We use a relatively simple continuum model to investigate the effects of dielectric inhomogeneity within confined liquid-crystal cells. Specifically, we consider, in planar, cylindrical, and spherical geometries, the stability of a nematic-isotropic interface subject to an applied voltage when the nematic liquid crystal has a positive dielectric anisotropy. Depending on the magnitude of this voltage, the temperature, and the geometry of the cell, the nematic region may shrink until the material is completely isotropic within the cell, grow until the nematic phase fills the cell, or, in certain geometries, coexist with the isotropic phase. For planar geometry, no coexistence is found, but we are able to give analytical expressions for the critical voltage for an electric-field-induced phase transition as well as the critical wetting layer thickness for arbitrary applied voltage. In cells with cylindrical and spherical geometries, however, locally stable nematic-isotropic coexistence is predicted, the thickness of the nematic region being controllable by alteration of the applied voltage.