A statistical study of ten years of solar wind particle and magnetic field observations, ionospheric convection measurements, and geomagnetic index data is combined with a case study of the interaction of the 18-21 October 1995 magnetic cloud event to illuminate several aspects of solar-terrestrial coupling. Models of polar cap responses to the solar wind are presented and compared to the observations from the case study. The sudden southward turning of the IMF during the event approximated a step function input to the coupled magnetosphere-ionosphere system. The resulting polar cap size, expansion rate, and polar cap potential are unusually large. This allows a straightforward analysis of effects which have traditionally been difficult to assess. During the event, the polar cap expanded by up to 5\sp∘MLAT/hour, which is roughly the fastest rate of polar cap expansion observed by DMSP in a decade of continuous in-situ measurements. The rapid expansion is used to compare flow observations, estimates of the polar cap potential, and the induced emf which corresponds to the polar cap expansion by Faraday's Law. The analysis also resolves earlier indications that the hypothesized saturation of the polar cap potential drop exists, and confirms the numerical and functional predictions of Hill et al (1976). The implications for high time resolution models of the total polar cap potential are discussed. The statistical analysis includes an expanded set of empirical proxies which relate commonly used magnetospheric parameters. An analysis of the solar wind and ionospheric data also confirms the predictions of Hill (1985) regarding the rate of magnetic flux loss along the length of the magnetotail. In addition, while the ratio of open flux to polar cap potential is often approximated as a constant, the analysis reveals a functional dependence of the ratio which has implications for the length scale of the magnetotail. The ionospheric data used came from six low altitude Defense Meteorological Satellites (DMSP), while WIND and the Interplanetary Monitoring Platform (IMP 8) solar wind monitoring satellites provided solar wind plasma and field data. The data set spans the period from 1987 through 1996.