that of a sphere of one centimetre radius, = 63 × 107 (electrostatic) units. The magnetic moment of the earth is, according to Gauss, no less than 85,000,000,000,000,000,000,000,000 times that of a magnet of unit strength and centim. length, i.e. its magnetic moment is 85 × 1024 units. The resistance of selenium is about 40,000,000,000, or 4 × 1010 times as great as that of copper; that of air is about 1026, or

100,000,000,000,000,000,000,000,000

times as great. The velocity of light is about 30,000,000,000 centimetres per second, or 3 × 1010. As a final example we may state that the number of atoms in the universe, as far as the nearest fixed star, can be shown to be certainly fewer than 7 × 1091

LESSON XXVI.-Electromagnets.

326. Electromagnets. In 1820, almost immediately after Oerstedt's discovery of the action of the electric current on a magnet needle, Arago and Davy independently discovered how to magnetise iron and steel by causing currents of electricity to circulate round them in spiral coils of wire. The method is shown in the

Fig. 114.

simple diagram of Fig. 114, where a current from a single cell is passed through a spiral coil of wire, in the

hollow of which is placed a bar of iron or steel, which is thereby magnetised. The separate turns of the coil must not touch one another or the central bar, otherwise the current will take the shortest road open to it and will not traverse the whole of the coils. To prevent such short-circuiting by contact the wire of the coil should be overspun with silk or cotton (in the latter case insulation is improved by steeping the cotton covering in melted paraffin wax) or covered with a layer of guttapercha. If the bar be of iron it will be a magnet only so long as the current flows; and an iron bar thus surrounded with a coil of wire for the purpose of magnetising it by an electric current is called an Electromagnet. Sturgeon, who gave this name, applied the discoveries of Davy and Arago to the construction of electromagnets far more powerful than any magnets previously made.

By applying Ampère's Rule (Art. 186), we can find which end of an electromagnet will be the N.-seeking pole; for, imagining ourselves to be swimming in the current (Fig. 114), and to face towards the centre where the iron bar is, the N.-seeking pole will be on the left. It is convenient to remember this relation by the following rules-Looking at the S.-seeking pole of an electromagnet, the magnetising currents are circulating round it in the same cyclic direction as the hands of a clock move; and, looking at the N.-seeking pole of an electromagnet the magnetising currents are circulating round it in the opposite cyclic direction to that of the hands Fig. 115 shows this graphically. These rules are true, no matter whether the beginning of the coils is at the end near the observer, or at the farther end from him, i.e., whether the spiral be a right-handed screw, or (as in Fig. 114) a left-handed screw. It will be just the same thing, so far as the magnetising power

of a clock.

Fig. 115.

O

is concerned, if the coils begin at one end and run to the other and back to where they began; or they may begin half-way along the bar and run to one end and then back to the other: the one important thing to know is which way the current flows round the bar when you look at it end-on.

327. Solenoid.-Without any central bar of iron or steel a spiral coil of wire traversed by a current acts as an electromagnet (though not so powerfully as when an iron core is placed in it). Such a coil is sometimes termed a solenoid. A solenoid has two poles and a neutral equatorial region. Ampère found that it will attract magnets and be attracted by magnets. It will attract another solenoid; it

a

b

has a magnetic field oo ooo oooooo ; "

resembling generally that of a bar

Fig. 116.

magnet. If so arranged that it can turn round a vertical axis, it will set itself in a North and South direction along the magnetic meridian. Fig. 116 shows a solenoid arranged with pivots, by which it can be suspended to a "table" like that shown in Fig. 121.

Reference to Fig. 86 and to Art. 192, will recall how a single loop of a circuit acts as a magnetic shell of equivalent form and strength. A solenoid may be regarded as made up of a series of such magnetic shells placed upon one another, all their N.-seeking faces being turned the same way. Since the same quantity of electricity flows round each loop of the spiral coil the loops will be of equal magnetic strength, and the total magnetic strength of the solenoid will be just in proportion to the number of turns in the coil; and if there be n turns, the number of magnetic lines of force running

through the solenoid will be n times as great as the number due to one single turn. The use of the iron core is by its greater magnetic induction to concentrate and increase the available number of lines of force at definite poles. The student has been told (Art. 191) that the lines of force due to a current flowing in a wire are closed curves, approximately circles (see Fig. 85), round the wire. If there were no iron core many of these little circular lines of force would simply remain as small closed curves around their own wire; but, since iron has a high coefficient of magnetic induction, where the wire passes near an iron core the lines of force alter their shape, and instead of being little circles around the separate wires, run through the iron core from end to end, and round outside from one pole back to the other, as in a steel magnet. A few of the lines of force do this when there is no iron; almost all of them do this when there is iron. Hence the electromagnet with its iron core has enormously stronger poles than the spiral coils of the circuit would have alone.

328. Laws of Electromagnets.-The following are the principal laws of electromagnets :

(a) The strength1 of an electromagnet is proportional to the strength of the magnetising current (i.e. to the quantity of electricity that circulates round it).

This is, however, only true when the iron core is still far from being "saturated" with its maximum intensity of magnetisation. If the iron is already strongly magnetised by a current, a current twice as strong will not make the iron into a magnet of double strength. According to Jenkin it is no use to make the current stronger than will give the "field" 135 units of intensity. Müller gave for the relation between the strength of the magnetising current and the strength of the electromagnet it produces, the following approximate rule :—

1 The word "strength" means here "magnetic strength," as defined in Art. 102, and must on no account be confused with "lifting power" or "sustaining power," which depends both on the magnetic strength and on the form of the magnet and of its poles.

The strength of an electromagnet is proportional to the angle whose tangent is the strength of the magnetising current; òr

m = A tan-1 C,

where C is the current in ampères and A a constant depending on the construction of the particular magnet. If the student will look at Fig. 90 and imagine the divisions of the horizontal line OT to represent strengths of current, and the number of degrees of arc intercepted by the oblique lines to represent strengths of magnetism, he will see that even if OT be made infinitely long, the intercepted angle can never exceed 90°. More accurate is the rule

m = BnC

I

I + onC'

where C is the current strength, n the number of turns of wire, B a constant depending on the construction of the magnet and the quality of the iron, and σ another constant (a small fraction) depending on the quantity and quality of the iron, and called the "saturation constant."

(b) The strength of an electromagnet is proportional to the number of turns of wire in its coils. This also is only true when the iron core is far below saturation; and it is only true when the current is kept constant. For if by putting on more coils of wire we add materially to the total resistance of the circuit, the strength of the current will, according to Ohm's Law (see Arts. 180 and 345), be thereby reduced. This has an important bearing on the construction of telegraphic and other instruments; for while electromagnets with "long coils," consisting of many turns of fine wire, must be used on long circuits where there is great resistance, such an instrument would be of no service in a circuit of very small resistance, for the resistance of a long thin coil would be disproportionately great: here a short coil of few turns of stout wire would be wanted. (See Art. 352.)

(c) The strength of an electromagnet is independent of the thickness and material of the conducting wire. The wire may be of any metal of any thickness, provided only it carries enough current a sufficient number of times round the core to produce a field of the requisite strength.