New analytic-numerical solutions for the mutual inductance of two coaxial circular coils with rectangular cross section in air

In this paper, we present analytic-numerical expressions for the calculation of the mutual inductance of two axisymmetric circular coils with rectangular cross section in air. This original and new method may seem complicated but it is explicit, accurate, and fast, even though all expressions are obtained by the complete elliptic integrals of the first and second kind, Heuman´s lambda function, and three terms that must be solved numerically. We confirm the validity of this approach by comparing it with other approaches (filament method and previously published data). We also compare the accuracy and the computational cost of this approach and that of the filament method. All results obtained by the various approaches are in excellent agreement