ELECTROSTATIC CAPACITY

107.] The capacity of a conductor is measured by the charge of electricity which will raise its potential to the value unity, the potential of all other con- ductors in the field being kept at zero. The capacity of a conductor depends not only on its own form and size, but on the form and position of the other conductors in the field. The nearer the uninsulated conductors are placed the greater is the capacity of the charged conductor.

An apparatus consisting of two insulated conductors, each presenting a large surface to the other with a small distance between them, is called a condenser, because a small electromotive force is able to charge such an ap- paratus with a large quantity of electricity.

The simplest form of condenser, that to which the name is most commonly applied, consists of two disks placed parallel to each other, the medium be- tween them being air. When one of these disks is connected to the zinc and the other to the copper electrode of a voltaic battery, the disks become charged with negative and positive electricity respectively, and the amount of the charge is the greater the nearer the disks are placed to each other, being approximately inversely as the distance between them.

Hence by bringing the disks very close to each other, connecting them with the electrodes of the bat- tery and then disconnecting them from the battery, we have two large charges of opposite kinds insulated on the disks. If we now remove one of the disks from the other we do work against the electric attraction which draws them together, and we may thus increase the energy of the system so much that, though the original electromotive force was only that of a single voltaic cell, either of the disks when separated may be raised to so high a potential that the gold leaves of an electrometer connected with it are deflected. It was in this way that Volta demonstrated that the electrification due to a voltaic cell is of the same kind as that due to friction, the copper electrode being positive with respect to the zinc electrode. In this condenser the capac- ity of each disk depends principally on the distance between it and the other disk, but it also depends in a smaller degree on the nature of the electric field at the back of the disk. There are other forms of condensers, however, in which one of the conductors is almost or altogether surrounded by the other. In this case the capacity of the inner conductor is almost or altogether independent of everything but the outer conductor. This is the case in the Leyden jar, and in a cable with a copper core surrounded by an insulator the outside of which is protected by a sheathing of iron wires.

DISCHARGE BY ALTERNATE CONTACTS

108.] But in most cases the charge of each conductor depends not only on the difference between its potential and that of the other conductor, but also in part on the difference between its potential and that of some other body, such as the earth, or the walls of the room where the experiment is made. The charges of the two conductors may, therefore, in the simpler cases be written Q = K(P − p) + HP, q = K(p − P ) + hp, (1) (2) where P and p are the potentials, that of the walls of the room being zero, Q and q the charges of the two conductors respectively, K is the capacity of the condenser in so far as it depends on the mutual relation of the two conductors, and H and h represent those parts of the capacity of each conductor which depend on their relation to external objects, such as the walls of the room. If we connect the second conductor with the earth we make p zero while Q remains the same, and we get for the new values of P, Q, and q, P1 = P − K p, K +H Q1 = (K + H)P1 , q1 = −KP1 , (3) If we now insulate the second conductor and connect the first with the earth we make P zero, and p2 = − K P , K +h 1 Q2 = −Kp2 , q2 = (K + h)p2 , (4) If we again insulate the first conductor and put the second to earth, P3 = − K p , K +H 2 Q3 = (K + H)P3 , q3 = −KP3 . (5)COMPARISON OF TWO CONDENSERS. 103 From this it appears that if we connect first the one and then the other conductor with the earth the values of the potentials and charges will be di- K2 minished in the ratio of to unity. (K + H)(K + h) Comparison of two condensers. 109.] Let us suppose the condensers to be Leyden jars having an inner and an outer coating. Let the inner coating of the first jar and the outer coating of the second be connected with a source of electricity and brought to the potential P, while the outer coating of the first and the inner coating of the second are connected with the earth. Then if Q1 and Q2 are the charges of the inner coatings of the two jars, Q1 = (K1 + H1 )P, Q2 = −K2 P. (7) Now let the outer coatings of both jars be connected with the earth, and let the inner coatings be connected with each other. Required the common potential of the inner coatings. Hence we have p1 ′ = p2 ′ = 0, Q1 + Q 2 = Q 1 ′ + Q 2 ′ , P1 ′ = P 2 ′ = P ′ , (8) (9) and we have to find P ′ . Equation (8) becomes, in virtue of (9), (K1 + H1 − K2 )P = (K1 + H1 + K2 + H2 )P ′ . If K1 + H1 = K2 the discharge is complete. 110.] The following method, by which the existence of a determinate re- lation between the capacities of four condensers may be verified, has beenCOMPARISON OF TWO CONDENSERS. 104 Fig. 25. employed by Sir W. Thomson.∗ It corresponds in electrostatics to Wheat- stone’s Bridge in current electricity.

In Fig. 25 the condensers are represented as Leyden jars. Two of these, P and Q, are placed with their external coatings in contact with an insulating stand β; the other two, R and S, have their external coatings connected to the earth. The inner coatings of P and R are permanently connected; so are those of Q and S. In performing the experiment the internal coatings of P and R are first charged to a potential, A, while those of Q and S are charged to a different potential, C. During this process the stand β is connected to the earth. The stand β is then disconnected from the earth and connected to one electrode of an electrometer, the other electrode being connected to earth. Since β is already reduced to potential zero by connection with the earth, there will be no disturbance of the electrometer unless there is leakage in some of the jars. We shall assume, however, that there is no leakage, and that the electrometer remains at zero.

The inner coatings of the four jars are now made to communicate with each other by dropping the small insulated wire w so as to fall on the two ∗ Gibson and Barclay.COMPARISON OF TWO CONDENSERS. 105 hooks connected with α and γ. Since the potentials of α and γ are different a discharge will occur, and the potential of β will in general be affected, and this will be indicated by the electrometer. If, however, there is a certain relation among the capacities of the jars the potential of β will remain zero. Fig. 26.