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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 $$\frac{c^{2}M}{2\pi }=ab{\int }_0^{2\pi }{(h^2+a^2+b^2-2ab\cos \theta )}^{-1/2}\cos \theta d\theta =2ab{\int }_{-1}^1\frac{tdt}{\sqrt{(1+t)(1-t)(a_3-2abt)}}=2abI({𝐞}_5),$$

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Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $\cos z$: cosine function, $dx$: differential of $x$ , $\int$: integral, $I(𝐦)$: integral, $M$: mutual inductance and $h$: distance

Referenced by:

§19.34

Permalink:

http://dlmf.nist.gov/19.34.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §19.34 and Ch.19

… ►

19.34.5 $$\frac{3c^2}{8\pi ab}M=3R_F(0,r_{+}^2,r_{-}^2)-2r_{-}^2{R}_D(0,r_{+}^2,r_{-}^2),$$

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Symbols:

$R_D(x,y,z)$: elliptic integral symmetric in only two variables, $R_F(x,y,z)$: symmetric elliptic integral of first kind, $\pi$: the ratio of the circumference of a circle to its diameter, $M$: mutual inductance and $r_{\pm }$

Permalink:

http://dlmf.nist.gov/19.34.E5

Encodings:

pMML, png, TeX

See also:

Annotations for §19.34 and Ch.19

… ►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

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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

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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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External Links:

ISSN 0002-9947, FullText, MathReview (Wayne J. Holman, III), ZentralBlatt

Referenced by:

§35.8(i), §35.8(ii), §35.8(iv), Ch.35.

Encodings:

BibTeX

… ►

Inductance Calculations. Van Nostrand, New York.

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Notes:

Reprinted by Dover, New York, 1962 and 2004

External Links:

ZentralBlatt

Referenced by:

§19.34.

Encodings:

BibTeX

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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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External Links:

Document, ZentralBlatt

Referenced by:

§10.73(iii).

Encodings:

BibTeX

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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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