  Above a critical field strength, the free surface of an electrified,
perfectly conducting viscous liquid, such as a liquid metal, is known to
develop an accelerating protrusion resembling a cusp with a conic tip. Field
self-enhancement from tip sharpening is reported to generate divergent power
law growth in finite time of the forces acting in that region. Previous studies
have established that tip sharpening proceeds via a self-similar process in two
distinct limits - the Stokes regime at $\textsf{Re}=0$ and the inviscid regime
$\textsf{Re} \to \infty$. Using finite element simulations to track the
acceleration of an electrified protrusion in a perfectly conducting Newtonian
liquid in vacuum held at constant capillary number, we demonstrate that the
conic tip \textit{always} undergoes self-similar growth irrespective of
Reynolds number. The computed blow up exponents at the tip for the terms in the
Navier-Stokes equation and interface normal stress condition reveal the
different forces at play as $\textsf{Re}$ increases. Rescaling of the tip shape
by the capillary stress exponent yields excellent collapse onto a universal
conic tip shape with interior half-angle dependent on the magnitude of the
Maxwell stress. The rapid acceleration of the liquid interface also generates a
thin surface boundary layer with very high local strain rate. Additional
details of the modeled flow, applicable to cone growth in systems such as
liquid metal ion sources, help dispel prevailing misconceptions that dynamic
cones resemble conventional Taylor cones or that viscous stresses at finite
$\textsf{Re}$ can be neglected.
