A model for the field-aligned propagation of transverse electric fields and associated field-aligned sheet currents is presented which takes into account the wave nature of the process. The model is applied to the separate cases of ionospheric and magnetospheric sources, and the resulting ionospheric electric field to field-aligned sheet current ratios are determined for comparison with experimental observations. It is found that the magnetospheric wave 'conductivity' for shear mode Alfv¿n waves is small with respect to typical values of the height-integrated ionospheric Pedersen conductivity. For plasma convecting across a stationary disturbance a dynamic equilibrium is achieved in which field-aligned currents flow continuously away from the source on convecting field lines. Consistency with typical ionospheric electric fields requires that the field-aligned sheet currents are limited to around 0.1 A/m for ionospheric polarization sources, while magnetospheric sources are easily capable of 1 A/m or more.