This paper deals with new expressions for calculating the mutual inductance between thin wall solenoids and thin disk coils in air. This original method which appears in this mathematical form for the first time may seem complicated but it is exact and fast, even though all expressions are obtained by the complete elliptic integrals of the first and second kind, Neumann's Lambda function and one member that has to be solved numerically. Results of the presented approach are compared to results obtained by the well-known filament method regarding the accuracy and computational cost. Also results of this approach are compared to previously published data These new expressions are accurate and simple for useful applications and they considerably reduce computational time.
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