# inductance

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## 1—10 of 12 matching pages

##### 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
$$\frac{{c}^{2}M}{2\pi}=ab{\int}_{0}^{2\pi}{({h}^{2}+{a}^{2}+{b}^{2}-2ab\mathrm{cos}\theta )}^{-1/2}\mathrm{cos}\theta d\theta =2ab{\int}_{-1}^{1}\frac{tdt}{\sqrt{(1+t)(1-t)({a}_{3}-2abt)}}=2abI({\mathbf{e}}_{5}),$$

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19.34.5
$$\frac{3{c}^{2}}{8\pi ab}M=3{R}_{F}(0,{r}_{+}^{2},{r}_{-}^{2})-2{r}_{-}^{2}{R}_{D}(0,{r}_{+}^{2},{r}_{-}^{2}),$$

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►References for other inductance problems solvable in terms of elliptic integrals are given in Grover (1946, pp. 8 and 283).
##### 2: Tom M. Apostol

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►Tom Apostol and his wife Jane were inducted into the MAA’s Icosahedron Society in 2010.
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##### 3: 10.51 Recurrence Relations and Derivatives

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##### 4: Frank W. J. Olver

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►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.
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##### 5: 10.29 Recurrence Relations and Derivatives

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##### 6: Bibliography G

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Special functions of matrix argument. I. Algebraic induction, zonal polynomials, and hypergeometric functions.
Trans. Amer. Math. Soc. 301 (2), pp. 781–811.
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Inductance Calculations.
Van Nostrand, New York.
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##### 7: Bibliography R

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The effective resistance and inductance of a concentric main, and methods of computing the $\mathrm{ber}$ and $\mathrm{bei}$ and allied functions.
Philos. Mag. (6) 17, pp. 524–552.
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##### 8: 10.6 Recurrence Relations and Derivatives

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##### 9: 15.5 Derivatives and Contiguous Functions

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##### 10: 23.2 Definitions and Periodic Properties

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