The influence of an external field on the effective anchoring energy of a nematic liquid crystal in contact with a substrate is theoretically analyzed. Our analysis is performed on the hypothesis that the electrodes are perfectly blocking and that there is no selective ion adsorption. The proposed theory predicts an effective anchoring energy dependent on the applied dc voltage. According to the sign of the dielectric anisotropy and of the flexoelectric coefficient the dependence of the anchoring energy strength with the bias can be monotonic or not. For large bias voltage the effective anchoring energy strength tends to a constant value. Our theory is in qualitative agreement with published data investigating the influence of the bias on the saturation voltage.