Induced electromotive forces

Theoretical investigations into the stability of electrified liquid drops take as their starting point a result due to Rayleigh. It was felt that this result is important enough to warrant a more complete derivation than that originally given by Rayleigh in the reference which is usually quoted. A literature search revealed a second paper of Rayleigh’s which is never quoted, but which contains important steps, not given elsewhere, towards his original calculation. Even when both papers are taken together, however, the calculation still seems incomplete. For this reason the entire calculation is presented using a modern formalism which in particular recognises the effects of electrostriction. To complement this the complete calculation as originally conceived by Rayleigh is presented in an appendix. R h m e Les vibrations d’une goutte d’un liquide conducteur portant une charge Clectrique ont t t t ttudites par Lord Rayleigh, puis, B sa suite, par divers auteurs, en utilisant un dkveloppement au second ordre par rapport i l’amplitude de vibration des difftrentes contributions i I’tnergie. On montre que les m&mes resultats sont retrouvts en evaluant au premier ordre seulement les difftrents efforts mtcaniques agissant sur la surface de la goutte. Initial investigations into the behaviour of electrified liquid drops were conducted by Lord Rayleigh towards the end of the 19th century. In 1879 he showed (Rayleigh 1879) that the angular frequency W of an oscillating but unelectrified spherical mass of liquid of density p and radius a is given by W ’ = n ( n I)(n + 2 ) u p a 3 , (1) where T is the surface tension. In this analysis Rayleigh obtained expressions for the potential and kinetic energies of the liquid drop which he substituted into Lagrange’s equations of motion to obtain (1). His calculations are given completely in appendix I1 of Rayleigh (1879). They are also reproduced in v01 I1 of his book Theory of Sound. 0143-0807/80/030143+04$01.50 The Institute of Physics