We theoretically investigate the mutual interaction of a nematic liquid crystal with a static electric field within the general framework of a variational theory for nematoacoustics recently proposed in [E. G. Virga, Phys. Rev. E, 80 (2009), 031705] and based on a coupling between the nematic director and the gradient of the mass density. The liquid crystal is confined in a nematic cell with strong planar anchoring conditions imposed at the boundaries. A linear and a nonlinear numerical analysis of the corresponding equilibrium equations are performed. We show that a Fréedericksz-type transition occurs at a threshold voltage applied at the plates of the cell, and a distortion of the director profile is induced and accompanied by a mass density undulation.