In this thesis we derive an analytical relationship between the Earth's magnetospheric potential drop and the ionospheric conductance by adopting a simple two-dimensional model of a magnetic field draping around the tail magnetopause. Two methods are used: (1) matching currents through the tail magnetopause and the Earth's ionosphere in analogy with the Alfven wing at the Jovian satellite Io, (2) minimizing the total power that the solar wind loses to the Earth's magnetosphere. We find, in both cases, that the magnetospheric potential drop, Δϕ\sbis, is inversely proportional to the ionospheric conductance, Σ\sbis, and we compare this result to the revised result of the numerical model of Fedder and Lyon (1987) and to the conclusions of Hill et al. (1976) and Hill (1984). Considering the derived proportionality factor as a 'magnetosheath conductance', Σ\sbmsh, we determine that the high-latitude tail magnetospheric 'driver' acts as a current generator as opposed to a voltage generator.