Evaluation of the vertical magnetic field generated by a spiral planar coil

The study of the magnetic field generated by planar spiral coils is important in several widespread application domains. However, calculating this magnetic field distribution is complex and requires expensive computational electromagnetic (CEM) tools. In this paper, we reduce this challenge to the evaluation of a single integral for the vertical field component for a general, planar spiral coil. We focus on the vertical field component due to its importance in most applications such as wireless power transfer. We verify our calculations by comparing them with the simulation results from the CEM tool `CST EM Studio'. Our results make it possible to quickly determine this field with any standard mathematical software package, thus without the need for an expensive CEM tool.