Numerical computations and order-of-magnitude estimates are used to describe the stationary creeping flow of a jet of a Newtonian liquid with finite electrical conductivity that is injected into a dielectric medium subject to a uniform electric field. The electric current carried by the jet is computed as a function of the parameters of the problem, showing that it increases with the conductivity and flow rate of the liquid and with the intensity of the electric field. The current also depends on the wetting conditions of the liquid at the injection orifice. Analysis of the transfer of current to the surface of the liquid and of the evolution of the jet under the electric stresses that act at its surface leads to scaling laws for the electric current and other properties of the solution. These laws fit the numerical results and are in qualitative agreement with experimental data.