Calculation of the magnetic field strength inside and outside of an infinite cylinder placed in an arbitrary external field

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Resumo

In the model of the infinite cylinder the formulas and the corresponding algorithm for finding the magnetic field strength inside and outside the homogeneous cylinder placed in the external magnetic field of arbitrary configuration are deduced. Testing the results of calculations on these formulas for their correspondence with known physical laws, as well as on their coincidence with well-known analytical answers in the limiting private cases of the forms of magnetics were carried out. A computer program in Fortran language has been compiled and debugged to implement calculations using the proposed algorithm.

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Sobre autores

V. Dyakin

M.N. Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences

Autor responsável pela correspondência
Email: defect@imp.uran.ru
Rússia, Yekaterinburg, 620108

O. Kudryaschova

M.N. Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences

Email: kudryashova_ov@imp.uran.ru
Rússia, Yekaterinburg, 620108

V. Raevskii

M.N. Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences

Email: ravskii@mail.ru
Rússia, Yekaterinburg, 620108

Bibliografia

  1. Dyakin V.V., Kudryashova O.V., Raevskij V.Ya. On the Use of Multipurpose Software Packages for Solving Problems of Magnetostatics // Defektoskopiya. 2018. No.11. P. 23—34.
  2. Dyakin V.V., Kudryashova O.V., Raevskij V.Ya. One Approach to the Numerical Solution of the Basic Equation of Magnetostatics for a Finite Cylinder in an Arbitrary External Field // Defektoskopiya. 2021. No. 4. P. 22—34.
  3. Dyakin V.V., Kudryashova O.V., Raevskij V.Ya. Calculating the Strength of Magnetic Field from a Homogeneous Cylinder of Finite Dimensions Placed in an Arbitrary External Field // Defektoskopiya. 2022. No. 4. P. 63—74.
  4. Dyakin V.V., Kudryashova O.V., Raevskij V.Ya. Calculating the Strength of Magnetic Field from a Homogeneous Cylinder of Finite Dimensions Placed in an Arbitrary External Field // Defektoskopiya. 2023. No. 5. P. 32—44.
  5. Hizhnyak N.A. Integral Equations of Macroscopic Electrodynamics. Kiev: Naukova Dumka, 1986. 280 p.
  6. Dyakin V.V. Mathematical Foundations of Classical Magnetostatics. Yekaterinburg: Ural Branch, Russ. Acad. Sci., 2016. 404 p.
  7. Friedman M.J. Mathematical study of the nonlinear singular integral magnetic field equation. 1. // SIAM Journal Appl. Math. 1980. V. 39. No. 1. P. 14—20.
  8. 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.
  9. 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.
  10. Bejtmen G., Erdeji A. Higher transcendental functions, V. 1. M.: Nauka, 1973. 294 p.
  11. Ahiezer A.I. General Physics. Electric and Magnetic Phenomena. Kiev: Naukova Dumka, 1981. 471 p.
  12. Non-destructive testing and diagnostics / Ed. V.V. Klyuev M.: Mashinostroenie, 1995. 487 p.
  13. Dyakin V.V., Kudryashova O.V., Raevskij V.Ya. Exact Formulas for Magnetic Field Strength inside and outside a Homogeneous Ellipsoidal Magnet Placed in an External Field Homogeneous in Magnet Vicinity // Defektoskopiya. 2022. No. 2. P. 51—63.

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2. Fig. 1. A homogeneous cylinder in a magnetic field.

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