The effects of axial and normal applied electrical fields on the transport of solutes in Poiseuille flows is investigated using the area average approach to the microscopic conservation equations. The averaged solute species continuity equation features an effective dispersion coefficient and an effective velocity that arise due to the applied electric fields, and that are functions of the electric field parameters. The three specific cases considered in this paper include (1) a single field applied parallel to the fluid flow, (2) a single field applied perpendicular to the flow, and (3) one field applied parallel to the flow and an additional field applied perpendicular to the flow. This analysis can be used to describe the transport of dilute noninteracting solutes in such separations as capillary electrophoresis with secondary fields and field flow fractionation with coaxial and perpendicular electric fields, and in electrostatic aerosol classifiers.