Studies of the field-induced alignment of the SmA phase using deuterium NMR spectroscopy have revealed a complex pattern of behaviour when the director is initially orthogonal to the aligning field. Here we report the electric field-induced alignment of the SmA director using time-resolved deuterium NMR when the aligning electric field E is at an angle with the magnetic field B of the spectrometer which is considerably smaller than 90degrees; here the director is initially aligned parallel to the magnetic field. The dynamics of the electric field-induced alignment of the director for the smectic phase of 4-alpha,alpha-d(2)-octyl-4'-cyanobiphenyl (8CB-d(2)) was investigated at two angles between B and E of roughly 45degrees and 54.5degrees the so-called magic angle, at different electric field strengths and also at two temperatures, 305.1 K and 302.6 K The dynamics of the SmA director alignment of 8CB-d(2) was monitored by measuring the deuterium NMR spectrum as a function of time. The results for the 45degrees and 54.5degrees geometries revealed, in contrast to the complex dynamics of alignment of the SmA director observed for the 90degrees geometry, a much simpler pattern of relaxation. Here the director appeared to be aligned almost as a monodomain. In general, for either of the two geometries employed here, the ultimate angle of alignment the director achieves relative to E depends on the electric field strength. Lowering the temperature by just 2.5degreesC from 305.1 K to 302.6 K has a dramatic effect on the rate of director relaxation presumably because of the large increase in the combined rotational viscosity and the elastic energy effects of the SmA phase with decreasing temperature. Furthermore for the 45 geometry at 302.6 K, the SmA sample separates on relaxation ultimately into two domains with different alignment angles.