On the equilibrium shape of a charged drop in an electrostatic field

Abstract

It is found analytically that the equilibrium shape of a charged drop in a uniform electrostatic field in calculations of the first order of smallness for the size of stationary deformation can be considered to be spheroidal, and its eccentricity depends on the charge size and on the intensity of an external electrostatic field. On the threshold of losing stability in relation to the superposition of its own and polarizing charges, the square of the equilibrium eccentricity of a strongly charged drop in a weak field is up to 0.34, and the square equilibrium eccentricity of a weakly charged drop in a strong field is up to 0.78 (in terms of opportunity to realize instability).