The flow of an electrified liquid layer moving over a prescribed topography is studied with the aim of determining the shape of the free surface. The steady flow is assumed to be inviscid, incompressible, and irrotational. The liquid is assumed to act as a perfect conductor and the air above the layer is assumed to act as a perfect dielectric. The electric field is produced by placing one or more charged electrodes at a distance above the free surface. A weakly nonlinear one-dimensional analysis is used to classify the possible solutions and nonlinear solutions are obtained numerically by boundary integral equation methods. It is found that the shape of the liquid layer's surface can be manipulated (using charged electrodes) to become wave-free.