Formation of Conic Cusps at the Surface of Liquid Metal in Electric Field

The formation dynamics is studied for a singular profile of a surface of an ideal conducting fluid in an electric field. Self-similar solutions of electrohydrodynamic equations describing the fundamental process of formation of surface conic cusps with angles close to the Taylor cone angle 98.6 are obtained. The behavior of physical quantities (field strength, fluid velocity, surface curvature) near the singularity is established.