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mutual inductance of coaxial circles

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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 ) ,
is the square of the maximum (upper signs) or minimum (lower signs) distance between the circles. … References for other inductance problems solvable in terms of elliptic integrals are given in Grover (1946, pp. 8 and 283).
2: 31.15 Stieltjes Polynomials
are mutually orthogonal over the set Q : …
3: Tom M. Apostol
Tom Apostol and his wife Jane were inducted into the MAA’s Icosahedron Society in 2010. …
4: 10.51 Recurrence Relations and Derivatives
5: 10.6 Recurrence Relations and Derivatives
10.6.10 p ν s ν q ν r ν = 4 / ( π 2 a b ) .
6: 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. …
7: 23.2 Definitions and Periodic Properties
23.2.14 η 3 ω 2 η 2 ω 3 = η 2 ω 1 η 1 ω 2 = η 1 ω 3 η 3 ω 1 = 1 2 π i .
8: 10.29 Recurrence Relations and Derivatives
9: 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.
  • 10: 17.2 Calculus
    17.2.6_1 ( q ; q ) = 2 π t exp ( π 2 6 t + t 24 ) ( q ^ ; q ^ ) , t > 0 ,
    17.2.6_2 ( q ; q ) = 1 2 exp ( π 2 12 t + t 24 ) ( q ^ 1 2 ; q ^ ) , t > 0 .