On the mutual potential energy of a plane network of doublets

Abstract

1. The object of this note is the determination of the mutual potential energy of a distribution of small electric or magnetic doublets lying in a plane with their axes perpendicular to the plane; reckoning the potential energy from a state of infinite dispersion of the doublets. The doublets are supposed to have a definite electric or magnetic moment, the same for all, whose value is determined by their constitution and does not depend on their mutual action. The problem bears on the energy of a layer of polarised molecules on the surface of a fluid, and the question as to the value of the energy, for a given number of molecules of given moment per unit area, was put by Dr. E. K. Rideal to Prof. S. Chapman, at whose suggestion the writer undertook this investigation. In actual surface layers the mode of packing of the molecules is not always known, and therefore two special cases are considered, in order to determine how the mode of packing influences the energy, the number of doublets per unit area being given. It is supposed that the doublets form either a simple square network, or an equi-triangular network; and it appears that the mutual potential energy differs only by about 2 per cent, in the two cases. It is thereforepossible to give (§ 4) a fairly definite estimate of the energy, which is likelyto be approximately true for any probable mode of packing of the molecules.