We introduce the inductive effects of polar cap motions towards and way from the Sun into magnetospheric electrodynamics and show how this explains observed Universal Time variations in hemispheric geomagnetic indices. The large (and growing) hemispheric asymmetry in the offsets of the geomagnetic (dip or eccentric dipole) poles from Earth’s rotational axis means that the effect is not cancelled out in global indices. By adding this effect to that of the Russell-McPherron effect on solar wind-magnetosphere coupling, that of ionospheric conductivities, and that of the solar wind dynamic pressure and dipole tilt on the near-Earth tail lobe field and cross-tail current sheet, we are able to model the persistent “equinoctial” time-of-day/time-of-year pattern (with additional net Universal time variations) observed in the an, as and am geomagnetic indices since 1959. We discuss the implications for the longitudinal dependence of the effects of extreme space weather events