Analytical solution of problem of shielding low-frequency magnetic field by thin-walled cylindrical screen in presence of cylinder
The analytical solution of boundary value problem describing the process of penetration of low-frequency magnetic field through thin-walled cylindrical screen with cylindrical inclusion is constructed by use of approximate boundary conditions. The source of the field is a thin thread of infinitely s...
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| Format: | Article |
| Language: | Russian |
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National Academy of Sciences of Belarus, the United Institute of Informatics Problems
2021-09-01
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| Series: | Informatika |
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| Online Access: | https://inf.grid.by/jour/article/view/1147 |
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| author | G. Ch. Shushkevich |
| author_facet | G. Ch. Shushkevich |
| author_sort | G. Ch. Shushkevich |
| collection | DOAJ |
| description | The analytical solution of boundary value problem describing the process of penetration of low-frequency magnetic field through thin-walled cylindrical screen with cylindrical inclusion is constructed by use of approximate boundary conditions. The source of the field is a thin thread of infinitely small length with an infinitely small cross-section where current circulates. Thread is located in a plane which is perpendicular to axis of cylindrical screen, in outer region with respect to a screen. Initially the potential of initial magnetic field is represented as spherical harmonic functions, then using addition theorems connecting spherical and cylindrical harmonic functions, it became as cylindrical harmonic functions superposition. Secondary potentials of magnetic field are also presented as superposition of cylindrical harmonic functions in three-dimensional space. It is shown that the solution of formulated boundary value problem is reduced to the solution of linear algebraic equations system for coefficients included in the representation of secondary fields. The influence of some aspects of the problem on the value of the screening coefficient of an external magnetic field when passing through a cylindrical copper screen in the presence of a cylindrical inclusion is studied numerically. Calculation results are presented in graphs form. Obtained results can be used to shield technical devices and biological objects against the effects of magnetic fields to provide ecological surrounding of operating electrical installations and devices. |
| format | Article |
| id | doaj-art-4aca8171c764452d87b9cf6abb0eeb5a |
| institution | Kabale University |
| issn | 1816-0301 |
| language | Russian |
| publishDate | 2021-09-01 |
| publisher | National Academy of Sciences of Belarus, the United Institute of Informatics Problems |
| record_format | Article |
| series | Informatika |
| spelling | doaj-art-4aca8171c764452d87b9cf6abb0eeb5a2025-02-03T11:40:29ZrusNational Academy of Sciences of Belarus, the United Institute of Informatics ProblemsInformatika1816-03012021-09-01183485810.37661/1816-0301-2021-18-3-48-58977Analytical solution of problem of shielding low-frequency magnetic field by thin-walled cylindrical screen in presence of cylinderG. Ch. Shushkevich0Yanka Kupala State University of GrodnoThe analytical solution of boundary value problem describing the process of penetration of low-frequency magnetic field through thin-walled cylindrical screen with cylindrical inclusion is constructed by use of approximate boundary conditions. The source of the field is a thin thread of infinitely small length with an infinitely small cross-section where current circulates. Thread is located in a plane which is perpendicular to axis of cylindrical screen, in outer region with respect to a screen. Initially the potential of initial magnetic field is represented as spherical harmonic functions, then using addition theorems connecting spherical and cylindrical harmonic functions, it became as cylindrical harmonic functions superposition. Secondary potentials of magnetic field are also presented as superposition of cylindrical harmonic functions in three-dimensional space. It is shown that the solution of formulated boundary value problem is reduced to the solution of linear algebraic equations system for coefficients included in the representation of secondary fields. The influence of some aspects of the problem on the value of the screening coefficient of an external magnetic field when passing through a cylindrical copper screen in the presence of a cylindrical inclusion is studied numerically. Calculation results are presented in graphs form. Obtained results can be used to shield technical devices and biological objects against the effects of magnetic fields to provide ecological surrounding of operating electrical installations and devices.https://inf.grid.by/jour/article/view/1147boundary value problempotentialmagnetic fieldthin-walled cylindrical screenaddition theoremsharmonic functions |
| spellingShingle | G. Ch. Shushkevich Analytical solution of problem of shielding low-frequency magnetic field by thin-walled cylindrical screen in presence of cylinder Informatika boundary value problem potential magnetic field thin-walled cylindrical screen addition theorems harmonic functions |
| title | Analytical solution of problem of shielding low-frequency magnetic field by thin-walled cylindrical screen in presence of cylinder |
| title_full | Analytical solution of problem of shielding low-frequency magnetic field by thin-walled cylindrical screen in presence of cylinder |
| title_fullStr | Analytical solution of problem of shielding low-frequency magnetic field by thin-walled cylindrical screen in presence of cylinder |
| title_full_unstemmed | Analytical solution of problem of shielding low-frequency magnetic field by thin-walled cylindrical screen in presence of cylinder |
| title_short | Analytical solution of problem of shielding low-frequency magnetic field by thin-walled cylindrical screen in presence of cylinder |
| title_sort | analytical solution of problem of shielding low frequency magnetic field by thin walled cylindrical screen in presence of cylinder |
| topic | boundary value problem potential magnetic field thin-walled cylindrical screen addition theorems harmonic functions |
| url | https://inf.grid.by/jour/article/view/1147 |
| work_keys_str_mv | AT gchshushkevich analyticalsolutionofproblemofshieldinglowfrequencymagneticfieldbythinwalledcylindricalscreeninpresenceofcylinder |