This paper proposes a new control-oriented model to compute the magnetic field created by a coil. A major challenge for untethered microscale mobile robotics is the control of objects for precise and fast displacements. In this work, we propose to use an alternative implementation of a model based on elliptic integral functions to control magnetically actuated micro-robots. It allows to compute the magnetic field even in the area close to the coil quickly and accurately. This model is evaluated numerically and compared to classical approaches - dipole approximation, map-based interpolation and classical elliptic integral models - in terms of accuracy, computation time and memory requirement. Simulation results show that this works allows to have an accurate model in the whole workspace by avoiding numerical issues encountered in previous works. It can be computed in a few milliseconds, making it the right candidate for closed-loop control of magnetically actuated micro-robots.