A two-dimensional hybrid MHD-kinetic model incorporating kinetic electrons is used to simulate a shear Alfv¿n wave pulse propagating in a constant density plasma and magnetic field. The pulse is rectangular in shape so that the perpendicular and parallel current regions are distinct. Two regimes are considered: the large-scale limit where the perpendicular-scale length L$perp$ $gg$ λe and the inertial limit (L$perp$ ≤ 10λe). In addition, a potential-current relation is derived from consideration of electron energy in the wave frame. It is found that the parallel electron current is carried by a uniform acceleration of the entire distribution function where larger current is carried by a correspondingly larger displacement. In the inertial limit the original rectangular shape of the pulse is distorted by a broadening and narrowing in the perpendicular direction at the leading and trailing edges, respectively, of the pulse, as well as by the propagation away from the corners of inertial Alfv¿n waves with perpendicular wavelengths of the order of 10λe (Alfv¿n resonance cones). In both limits, and in spite of the added structure in the inertial case, the parallel electric field calculated from a derived effective potential reproduces the simulation parallel electric field accurately.