Page:Encyclopædia Britannica, Ninth Edition, v. 8.djvu/81

Rh ELECTltOMAGNKTISM.J ELECTRICITY 7! tion with the screw 5 and the cup q. B is a light conductor, 1 con sisting of two parallelograms of wire, in which the current circulates in opposite directions, the object of which is to eliminate the magnetic action of the earth. The conductor is hung in the cups p and q, so as to be easily movable abont a vertical axis. C is a frame on which several turns of wire are wound, so that when a current is passed through, we have a num ber of parallel conduc tors, all of which act in the same way on the vi-rtical branch uv of the movable conductor. Ow ing to the opposite direc- | r, - _. . &quot;=^ii1 tions of the currents in the tube and the wire inside it, there is no action on yz due to that part of the apparatus. p;,,. 35 It is clear, therefore, that the action of C on uv will prevail and determine the motion. The action of straight conductors, making an angle with each other, may be shown by means of the conductor D, represented in tig. 36, which may be fitted to the stand shown in fig. 35. In a very large class of practical cases, circular circuits Ult - play an important part. The most convenient way of dealing with these, as a rule, is to replace them by the equivalent magnets or magnetic shells. The action of a circular circuit may be represented by two layers of north and south magnetism, w^hose surface densities are i-f-r, where i is the strength of the current and T the distance between the layers. For details concerning the calcula tions in a variety of cases, ve refer the reader to Maxwell s Electricity and Magnetism, vol. ii. cap. xiv. We may calculate the force exerted (see fig. 37) by a circular current AB on a unit north pole at its centre C, as A A follows. Replace the current by two discs AB and A 15, of north and south magnetism, the: distance be tween which is r ; the surface densities are 4-i-f T and -i -rr. The first of these exerts a repulsive force -iTi -rT, the second an attractive force h&quot;ti je the resultant repulsive force is 2iUC03 A C B -T-T = liri -r-r , r being the radius of the disc. Hence a unit of length of the current exerts a force i-^-r- at the distance r. t of It follows therefore that the statement of our funda- ent mental principle (p. 67) involves a unit of current strength such that unit length of the unit current, formed into an arc whose radius is the unit of length, exerts a unit of force on a unit pole placed at the centre of the arc. From this statement and the definition of a unit negative pole it fallows at onco that the dimension of the unit of current is noul. One arrangement of circular currents has become famous from the part it plays in Ampere s theory of magnetism. A wire wound into a cylindrical helix, such as that represented in figure 38, the ends of the wire being returned paral lel to the axis of the helix, and bent in to pivots, so that it can be hung upon Am pere s stand (tig. 35), is called a solenoid. The conductor thus formed is obviously equi valent to a series of circular currents disposed in a uni form, manner perpendicular to a common axis. In the case represented in figure 38, this axis is straight ; but the name solenoid is not restricted to this particular case, 1 Aluminium is often used. and what we are about to advance will apply to a solenoid whose axis is a curve of any form. Let there be nils of the circular currents (each of area A) in the arc d* of the axis of the solenoid. As we sup pose the distribution to be uniform, n is constant. We may suppose each current to be placed at the middle of a length - of the axis, which it occupies for itself. Hence, if each circular current be replaced by a shell of thickness -, the surface densities of the magnetism on each of these shells will be ni, and the north magnetism of each shell will coincide with the south magnetism of the next; so that the whole action at paints external to the solenoid reduces to the action of a quantity ni of magnetism spread over one end of the solenoid, and a quantity - ni spread over the other. The positive or north end of the solenoid is obtained, as usual, from the direction of the current, by means of the right-handed screw relation. If X be very small, or if the system acting on, or acted upon by, the solenoid is at a distance very great compared with the dimensions of X, then we may suppose the representa tive magnetism concentrated at the ends of the axis of the solenoid. Hence the particular arrangement of electric currents, which we have called a solenoid, acts and is acted on exactly like an ideal linear magnet (whose poles coincide with the ends of its axis). Thus the north pole of a magnet or solenoid repels the north end and attracts the south end of a solenoid; a solenoid tends to set under tha action of the earth, its north end behaving like a magnetic north pole, and so on. In a cylindrical bobbin wound to a uniform depth with silk- Cylin- covered wire we have an arrangement which is equivalent to a drical number of solenoids all having a common axis. Each of these bobbin- solenoids may be replaced by the equivalent terminal discs of posi tive and negative magnetism, and the external action of the whole thus calculated. The magnetic disc at each end will, of course, not be of uniform density, 4 but if the points acted on be at a distance which is infinitely great compared with the lateral dimen sions of the bobbin, we may collect the magnetism at the ends of the axis ; the quantities will be where a and b are the outer and inner radii of the shell of wire, m the number of layers in the depth, and n the number of turns per unit of length of each layer. The magnetic moment of the bobbin is therefore where p denotes the number of turns in each layer, and nip the whole number of turns on the bobbin. The above is a simple case of the kind of calculation on which Weber founded his verification of Ampere s theory. He did not, however, replace the circular currents by the equivalent magnetic distributions, but calculated directly from Ampere s formula (18). The instrument (electrodyuamometer) which he used in his experiments was invented by himself. It consists essentially of a fixed coil and a movable coil, usually sus pended in the bifilar manner, and furnished with a mirror, so that its motions about a vertical axis can be read off in the subjective manner (see art. GALVANOMETER) by means of a scale and telescope. Two varieties of the instrument were used by Weber. In one of these (A), the movable coil was suspended within the fixed coil ; in the other (B), the movable coil was ring-shaped, and embraced the fixed coil, which, however, was so supported that it could be arranged either inside the movable coil or outside it at any distance and in any relative position with respect Weber s experi- ments&amp;gt;
 * The reader will easily find the law for himself.