Two-parametric family of exact solutions for the profile of the surface of a conducting liquid in a nonuniform electric field

Possible equilibrium configurations of the free surface of a conducting liquid in an external nonuniform electric field are investigated. The liquid is at the tip of a wedge-shaped electrode, and the counter-elecrode is a thin straight conducting filament parallel to the edge of the wedge. The conformal mapping method is used to obtain a two-parametric family of exact solutions for the shape of the surface. The solutions describe the deformation of the surface right to separation of a drop from the electrode.