Abstract Inductive coupling of a global magnetospheric model to a global ionospheric–thermospheric model is described. Existing schemes based on electrostatic coupling are valid for magnetospheric variability occurring on time scales of order 100 s or longer. The formulation developed here extends the validity of the coupling model to time scales of order 10 s, while retaining the physics of quasi-static coupling as the long time-scale limit. Both lumped and distributed formulations for the coupling region are derived. The induction gives rise to magnetic and ion kinetic energy storage at low altitude. The induced ion polarization current on average causes an upward magnetic body force on the plasma which may facilitate massive outflow.