Exact solutions to the problem on the shape of an uncharged conducting liquid jet in a transverse electric field

Exact solutions are obtained for the problem of an equilibrium configuration of an uncharged cylindrical jet of a conducting liquid in a transverse electric field. The transverse cross section of the jet moving between two planar electrodes is deformed under the action of electrostatic forces (capillary forces play a stabilizing role). According to the solutions obtained, the initially circular cross section of the jet may be significantly (formally, unboundedly) stretched along the lines of forces of the field, and the boundaries of the jet asymptotically approach the electrodes.