New procedures for calculating the mutual inductance of the system: filamentary circular coil-massive circular solenoid

New and fast procedures for calculating the mutual inductance between a thin circular filament coil and a massive circular solenoid in air are presented. The coils are axisymmetric. These results are expressed over the complete elliptical integrals of the first and second kind, Heumann's Lambda function, and one term that has to be solved numerically. The numerical integration of this term is based on some numerical integrations to get the satisfactory accuracy and computational cost. These new expressions are accurate and simple to apply for useful applications. Also, another comparative method based on an approximation of the massive solenoid by Maxwell's coils is given. The paper discusses the computational cost and the accuracy. Results obtained by the two approaches are in excellent agreement.