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Progress In Electromagnetics Research B | ISSN: 1937-6472 |

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## MUTUAL INDUCTANCE FOR AN EXPLICITLY FINITE NUMBER OF TURNSBy J. T. Conway
Abstract:
Non coaxial mutual inductance calculations, based on a Bessel function formulation, are presented for coils modelled by an explicitly finite number of circular turns. The mutual inductance of two such turns can be expressed as an integral of a product of three Bessel functions and an exponential factor, and it is shown that the exponential factors can be analytically summed as a simple geometric progression, or other related sums. This allows the mutual inductance of two thin solenoids to be expressed as an integral of a single analytical expression. Sample numerical results are given for some representative cases and the approach to the limit where the turns are considered to be smeared out over the solenoid windings is explored.
2. Wolfram, S., 3. Conway, J. T., "Inductance calculations for noncoaxial coils using Bessel functions," 4. Watson, G. N., 5. Graf, J. H., "Ueber die addition und subtraction der argumente bei Bessel'schen functionen nebst einer anwendung ," 6. Gervois, A. and H. Navelet, "Integrals of three Bessel functions and Legendre functions I and II," 7. Gradshteyn, I. S. and I. M. Rhyzik, "Table of Integrals, Series and Products," 8. Abramowitz, M. and I. A. Stegun, 9. Conway, J. T., "Inductance calculations for circular coils of rectangular cross section and parallel axes using Bessel and Struve functions," 10. Akyel, C., S. I. Babic, and M. M. Mahmoudi, "Mutual inductance calculations for non-coaxial circular air coils with parallel axes," |

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