XIX. The residual charge of the Leyden jar

Abstract

1. Suppose that the state of a dielectric under electric force is somewhat analogous to that of a magnet, that each small portion of its substance is in an electropolar state. Whatever be the ultimate physical nature of this polarity, whether it arises from conduction, the dielectric being supposed heterogeneous (see Maxwell’s 'Electricity and Magnetism,’ vol. i. arts. 328-330), or from a permanent polarity of the molecules analogous to that assumed in Weber’s theory of induced magnetism, the potential at points external to the substance due to this electropolar state will be exactly the same as that due to a surface distribution of electricity, and its effect at all external points may be masked by a contrary surface distribution. Assume, further, that dielectrics have a property analogous to coercive force in magnetism, that the polar state does not instantly attain its full value under electric force, but requires time for development and also for complete disappearance when the force ceases. The residual charge may be explained by that part of the polarization into which time sensibly enters. A condenser is charged for a time, the dielectric gradually becomes polarized; on discharge the two surfaces of the condenser can only take the same potential if a portion of the charge remain sufficient to cancel the potential, at each surface, of the polarization of the dielectric. The condenser is insulated, the force through the dielectric is insufficient to permanently sustain the polarization, which therefore slowly decays; the potentials of the polarized dielectric and of the surface charge of electricity are no longer equal, the difference is the measurable potential of the residual or return charge at the time. It is only necessary to assume a relation between the electric force, the polarization measured by the equivalent surface distribution, and the time. For small charges a possible law may be the following:—For any intensity of force there is a value of the polarization proportional to the force to which the actual polarization approaches at a rate proportional to its difference therefrom. Or we might simply assume that the difference of potentials E of the two surfaces and the polarization are connected with the time by two linear differential equations of the first order. If this be so, E can be expressed in terms of the time t during insulation by the formula E = (A + B ε - μt ) ε - λt where λ and μ are constants for the material, and A and B are constants dependent on the state of the dielectric previous to insulation. It should be remarked that are constants for the material, and A and B are constants dependent on the state of the dielectric previous to insulation. It should be remarked that λ does not depend alone on the conductivity and specific inductive capacity, as ordinarily determined, of the material, but also on the constants connecting polarization with electric force. Indeed if the above view really represent the facts, the conductivity of a dielectric determined from the steady flow of electricity through it measured by the galvanometer will differ from that determined by the rate of loss of charge of the condenser when insulated. 2. A Florence flask nearly 4 inches in diameter was carefully cleansed, filled with strong sulphuric acid, and immersed in water to the shoulder. Platinum wires were dipped in the two fluids, and were also connected with the two principal electrodes of the quadrant electrometer. The jar was slightly charged and insulated, and the potentials read off from time to time. It was found (1) that even after twenty-four hours the percentage of loss per hour continued to decrease, (2) that the potential could not be expressed as a function of the time by two exponential terms. But the latter fact was more clearly shown by the rate of development of the residual charge after different periods of discharge, which put it beyond doubt that if the potential is properly expressed by a series of exponential terms at all, several such terms will be required.