Abstract
To solve direct and inverse magnetic thickness gauging problems, analytical formulas for the calculation of resultant magnetic fields for two-layer magnets with an arbitrary external field are introduced.
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Khizhnyak, N.A., Integral’nye uravneniya klassicheskoi elektrodinamiki (Integral Equations of Classical Electrodynamics), Kiev: Naukova dumka, 1986.
Raevskii, V.Ya., Some properties of operators of the potential theory and their application to studying the fundamental equation of the electro- and magnetostatics, Teor. Mat. Fiz., 1994, vol. 3, no.100, pp. 323–331.
Friedman, M.J., Mathematical study of the nonlinear singular integral magnetic field equation. Part 1, SIAM Journal Appl. Math., 1980, vol. 39, no. 1, pp. 14–20.
Friedman, M.J., Mathematical study of the nonlinear singular integral magnetic field equation. Part 3, SIAM Journal Appl. Math., 1981, vol. 12, no. 4, pp. 536–540.
Raevskii, V.Ya., On properties of quasihermitian operators and their application to studying operators of the potential theory and fundamental equation of electro- and magnetostatics, Preprint of Inst. of Metal Physics, Russ. Acad. Sci., Yekaterinburg, 2011, no. 24/48(01).
Dyakin, V.V. and Umergalina, O.V., Calculation of the field of a flaw in three-dimensional half-space, Russ. J. Nondestr. Test., 2003, vol. 39, no. 4, p. 297.
Dyakin, V.V., Raevskii, V.Ya., and Umergalina, O.V., On an approach to solution of the magnetostatic problem for bodies with foreign particulates in the inhomogeneous external field, Zh. Vychisl. Mat. Mat. Fiz., 2009, vol. 49, no. 1, p. 178–188.
Dyakin, V.V., Raevskii, V.Ya., and Kudryashova, O.V., A Flaw in a Sphere, Russ. J. Nondestr. Test., 2009, vol. 45, no. 9, p. 604.
Dyakin, V.V. and Kudryashova, O.V., A Flaw in a Sphere (Continuation), Russ. J. Nondestr. Test., 2010, vol. 46, no. 11, p. 819.
Dyakin, V.V., Raevskii, V.Ya., and Kudryashova, O.V., The field of a finite defect in a plate, Russ. J. Nondestr. Test., 2009, vol. 45, no. 3, p. 199.
Dyakin, V.V., Raevskii, V.Ya., and Umergalina, O.V., A magnetostatic problem for a half-space with a spherical flaw in the field of a coil, Russ. J. Nondestr. Test., 2008, vol. 44, no. 2, p. 102.
Mikhlin, S.G., Lineinye uravneniya v chastnykh proizvodnykh (Linear Equations in Private Derivatives), Moscow: Vysshaya shkola, 1977.
Pechenkov, A.N. and Shcherbinin, V.E., A mathematical two-pole point magnetization model for evaluating thickness of nonmagnetic coatings, Russ. J. Nondestr. Test., 2013, vol. 49, no. 12, p. 673.
Zatsepin, N.N., Linear magnetostatics of media in two-dimensional magnetic field, in Ob elektromagnitnykh metodakh kontrolya kachestva izdelii (On electromagnetic methods of testing quality of products), Sverdlovsk: Sredne-Ural’skoe knizhnoe izdatel’stvo, 1965, pp. 189–240.
Gradstein, I.S. and Ryzhik, I.M., Tablitsy integralov, ryadov i proizvedenii (Tables of Integrals, Series, and Products), St. Petersburg: BKhV-Peterburg, 2011.
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Original Russian Text © V.V. Dyakin, O.V. Kudryasheva, V.Ya. Raevskii, 2014, published in Defektoskopiya, 2014, Vol. 50, No. 9, pp. 11–21.
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Dyakin, V.V., Kudryasheva, O.V. & Raevskii, V.Y. An application of the fundamental magnetostatics equation to magnetic thickness gauging problems. Part 1.. Russ J Nondestruct Test 50, 506–514 (2014). https://doi.org/10.1134/S1061830914090046
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DOI: https://doi.org/10.1134/S1061830914090046