KLECTROMAGNETISM.] ELECTR1CI T V Ampere has given a general theory of the rotation of a circuit under the action of a magnet. Let AB (fig. 40) be any circuit, which we may suppose connected with the axis of the mag net, but free to rotate about it. We suppose the magnet replaced by quanti ties m of magnetism at its poles. Take the axis of the magnet for axis of z, and the other axes as in the figure, being the centre of the magnet, and let ON = OS = c. Let PQ be any arc ds of AB, and let the coordinates of P be x,y,z; then if I, m, n be the direction cosines of NP, and NP-=D, we have also the direction cosines of P^, which is perpen dicular to NP and PQ, . . and is the direction of the force exerted by the pole N on P, are ( n -r -m T WsinQPK, &c.
" s wo /
Hence by formula (6) the components of the force acting on PQ are / dy dz , (nf -m T lids, kc.
ds dtj
- se forc<
-(-I- y Hence, if K denote the moment of these forces about OZ, we have from the north pole alone ,dz ^ If we substitute the values of I, m, n this reduces to d fz-c ds 1 dx
- v }x
ds dz m 7 ds (dn . If therefore ^ , o, , /8, , o a denote the anglen BNZ, ANZ, BSZ, ASZ, we have, adding the ivsults from both poles, K = mi (cos & - cos <! - cos 2 + cos oj) . . (21). It follows from this remarkable formula that the couple K tending to turn a part AB of an electric circuit about the axis of a magnet depends merely on the position of the ends A and B. In particular, if A coincide with B, i.e. if AB form a closed circuit, or if A and B both lie on parts of the axis not included between N and S, 1 the couple will be nil, and there will be no rotation. The application of this formula to cases where there are sliding contacts at A and B not lying on the axis presents no difficulty ; ve leave it to the reader. it ion Several of these rotations may be exhibited by moans of the "a- apparatus represented in figure 41 . A BC is a horizontal coil of wire 1 We might consider what would happen if A or B lay on NS but the rase never arises in practice, for all magnets have a finite thickness ISue on this subject Wiedeniann, Bd. ii. 119). terminating at the binding screws a,b. FG is a ring-shaped trough of mercury for the sliding contacts. A wire connects the mercury with the binding screw d. DE is an upright support screwed into a metal base D in connection with the binding screw c, and ter minating above in a mercury cup E. When required, DE can be replaced by the shorter supports D E and D"E". II LK is a support for a screw L, which carries an adjustible centre. 1. Poise in the cup E the wire stirrup MN, so that the ends just dip in the mercury trough. Then, if a strong current be sent from c to d, MN will rotate (in northern latitudes) in a direction opposite to the hands of a watch. 2. If we fix a vertical mngnet n "s" to DE by means of a clip at Y, then the rotation will take place with a weaker current in the same direction as before, if the north pole of the magnet be upwards (as shown in figure), but in the opposite direction if the magnet be reversed. 3. Reversing the current alone in either of the last two cases causes the direction of rotation to be reversed. 4. The magnet may be removed and a current sent from a to b round ABC in the direction opposite to the hands of a watch. The result is the same as for the magnet with its north pole upwards. If the current in ABC is reversed, the rotation is reversed ; and so on. 5. The support D E with the two magnets ns, n sf may be screwed into D instead of DE, the wire P now dipping into the mercury. If the current be sent from c to d, the vertical current in D E will act on * and s , and cause the magnet to rotate in the direction of the hands of a watch. This rotation is reversed if the current go from d to c. 6. We may consider any magnet of finite size as made up of a series of magnets like ns and n s arranged about an axis. Hence, if we replace D E and the magnets D"E" by the single magnet supported by means of the pivot L , there will still be rotation. Figure 42 represents a very elegant piece of apparatus devised by Faraday, to show the ro tation at once of a magnet and of a movable conductor. The rotating pieces are the magnet sn, which is tied to the copper peg at the bottom of G by means of a piece of string, and swims round the vertical current buoyed up by the mercury in G, and the wire DE, which is hinged to D by a thin flexible wire, and swims round the pole of the vertical magnet nY. Another apparatus in vented by Barlow, and known by the name of Barlow s wheel, is represented in figure 43. A current is caused to pass fro:n the mercury trough C along the radius of the disc A th rough the field of magnetic force due to tho Fig. 42. Fig. 43. horse-shoe magnet NO. The result is that the wheel rotates in the direction indicated by the arrow. Fluid conductors may also be caused to rotate under Fluid ro the action of a magnet. We mentioned "in our historical tations. sketch the experiment by which Davy demonstrated this rotation in the case of mercury. A variety of such experi ments have been since devised. The following is a simple one. Fill a small cylindrical copper vessel with dilute sulphuric acid and set it upon the north pole of a power ful electromagnet. If a thick /cine wire be connected by a piece of copper wire to the copper vessel, and then im mersed in the acid so as to be in the axis of the vessel, a current is set up in the liquid which flows radially from the zinc to the copper across the lines of force. Tlu
VIII. 10