Understanding the storm-substorm relationship is an important problem in magnetospheric dynamics. In the past this question has been explored using statistical techniques and empirical relationships involving the Dst and AE/AL indices. In this research we have developed a relationship between AL and Dst based on the physics of the process. We argue that the magnetospheric electric field causes both the westward auroral electrojet and the particle injection into the ring current region. The adiabatic acceleration of ring current particles and the thermal properties of the ring current source have been included in the calculations. The injection function deduced is found to be a function of AL index and the solar wind dynamical pressure Pdyn. For AL>AL0 (~-500 nT) the injection function is proportional to AL <Pdyn (t - td)>0.33with a time lag td≈ 45 min; while for large AL < AL0(~-500 nT) the injection function is proportional to -|AL|1.7 <Pdyn(t - td)>0.33. This result is consistent with previous statistical results. We also find that the ring current decay time is a function of AL. Finally, we obtain an algorithm which predicts Dst from ALand the solar wind dynamical pressure Pdyn. The correlation coefficients between Dst predicted by the algorithm and the observed Dst index are 0.84 and 0.80 for the years 1998 and 1999, respectively.