We consider a twisted nematic liquid crystal confined by two parallel boundary plates. The nematic is subject to an in-plane magnetic field applied in a direction parallel to the plates. At the lower plate the director is strongly anchored so that the director twist is fixed. On the upper surface we introduce an easy direction for the director. Although the director prefers to align with the easy direction, the actual twist exhibited at the upper surface may differ front the easy direction. twist. This is due to the competition between elastic, magnetic and anchoring effects. We examine and compare two surface energies that model the weak anchoring at the upper plate. For both energies, equilibrium twist profiles for the director within the sample have been obtained by Minimizing the total free energy for the system.