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1: 19.34 Mutual Inductance of Coaxial Circles
§19.34 Mutual Inductance of Coaxial Circles
The mutual inductance M of two coaxial circles of radius a and b with centers at a distance h apart is given in cgs units by
19.34.1 c 2 M 2 π = a b 0 2 π ( h 2 + a 2 + b 2 2 a b cos θ ) 1 / 2 cos θ d θ = 2 a b 1 1 t d t ( 1 + t ) ( 1 t ) ( a 3 2 a b t ) = 2 a b I ( 𝐞 5 ) ,
19.34.5 3 c 2 8 π a b M = 3 R F ( 0 , r + 2 , r 2 ) 2 r 2 R D ( 0 , r + 2 , r 2 ) ,
References for other inductance problems solvable in terms of elliptic integrals are given in Grover (1946, pp. 8 and 283).
2: Tom M. Apostol
Tom Apostol and his wife Jane were inducted into the MAA’s Icosahedron Society in 2010. …
3: 10.51 Recurrence Relations and Derivatives
4: Frank W. J. Olver
Department of Commerce Gold Medal, the highest honorary award granted by the Department, and was inducted into the NIST Portrait Gallery of Distinguished Scientists, Engineers, and Administrators. …
5: 10.29 Recurrence Relations and Derivatives
6: Bibliography R
  • A. Russell (1909) The effective resistance and inductance of a concentric main, and methods of computing the ber and bei and allied functions. Philos. Mag. (6) 17, pp. 524–552.
  • 7: Bibliography G
  • K. I. Gross and D. St. P. Richards (1987) Special functions of matrix argument. I. Algebraic induction, zonal polynomials, and hypergeometric functions. Trans. Amer. Math. Soc. 301 (2), pp. 781–811.
  • F. W. Grover (1946) Inductance Calculations. Van Nostrand, New York.
  • 8: 10.6 Recurrence Relations and Derivatives
    9: 15.5 Derivatives and Contiguous Functions
    10: 23.2 Definitions and Periodic Properties