Improvement in the mutual inductance calculation between coaxial circular coils of rectangular cross section and thin coaxial circular coils with constant current density in air

This paper deals with an efficient and fast approach for determining the mutual inductance between coaxial circular coils of rectangular cross section in combination with thin coaxial circular coils as the thin wall solenoid, the thin disk coil and the filamentary coil. This approach is based on the filament method where conductors are approximated by the set of Maxwell's coils. The obtained expressions are expressed over the complete elliptical integrals of the first and second kind and permit fast calculation of the mutual induction for mentioned systems. These new expressions are accurate and simple for useful applications. The paper also points out the computational cost and the accuracy.