The equilibrium shapes of a conducting drop in a uniform electric field E_¥ are virtually prolate spheroids and are stable with respect to all infinitesimal-amplitude disturbances. Inviscid oscillations about these states are analyzed by solving numerically Bernoulli’s equation for drop shape and Laplace’s equation for the velocity potential inside and the electrostatic potential outside the drop. The drops are impulsively set into motion by either a step change in electric field strength from E∞⁽¹⁾ for time t < 0 to E∞⁽²⁾ for t ≥ 0 or subjecting them at t = 0 to an impulse of magnitude Ø₂ in velocity potential proportional to the second spherical harmonic. For initially spherical drops that are set into oscillation by impulsively changing the field strength, the oscillation frequency computed for small field strengths accords with domain perturbation results.

When the field strength E∞⁽²⁾ is sufficiently large, the drops do not oscillate but become unstable by issuing jets from their tips, which are computed here for the first time. Whereas drops set into motion by a step change in field strength do evolve in time through a succession of virtually spheroidal shapes as surmised by previous spheroidal approximations, ones set into motion by an initial velocity potential disturbance exhibit radically different dynamics. Moreover, such drops go unstable by issuing jets from their conical tips when Ø₂ is large but fission when Ø₂ is small.