Systems that employ stimulating and implantable monitoring devices utilize inductive links, such as external and implanted coils. The calculation of the mutual inductance and the magnetic force between these coils is important for optimizing power transfer. This paper deals with an efficient and new approach for determining the mutual inductance and the magnetic force between two coaxial coils in air. The setup is comprised of a thick circular coil of the rectangular cross section and a thin

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... l solenoid. We use an integro-differential approach to calculate these electrical parameters. The mutual inductance and the magnetic force are obtained using the complete elliptic integrals of the first and second kind, Heuman's Lambda function and one term that has to be solved numerically. All possible regular and singular cases were solved. The results of the presented work have been verified with the filament method and previously published data.