The fundamental electromechanical interactions in a passive -flux electrodynamic maglev system (EDS) are mediated by the voltages induced in the levitation coils by the sled magnets, and by the forces exerted on the sled as a result of the induced currents. This work presents a reliable and compact method to calculate these interactions by using analytical expressions of the magnetic field of a permanent magnet. The proposed approach provides a highly efficient and numerically stable approach to the computation of the flux induced in the levitation coils as well as the induced voltages and currents and lift, drag, and guidance forces acting on the sled's magnets. The analytical model is compared to a simplified algebraic model suitable for real-time control of EDS maglev suspension dynamics. Both models are compared with measurements and show good predictive quality.