  In this study we consider the problem of the interface motion under the
capillary-gravity and an external electric forces. The infinitely deep fluid
layer is assumed to be viscous, perfectly conducting and the flow to be
incompressible. The weak viscous effects are introduced using the
Helmholtz-Leray decomposition and the visco-potential flow approach. The
electric charge distributions above and on the free surface are considered.
Finally, we derive some linearized analytical solutions for the free surface
elevation shape under the localised pressure distribution and the combined
action of the forces mentioned hereinabove.
