The central plasma sheet (CPS) of the Earth's magnetosphere contains a thermally differentiated plasma, whose ion temperature exceeds severalfold its electron temperature. The gradient/curvature drift of ions and electrons of the CPS plasma tend to separate the two species in the dawn-dusk direction. Because of the temperature difference, the dusk CPS, which gains a surplus of hotter ions, is expected to have a larger plasma pressure than its dawnside counterpart. Preliminary analysis of ISEE 1 plasma data confirmed the pressence of such a pressure asymmetry in the CPS during the quiet and the growth-of-driven conditions. The closure of the electric current created by this pressure asymmetry usually requires the flow of a field-aligned current, whose effects of the E¿B drift of the CPS plasma are the central focus of this paper. The dawn-dusk asymmetry in the magnetosphere generally leads to an azimuthally asymmetric ionospheric convection, with close resemblance to the streamline structure first identified by Heppner (1977). The field-aligned current associated with the asymmetry has a strong effect in shielding the inner magnetosphere, in which the imposed electric field decreases exponentially for polytropic indices greater than 1. The asymmetry also affects the location of the inner edge of the plasma sheet. We present a simplified model in this paper, using an analytic paradigm to portrary the general properties of the asymmetry-induced effects. A limited attempt is made to examine how a departure from the idealized condition would change the solution of the problem.