A theoretical study of high-latitude electric fields and currents, using analytic Fourier analysis methods, is conducted. A two-dimensional planar model of the ionosphere with an enhanced conductivity auroral belt and field-aligned currents at the edges is employed. Two separate topics are treated. A field-aligned current element near the cusp region of the polar cap is included to investigate the modifications to the convection pattern by the east-west component of the interplanetary magnetic field. It is shown that a sizable one-cell structure is induced near the cusp which diverts equipotential contours to the dawnside or duskside, depending on the sign of the cusp current. This produces characteristic dawn-dusk asymmetries to the electric field that have been previously observed over the polar cap. The second topic is concerned with the electric field configuration obtained in the limit of perfect shielding, where the field is totally excluded equatorward of the auroral oval. When realistic field-aligned current distribution are used, the result is to produce severely distorted, crescent-shaped equipotential contours over the cap. Exact, analytic formulae applicable to this case are also provided.