Abstract
The problem of an arbitrarily shaped defect in a ferromagnetic half-space and a plane-parallel plate plate is solved. The solution is expressed as an integral equation in which the integration was performed only over the defect surface. This integral equation is solved by the iteration method, which allows one to represent the solution as a series in powers of the small parameter \(\lambda /2\pi \left( {\lambda = \frac{{\mu - 1}} {{\mu + 1}}} \right)\). The numerical results are obtained for a defect in the form of an ellipsoid.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Reutov, Yu.Ya., Gobov, Yu.L., and Loskutov, V.E., Feasibilities of using the ELCUT software for calculations in nondestructive testing, Russ. J. Nondestr. Test., 2002, no. 6, pp. 425.
Vladimirov, V.S. and Zharinov, V.V., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Fizmatlit, 2003.
Dyakin, V.V. and Umergalina, O.V., Calculation of the field of a flaw in three-dimensional half-space, Russ. J. Nondestr. Test., 2003, no. 4, pp. 297.
Dyakin, V.V., Umergalina, O.V., and Raevskii, V.Ya., The field of a finite defect in a 3D semispace, Russ. J. Nondestr. Test., 2005, no. 8, pp. 502.
Dyakin, V.V., Raevskii, V.Ya., and Kudrjashova, O.V., The field of a finite defect in a plate, Russ. J. Nondestr. Test., 2009, no. 3, pp. 199.
Smythe, W., Static and Dynamic Electricity, New York: McGraw-Hill, 1950.
Landau, L.D. and Lifshitz, E.M., Teoreticheskaya fizika. Elektrodinamika sploshnykh sred (t. VIII) (Course of Theoretical Physics. Vol. 8. Electrodynamics of Continuous Media), Moscow: Nauka, 1982.
Shur, M.L. and Shcherbinin, V.E., Magnetostatic field of the flaw located in the plain-parallel plate, Defektoskopiya, 1977, no. 3, pp. 92–96.
Shcherbinin, V.E. and Shur, M.L., Accounting the influence of the product boundary on the field of the cylindrical flaw, Defektoskopiya, 1976, no. 6, pp. 30–35.
Vonsovskii, S.V., Simplest calculations for problems of magnetic defect detection, Zh. Tekh. Fiz., 1938, vol. 8, no. 16, pp. 1453–1467.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.L. Shur, A.P. Novoslugina, Ya.G. Smorodinskii, 2015, published in Defektoskopiya, 2015, Vol. 51, No. 11, pp. 14–27.
Rights and permissions
About this article
Cite this article
Shur, M.L., Novoslugina, A.P. & Smorodinskii, Y.G. The magnetic field of an arbitrary shaped defect in a plane-parallel plate. Russ J Nondestruct Test 51, 669–679 (2015). https://doi.org/10.1134/S1061830915110054
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1061830915110054