  We use boundary-integral methods to compute the time-dependent deformation of
a drop of dielectric fluid immersed in another dielectric fluid in a uniform
electric field E. Steady state theory predicts, when the permittivity ratio,
\beta, is large enough, a conical interface can exist at two cone angles, with
\theta_<(\beta) stable and \theta_>(\beta) unstable. Our numerical evidence
instead shows a dynamical process which produces a cone-formation and a
transient finite-time singularity, when E and \beta are above their critical
values. Based on a scaling analysis of the electric stress and the fluid
motion, we are able to apply approximate boundary conditions to compute the
evolution of the tip region. We find in our non-equilibrium case where the
electric stress is substantially larger than the surface tension, the ratio of
the electric stress to the surface tension in the newly-grown cone region can
converge to a \beta dependent value, \alpha_c(\beta)>1, while the cone angle
converges to \theta_<(\beta). This new dynamical solution is self-similar.
