A theoretical model for mid- and high-latitude electric fields and currents is constructed using Fourier analysis methods. A two-dimensional ionosphere with an enhanced conductivity auroral belt and field-alignted currents at the edges is employed. The postulate that the electric field and currents adjust self-consistently to minimize the global Joule dissipation rate defines a theoretical relation between the primary and secondary field-aligned currents. This so-called minimal dissipation configuration is examined using several input field-aligned current models, and graphical solutions for the electric field and ionospheric current are shown. A detailed discussion and interpretation of the solutions with relation to diverse observations and high-latitude phenomenology are included.