A thin layer of nematic liquid crystal (NLC) across which an electric field is applied is a setup of great industrial importance in liquid crystal display devices. There is thus a large literature modeling this situation and related scenarios. A commonly used assumption is that an electric field generated by electrodes at the two bounding surfaces of the layer will produce a field that is uniform: that is, the presence of NLC does not affect the electric field. In this paper, we use calculus of variations to derive the equations coupling the electric potential to the orientation of the NLC's director field, and use a simple one-dimensional model to investigate the limitations of the uniform field assumption in the case of a steady applied field. The extension of the model to the unsteady case is also briefly discussed.