Using electro- and magneto-optical techniques, we investigated orientational transitions in the ensembles of domains in a nematic liquid crystal on the polycarbonate film surface under the conditions of competing surface forces that favor radial and uniform planar alignment of nematic molecules. Having analyzed field dependences of the intensity of light passed through a sample, we established the threshold character of the orientational effects, plotted the calculated intensity versus magnetic coherence length, and compared the latter with the equilibrium length that characterizes the balance of forces on the polymer surface.