Improved Formulae for the Inductance of Straight Wires

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H. A. Aebischer
B. Aebischer


The best analytical formulae for the self-inductance of rectangular coils of circular cross section available in the literature were derived from formulae for the partial inductance of straight wires, which, in turn, are based on the well-known formula for the mutual inductance of parallel current filaments, and on the exact value of the geometric mean distance (GMD) for integrating the mutual inductance formula over the cross section of the wire. But in this way, only one term of the mutual inductance formula is integrated, whereas it contains also other terms. In the formulae found in the literature, these other terms are either completely neglected, or their integral is only coarsely approximated. We prove that these other terms can be accurately integrated by using the arithmetic mean distance (AMD) and the arithmetic mean square distance (AMSD) of the wire cross section. We present general formulae for the partial and mutual inductance of straight wires of any cross section and for any frequency based on the use of the GMD, AMD, and AMSD. Since partial inductance of single wires cannot be measured, the errors of the analytical approximations are computed with the help of exact computations of the six-dimensional integral defining induction. These are obtained by means of a coordinate transformation that reduces the six-dimensional integral to a three-dimensional one, which is then solved numerically. We give examples of an application of our analytical formulae to the calculation of the inductance of short-circuited two-wire lines. The new formulae show a substantial improvement in accuracy for short wires.


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Aebischer, H., & Aebischer, B. (2014). Improved Formulae for the Inductance of Straight Wires. Advanced Electromagnetics, 3(1), 31-43.
Research Articles


  1. E. B. Rosa, The self and mutual inductances of linear conductors, Bulletin of the Bureau of Standards, vol. 4, no. 2, Washington, 1907.

  2. C. R. Paul, Inductance, John Wiley & Sons, Hoboken NJ, 2010. 

  3. A. Sommerfeld, Elektrodynamik, Verlag Harry Deutsch, Frankfurt am Main, 1988, 4th ed. 2001. 

  4. J. C. Maxwell, A Treatise on Electricity and Magnetism, vol. 2., Dover Publications, New York, 1954, unabridged 3rd ed. of 1891.

  5. F. W. Grover, Inductance Calculations, Dover Publications, New York, 2009, first published by D. Van Nostrand Co., New York, 1946. 

  6. I. N. Bronstein und K.A. Semendjajew, Taschenbuch der Mathematik, Verlag Harry Deutsch, Thun, 1979.

  7. R. W. P. King and S. Prasad, Fundamental Electromagnetic Theory and Applications, Prentice Hall, Englewood Cliffs N.J., 1986.

  8. H. H. Meinke und F. W. Gundlach, Taschenbuch der Hochfrequenztechnik, Springer-Verlag, Berlin, 1992.

  9. M. Wien, Ueber die Berechnung und Messung kleiner Selbstpotentiale, Wiedemanns Annalen  53 (Annalen der Physik 289): 928-947, 1894.