The presence of end reservoirs often alters the electrical potential distributions inside narrow fluidic confinements of electrokinetically actuated miniaturized devices to a significant extent. This paper examines the influence of finite size effect of the end reservoirs on the concerned potential distribution analytically, using the Schwarz-Christoffel conformal mapping. The effective electric field directly acting across the channel is accordingly represented by a calibration curve, which sums up the role of the key geometric parameters (reservoir-to-channel height and length ratios) on the potential distribution. The analytical model is further augmented to assess the flow characteristics through the channel. The results indicate that the alterations in the flow characteristics due to alterations in the effective electric field on account of the finite size effects of the end reservoirs can turn out to be significantly more prominent than the corresponding alterations due to the axial pressure gradients induced by the sudden contraction and expansion effects associated with the end reservoirs. The derived results can be further utilized to facilitate the practical design of miniaturized fluidic devices, using conveniently tractable analytical tools.