which were passed through holes in a sheet of glass on which iron filings were sprinkled. In Fig. 194 the currents flow in the same direction; in Fig. 195 in opposite directions. In the first case the stresses in the field (Art. 119) tend to pull them together, in the second to push them apart.*

390. Laws of Parallel and Oblique Circuits. - The following are the laws discovered by Ampère:

(i.) Two parallel portions of a circuit attract one another if the currents in them are flowing in the same direction, and repel one another if the currents flow in opposite directions.

This law is true whether the parallel wires be parts of two different circuits or parts of the same circuit. The separate turns of a spiral coil, like Fig. 193, when traversed by a current attract one another; such a coil, therefore, shortens when a current is sent through it. But this is equally well explained

See article by the author in the Philosophical Magazine, November 1878, p. 848.

by the general law of electromagnetic systems (Art. 379), because shortening will reduce the reluctance of the magnetic circuit and increase the flux.

(ii.) Two portions of circuits crossing one another obliquely attract one another if both the currents run either towards or from the point of crossing, and repel one another if one runs to and the other from that point.

Fig. 196 gives three cases of attraction and two of repulsion that occur in these laws.

(iii.) When an element of a circuit exerts a force on another element of a circuit, that force always tends to urge

Fig. 196.

the latter in a direction at right angles to its own direction. Thus, in the case of two parallel circuits, the force of attraction or repulsion acts at right angles to the currents themselves.

An example of laws ii. and iii. is afforded by the case shown in Fig. 197. Here two currents ab and ca are movable round O as a centre. There will be an apparent repulsion between a and d and between c and b, while in the other quadrants there will be an apparent attraction, a attracting c, and b attracting d.

The foregoing laws may be summed up in one, by saying that two portions of circuits, however situated, set up stresses

in the surrounding a
medium tending to set
them so that their cur-

rents flow as nearly in
the same path as
possible.

(iv.) The force exerted be

Fig. 197.

tween two parallel portions of circuits is proportional to the product of the strengths of the two currents, to the length of the portions, and inversely proportional to the simple distance between them.

391. Ampère's Table. In order to observe these attractions and repulsions, Ampère devised the piece of

apparatus known as Ampère's Table, shown in Fig. 198, consisting of a double supporting stand, upon which wires, shaped in different ways, can be so hung as to be capable of rotation. The ends of the suspended wires