The molecular orientation of a nematic sample limited by two concentric cylinders is theoretically investigated. The surfaces are assumed as having an inhomogeneous distribution of easy directions. The results are found in the one-constant approximation, in the presence of an external electric field, for weak anchoring of the molecules at the surfaces. In order to validate our approximations, the analytical results are compared with the ones obtained by numerically solving the non-linear bulk differential equation for the tilt angle profile subjected to non-linearized boundary conditions. We show that the agreement improves as the extrapolation length increases.