The magnetospheric electron number density and the magnetic field strength near 8 R_E over the polar cap increased dramatically after the arrival of an interplanetary magnetic cloud on 31 March 2001. These parameters were determined with high accuracy from the plasma resonances stimulated by the Radio Plasma Imager (RPI) on Imager for Magnetopause-to-Aurora Global Exploration (IMAGE) near apogee during both quiet (30 March 2001) and disturbed (31 March 2001) days. The quiet day and disturbed day values were each compared with magnetospheric magnetic field and electron density models; good agreement was found with the former but not the latter. The magnetospheric response was also expressed in terms of the ratio of the electron plasma frequency f_pe to the electron cyclotron frequency f_ce, which is proportional to the ratio of the electron gyroradius to the Debye radius. Simultaneous Wind measurements of the solar wind magnetic field strength, speed, and plasma density were used to calculate the solar wind quasi-invariant QI. This index is equivalent to the ratio of the solar wind magnetic pressure to the solar wind ram pressure or to the inverse of the magnetic Mach number squared. These nondimensional quantities, QI and f_pe/f_ce, have fundamental meanings in the solar wind MHD regime and in the relation between electric and magnetic forces on electrons in the magnetosphere, respectively. During the large 31 March 2001 storm, IMAGE was at the right place at the right time so as to enable comparisons between RPI f_pe/f_ce and Wind QI determinations. Both QI and ff_pe/f_ce formed maxima during 6-hour observing intervals during this storm that were found to be highly correlated (87%) with a magnetospheric time lag of about 3 hours far f_pe/f_ce.. These results, based on a detailed case study of this important event, suggest that the plasma parameter f_pe/f _ce may serve as a useful magnetospheric index.