A quantitative model of the magnetic field in the ring current region of Earth's magnetosphere is developed by using poloidal vector fields. The magnetic field is divergence-free by construction. The main features are described by a two-term model, but a third term is necessary to describe the tilt effects. Contour plots of constant ΔB are in agreement with magnetometer data. Analytial expressions for the current density are derived, and the contour plots of constant J&PHgr; are in topological agreement with those obtained from self-consistent models. ¿ American Geophysical Union 1989