An exact particular solution for an equilibrium uncharged conducting jet configuration in a transverse electric field

The problem concerning the equilibrium configurations of the surface of an uncharged conducting jet in a transverse electric field has been considered. It is established that this electrostatic problem is analogous to the problem of the potential streamlining of a two-dimensional gas bubble by the ideal liquid, for which effective analytical solution methods are available. Using this analogy, an exact solution for the jet shape has been constructed and studied with respect to stability in the particular case in which the difference of pressures inside and outside the jet is zero. This solution is characterized by a significant degree of deformation, whereby the aspect ratio of the jet cross section amounts to 23/4.