Email this article DIRECT PROBLEM OF MAGNETOSTATICS FOR A UNIFORMLY MAGNETIZED CYLINDER
- Authors: Dyakin V.V.1, Kudryashova O.V.1, Rayevskii V.Y.1
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Affiliations:
- M.N. Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences
- Issue: No 12 (2025)
- Pages: 13-24
- Section: Electromagnetic methods
- URL: https://journals.rcsi.science/0130-3082/article/view/316628
- DOI: https://doi.org/10.31857/S3034543X25120021
- ID: 316628
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Abstract
Formulas for calculating the strength of the reaction field inside and outside a uniformly magnetized magnet in the form of a cylinder of finite dimensions are obtained. A Fortran program has been written that implements the methodology proposed on the basis of these formulas. The possibilities of applying this method to solve the geometric inverse problem of magnetostatics for magnetics or for through and internal cavities of the corresponding shape were discussed. The obtained formulas were tested for their compliance with physical laws, as well as with known formulas for both specific cases of the considered configuration and the limiting cases of the studied geometric shape of the magnet
About the authors
Vilyam Vyacheslavovich Dyakin
M.N. Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences
Email: kudryashova_o.v@mail.ru
professor, scientific consultant of the laboratory of the theoretical physics
Russian Federation, 620108 Yekaterinburg, S. Kovalevskoy str., 18Olga Valeryevna Kudryashova
M.N. Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences
Author for correspondence.
Email: kudryashova_o.v@mail.ru
ORCID iD: 0000-0003-3487-0605
к.ф.-м.н., с.н.с., лаборатория теоретической физики
Russian Federation, 620108 Yekaterinburg, S. Kovalevskoy str., 18Veniamin Yakovlevich Rayevskii
M.N. Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences
Email: ravskii@mail.ru
senior researcher, senior researcher at the laboratory of theoretical physics
Russian Federation, 620108 Yekaterinburg, S. Kovalevskoy str., 18References
- Pechenkov A N., Shcherbinin V.E. Nekotorye pryamye i obratnye zadachi tekhnicheskoj magnitostatiki. Ekaterinburg: Izd-vo UrO RAN, 2004. 177s.
- Pechenkov A.N., Shcherbinin V.E. O reshenii obratnoj zadachi magnitostaticheskoj tomografii // Defectoskopiya. 2009. No. 3. P. 37—55.
- Pechenkov A.N., Shcherbinin V.E. K voprosu o needinstvennosti resheniya obratnoj zadachi magnitostaticheskoj defektoskopii // Kontrol'. Diagnostika. 2006. No. 9. P. 59—60.
- Pechenkov A.N. O vliyanii formy tela na edinstvennost' resheniya obratnoj zadachi magnitostaticheskoj defektoskopii // Defectoskopiya. 2006. No. 10. P. 24—26.
- Dyakin V.V. Pryamaya i obratnaya zadacha magnitostatiki // Defektoskopiya. 1996. No. 3. P. 3—6.
- Dyakin V.V., Kudryashova O.V., Raevskij V.Ya. K voprosu o korrektnosti pryamoj i obratnoj zadachi magnitostatiki. Chast' 2 // Defectoskopiya. 2018. No. 10. P. 15—24.
- Reutov Yu.Ya., Gobov Yu.L., Loskutov V.E. O vozmozhnostyah ispol'zovaniya programmy ELCUT v raschetah po defektoskopii // Defectoskopiya. 2002. No. 6. P. 34—40.
- Zagidulin R.V., Dyakin V.V., Dudarev M.S., Shcherbinin V.E. K opredeleniyu geometricheskih razmerov poverhnostnogo defekta / Fizicheskie metody i pribory NK. Tezisy dokladov X Ural'skoj nauchnoj tekhnicheskoj konferencii. Izhevsk. 1989. P. 83.
- Novoslugina A.P., Smorodinskij Ya.G. Raschetnyj sposob ocenki parametrov defektov v stalyah // Defectoskopiya. 2017. No. 11. P. 13—19.
- Dyakin V.V., Raevskij V.Ya., Kudryashova O.V. Pole konechnogo defekta v plastine // Defectoskopiya. 2009. No. 3. P. 67—79.
