261 CHAPTER XI FORCES EXERTED UPON A CURRENT-CONDUCTOR IN A IN Chapter IX. we gave some account of the mutual actions of currents and magnets, the former being supposed fixed while the latter were free to move. But these mutual actions give rise to a new series of phenomena when long or short portions of a current-conductor have freedom to move through a magnetic field. Here again one of the fields concerned in the action has a coaxal distribution, and it is therefore not surprising that in many cases the forces exerted are such as produce rotations. 187. Movable sliding-piece in a uniform field. In order to determine the force exerted upon a current-conductor in a magnetic field, a portion of the conductor must be given such freedom of motion as will allow it to follow in the direction of the impressed force, without at the same time severing its connection with the fixed parts of the conductor. In nearly all the arrangements designed for this purpose there is a sliding-piece in the circuit of the conductor that is, a rod or wire sliding upon a pair of rails or channels filled with mercury, each rail or channel having one end connected to wires which form part of the circuit. The blind ends of the rails or channels which project beyond the slider are not traversed by the current, and give rise to no lines of force. Fig. 79 shows a sliding arrangement of this kind, suitable for exhibiting the phenomenon to a large audience. The base-board AA, 45 cm. long and 20 cm. wide, is provided with feet, with a projecting rim and with a hole which can be closed or opened at pleasure; this last being intended to facilitate the removal of any mercury which may have been spilt. To AA are fastened two vertical stems BB, which in turn support the board CC. Suspended by the two threads fi f2 is a hoop of copper wire m, bent twice at right angles, and loaded with a small piece of brass; this constitutes the sliding-piece. The ends of m, which are bent downwards, are armed with narrow blades of platinum foil (not specially indicated in the figure, where they appear foreshortened to straight lines). These blades dip into mercury contained in channels which are excavated in wooden bars H1, H2, seen in end 2 view in the figure. The bars H1, H2 are provided with projecting pins, which fit into holes in the board AA and serve to keep the bars fixed in their proper places. From them thick but easily removable metallic connections (conducting wires) pass to the terminals K, K2, these connections being kept above the baseboard, so as to be easily recognised. Between the two wooden bars is a block of iron E, which serves to collect together the lines of force. The threads fi, f2 are attached to the board CC by means of the pegs s1, S2. The paper vanes F1, F2 allow even small to-and fro movements of the wire hoop to be seen from a distance, especially when the narrower side of the apparatus is turned towards the audience. Above the movable wire and within a little distance of it is the strong bar magnet MM, which can be clamped in position in the brass socket T, attached to the board CC. When the circuit of the current is closed, the hoop m is displaced to one side or the other in the magnetic field between M and E, and when the circuit is broken again the hoop returns to its position of rest. If it is desired to maintain the field of the current continuously, and to move the magnet MM nearer to and further from the movable wire, the brass sleeve S may be firmly clamped upon the magnet, while the screw belonging to T is relaxed, so that now the magnet may be rapidly lowered to within a little distance of the hoop m without fear of an actual contact between the two. When a magnet-pole is approached to a movable wire conveying a current, or when a current commences to flow in a movable conductor placed in a fixed magnetic field, the forces acting upon the conductor in question are found to be perpendicular to the lines of force of the magnetic field, and also perpendicular to the conductor itself. Thus with the view of our apparatus shown in fig. 79, the displacement of the hoop m is towards or from the observer. Eight permutations of the experimental conditions may be made: (1) Magnet fixed (a) north pole downward: (a) current in one sense (B) current in the opposite sense (superposition of a current-field upon a magnetic field already existing). (b) south pole downward: the displacements corresponding to (a) and (B) are now reversed in direction. (2) The current flowing continuously, the magnet is lowered towards the movable wire (a) with north pole downward (b) with south pole downward. When the direction of the current is reversed (a) and (B) give corresponding reversal of the direction of displacement (superposition of a magnetic field on an already existing current-field, which is driven away by it). The displacement of a movable conductor in a magnetic field thus exhibits a twofold symmetry, a reversal of direction being produced by a reversal of the current as well as by a reversal of the lines of force in the field of the magnet. The direction in question, then, depends both on the direction of the current and on that of the lines of force of the magnet. We shall use blue arrows to indicate the direction in which the conductor moves, just as we have already used red arrows to indicate the direction of the current in the conductor, and white arrows for the direction of the lines of force. Experiment 64. The same phenomena may be shown with less completeness, but at the same time quite strikingly, by placing between the poles of a powerful compound horse-shoe magnet or electro-magnet some part of a flexible conductor, through which a current is then made to pass. Gold strip such as is used for binding hair is well suited to the purpose, and will stand a current of 20 ampères or more if the circuit is only closed for a short time. When the direction of the current is reversed, the strip rushes suddenly across the field to one side or the other. 188. The left-hand rule.-All cases of motion of a movable portion of a current-conductor placed in a fixed magnetic field are in accordance with one simple rule, however complicated the relations involved may seem to be in individual instances. By extending the thumb and first two fingers of one hand, so that they are mutually at right angles, we have a means of representing the twofold symmetry which was shown in the last paragraph to characterise the phenomenon. If the hand is turned through half a revolution about the middle finger as axis, the direction in which the thumb points becomes exactly reversed, and the same result also holds when the half-revolution is made about the forefinger as axis. If we perform all the permutations of the experiment described in the last paragraph, combining each direction of the current with each direction of the field of the magnet, we shall find that there is an invariable relation connecting the three directions: of the current, of the lines of force of the magnet, and of the resulting displacement of the conductor. We have already used the forefinger to indicate the direction of the magnetic lines of force, from north pole to south pole, while the middle finger has been used to indicate the direction of the current. We shall accordingly find that the direction in which the current is displaced, across the direction of the magnetic lines of force, is always that indicated by the extended thumb, provided we are using the fingers of the left hand. This is FLEMING's three-finger rule, which may be formally stated as follows: If we hold the forefinger of the left hand in the direction of the lines of force of a fixed magnetic field, and the middle finger in the direction of the current, the current-conductor will be urged in the direction of the thumb of the same hand, across the direction of the lines of force. (Left-hand rule.') It will be well to verify this rule for all the eight combinations named above. The thumb and two fingers of the left hand, pointing in mutually perpendicular directions, constitute a lefthanded system of co-ordinates. In the sequel we shall find it convenient to cover the two fingers and the thumb with cylinders of white, red, and blue paper respectively, corresponding to the directions of the lines of force, the current, and the displacement of the current-conductor. When we come to deal with the phenomena of induction, we shall have to formulate a 'right-hand rule,' which is geometrically the opposite of that now considered. Our present rule also includes the cases to which the thumb-rule and swimming rule of § 160 are applicable; those cases, namely, where the current is fixed and the origin of the magnetic lines of force movable. Since for every action there is an equal and opposite reaction, it follows that when the current is fixed the bundle of lines of force proceeding from the north pole of the magnet will be urged in the direction opposite to that of the thumb; but the direction thus specified coincides with that in which the thumb of the right hand points when the palm of the hand is turned towards the source of the lines of force that is, towards the north pole of the magnet. The reader may easily satisfy himself of the correctness of this statement by laying the right hand upon the middle finger of the |