Electrostatic stability of the liquid layer surface on a hard wettable cylindrical substrate

The wave motion in a cylindrical layer of an ideal conducting liquid on a hard rod kept at a constant electrical potential is calculated accurate to the first order of smallness in dimensional perturbation of the free surface. The instability of the free surface is also considered. A dispersion relation is derived. It is shown that the range of instability waves depends on only the electric field strength near the free surface and the instability increments of capillary waves decrease as the layer gets thinner. The influence of the hard rod becomes tangible only when its radius becomes comparable to the thickness of the liquid layer.