- Krotov L.N. Rekonstrukciya granicy razdela sred po prostranstvennomu raspredeleniyu magnitnogo polya rasseyaniya. 1. Issledovanie svojstv resheniya vspomogatel'noj pryamoj zadachi // Defectoskopiya. 2004. No. 2. P. 76—82.
- Krotov L.N. Rekonstrukciya granicy razdela sred po prostranstvennomu raspredeleniyu magnitnogo polya rasseyaniya. 2. Postanovka i metod resheniya obratnoj geometricheskoj zadachi magnitostatiki // Defectoskopiya. 2004. No. 6. P. 76—82.
- Slesarev D.A., Barat V.A., Chobanu P.M. Snizhenie pogreshnosti statisticheskogo metoda ocenki parametrov defektov v magnitnoj defektoskopii // Defectoskopiya. 2012. No. 1. P. 69—74.
- Ahiezer A.I. Obshchaya fizika. Elektricheskie i magnitnye yavleniya. Kiev: Naukova dumka, 1981. 471 p.
- Pechenkov A.N., Shcherbinin V.E. Metod sozdaniya odnorodnoj namagnichennosti i opredeleniya magnitnoj vospriimchivosti // Defectoskopiya. 2002. No. 7. P. 47—50.
- Samohin A.B. Ob”emnye singulyarnye integral'nye uravneniya elektrodinamiki. M.: Tekhnosfera, 2021. 217 p.
- Hizhnyak N.A. Integral'nye uravneniya makroskopicheskoj elektrodinamiki. Kiev: Naukova dumka, 1986. 279 p.
- Friedman M.J. Mathematical Study of the Nonlinear Singular Integral Magnetic Field Equation. 1 // SIAM J. Appl. Math. 1980. V. 39. No. 1. P. 14—20.
- Friedman M.J. Mathematical Study of the Nonlinear Singular Integral Magnetic Field Equation. 2 // SIAM J. Numer. Anal. 1981. V. 18. No. 4. P. 644—653.
- Friedman M.J. Mathematical Study of the Nonlinear Singular Integral Magnetic Field Equation. 3 // SIAM J. Math. Analys. 1981. V. 12. No. 4. P. 536—540.
- Dyakin V.V. Matematicheskie osnovy klassicheskoj magnitostatiki. Ekaterinburg: RIO UrO RAN, 2016. 403 p.
- Raevskij V.Ya. O svojstvah kvaziermitovyh operatorov i ih primenenii k issledovaniyu operatorov teorii potenciala i osnovnogo uravneniya elektro- i magnitostatiki / Preprint No. 24/48(01). Ekaterinburg: IFM UrO RAN, 2001.
- Raevskij V.Ya. Nekotorye svojstva operatorov teorii potenciala i ih primenenie k issledovaniyu osnovnogo uravneniya elektro- i magnitostatiki // Teoreticheskaya i matematicheskaya fizika. 1994. V. 3. No. 100. P. 323—331.
- Fihtengol'c G.M. Kurs differencial’nogo i integral’nogo ischisleniya. T. 3. M.: Nauka, 1966. 656 p.
- Prudnikov A.P., Brychkov Yu.A., Marichev O.I. Integraly i ryady. T. 1. M.: Fizmatlit, 2003. 632 p.
- Bronshtejn I.N., Semendyaev K.A. Spravochnik po matematike dlya inzhenerov i uchashchihsya vtuzov. M.: Nauka, 1980. 976 p.
- Zegrya G.G., Veksler M.I., Smirnova I.G., Ustinova I.A. Raschet stacionarnyh elektricheskih i magnitnyh polej. SPb.: Universitet ITMO, 2019. 96 p.
- Antonov L.I., Dedenko L.G., Matveev A.N. Metodika resheniya zadach po elektrichestvu. M.: Izd-vo MGU, 1982. 89 p.
- Dyakin V.V., Kudryashova O.V., Raevskij V.Ya. Raschet napryazhennosti magnitnogo polya vnutri i vne beskonechnogo cilindra, pomeshchennogo v proizvol’noe vneshnee pole // Defectoskopiya. 2024. No. 3. P. 33—46.
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