length of the circuit, the current in the circuit, and inversely as the square of the radius of the circular circuit. Imagine a very long magnet, with poles of unit strength, hung vertically with its North pole in the centre of a circular conductor having a radius of one centimetre, so that the magnetic field of the circular current acts only on the North pole. Let a current be passed through this circular conductor in such a direction that it tends to lift or repel the unit North pole with a mechanical force of 6.2832 dynes—that is to say, let every unit of length of the circular current act with a unit of force on a unit magnetic pole; then the whole circumference of the circular current will act with a force of 2π dynes (= 6.2832 dynes) on the unit North pole. A current having this magnitude is called an absolute unit of current on the C.G.S. system. This absolute unit of current is equal to 10 amperes. The magnetic force, or flux density, at the centre of a circular current of one turn, and having a radius v centimetres, is 2п С r units, or 2п А units, according as the current is measured in absolute C.G.S. units (C) or in amperes (A). This magnetic force is numerically of the same value as the mechanical force on a unit magnetic pole held at the centre of the circular current. Starting from this fact, we can construct what is called an absolute tangent galvanometer for measuring electric currents in the following way : Let a wire be bent into a circle of one turn, and let it have a radius of (say) 50 centimetres. In the centre of the circle hang a very small magnetic needle, and let the plane of the circle be the direction of the magnetic meridian of the place. Let H be the value of the earth's horizontal magnetic force at that spot. Pass a current through the circular conductor: it will cause the needle to be deflected through an angle (call it ) from the meridian. Then, as explained in § 2 of this chapter, the tangent of the angle is the ratio of the magnetic L force due to the coil to the earth's horizontal magnetic force. The magnetic force due to the coil is equal to 2π A C.G.S. units, where A is the current in amperes flowing through the circular conductor and is the radius of the conductor in centimetres. Hence ΙΟΥ Therefore, if we know the value of r in centimetres, and the value of the earth's horizontal force in C.G.S. units, we can determine the value of the current in amperes from the observed deflection of the needle. Thus, since H=18 (nearly) in England, if the circular coil had a radius of 50 centimetres, and the deflection of the needle was observed to be 45° (tangent 45° 1), we should know that the value of the current producing the deflection was IO X 50 2 X 3'1416 = X 18 X I = 14°3 amperes. In this manner a current may be measured in amperes, if the value of the earth's horizontal magnetic force H* at that spot is known. For the method of measuring this quantity, see Appendix. 147 CHAPTER VI. ELECTROMAGNETIC INDUCTION. §1. Faraday's Discovery of Electromagnetic Induction. In the autumn of 1831, Faraday made a discovery of far-reaching importance, and which has formed the foundation of much which has since been accom. plished in electrical invention. He discovered that if a conducting circuit is traversed by magnetic flux, any change in the total amount of this flux passing through the circuit creates in that co-linked conducting circuit an electromotive force. Thus, the movement of a conducting circuit in a field of magnetic flux, is sufficient to set up in it a current, provided the movement is such as to change the total amount of the flux passing through the circuit. The fundamental facts can be best illustrated as follows. Let the student take the ring coil described on p. 108 and connect it by long and rather thick wires to a mirror galvanometer. The galvanometer should be placed at such a distance from the coil that the presence of a bar magnet will not disturb its indications. Place the coil, as in Fig. 36, close to the North pole of the magnet. In this position, magnetic flux proceeding from the North pole passes through the ring coil, and the lines of the flux are said to be linked with the conducting circuit. (See Fig. 37.) As soon as the galvanometer needle has come to rest, move the coil quickly away from the pole to a place farther off. It will be seen that the galvanometer needle makes a sudden deflection, and then returns to rest. This indicates the passage of a short or transient current through the galvanometer in one direction. In the next place, move the coil back to its original position. The needle will make a single swing in the opposite direction. By placing against the tongue Fig. 36. Current induced by a Magnet. C, Secondary Coil; N Fig. 37.-Magnetic Flux from a North Pole linked with, or a small piece of zinc and a silver coin, attached to the leading wires of the galvanometer, the student should de termine the direction of the current which, when passing through the galvanometer, causes it to deflect in either direction. It will then be easy to determine the direction in which the current was set flowing in the ring coil, when it was moved from or to the magnet, and it will be found that, looking at the ring from the same side as that on which the North pole of the magnet is situated, the current induced in the ring coil flows round it clockwise, or in the same direction as the hands of a clock rotate, when the ring is moved from the North pole; and counter-clockwise when it is moved to the North pole. The following rules must then be stored up in the memory: The positive direction of rotation is the direction opposite to that in which the hands of a clock appear to rotate, or counter-clockwise rotation is positive rotation. (See Fig. 38.) The positive direction along a line of magnetic flux is the direction from the North pole to the South pole, through the space outside the magnet. Hence magnetic flux is said to come out from a North pole, and is always considered as proceeding from that pole. Then the student must remember, that if magnetic flux is put into or linked with an electric circuit, it creates a positively |