Geomagnetic pole reversals occur frequently throughout geologic history, although one has not yet occurred in recorded time. Magnetohydrodynamic models of Earth’s core have revealed that during a reversal, the magnetic dipole moment disappears, leaving higher-order moments. Previous research examined quadrupole magnetic field topologies and quantitatively specified the magnetic equators of those topologies but did not fully examine charged particle drift motion and stability in the inner magnetosphere. Earth’s closed magnetosphere is primarily dominated by two electric fields, the corotational and convection generated electric fields. E x B drifts from these fields ultimately drives the behavior of the cold plasma of the plasmasphere. In a quadrupole-dominated magnetic field, the plasma motion generated by the E x B drifts would be dramatically different from the classical dipole field plasma convection. Three quadrupole topologies were evaluated, and the E x B drift was analyzed along the magnetic equators of these topologies to characterize and quantify the resultant plasma motion and evaluate the behavior, structure and stability of the plasmasphere. We also tested for plasmaspause and magnetopause boundary sensitivity to magnetic field strength. The direction of the convection flow is hemispherically dependent for the η = 0 and 0.5 quadrupole topologies, that is, the plasma in the Northern Hemisphere convects tailward, and the Southern Hemisphere convects sunward. The η = 1 topology demonstrates evidence of strong plasmasphere erosion due to the intersection of the magnetic equators, and is particularly sensitive to reductions in magnetic field strength.