Mutual inductance and forces between two non-coaxial co-planar circular thin-wall air coils

Purpose This paper aims to present new analytical expressions for the mutual inductance and forces between non-coaxial co-planar circular thin-wall air coils. Design/methodology/approach The expressions are based on an integration method found in the literature, so far used only to describe mutual inductances. It is new to apply this method as a starting point to get the forces between non-coaxial co-planar rings and coils. The approach is further extended to include non-coaxial co-planar thin-wall cylindrical coils. Findings This new method enables interaction modelling between coils by solving integrals numerically, covering fully, partially and non-overlapping coils in a single form. The expressions are verified by comparing the results with alternatives methods. Research limitations/implications The forces and mutual inductances of non-coaxial co-planar circular coils are obtained with analytical expressions, fitted well for optimization studies. The study is limited to coils in free air. Practical implications A typical application is the interaction between coils in a wireless energy transfer system (as applied for battery loading for mobile phones and automotive). The expressions can be used to also predict the forces between two non-coaxial disk or ring magnets as used in magnetic levitation systems. Originality/value Maxwell described the coupling between two coaxial co-planar rings, and steadily more and more equations describing the interaction between circular coils became available in the past decades. The target of this study is to obtain compact equations for non-coaxial co-planar circular coils. This is realized with the combination of existing literature and mathematical modelling tools.