The Induction of Electric Currents in a Conducting Spherical Cap with Geomagnetic Applications: A Semi-analytical Approach for the Axisymmetric Case
The objective is to introduce a semi-analytical method for solving axisymmetric problems of electromagnetic induction in thin spherical caps placed in a time-varying magnetic field due to an axial magnetic dipole or in a time-varying uniform axial magnetic field. This method provides approximate sol...
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| Format: | Article |
| Language: | English |
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Sultan Qaboos University
2012-12-01
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| Series: | Sultan Qaboos University Journal for Science |
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| Online Access: | https://journals.squ.edu.om/index.php/squjs/article/view/401 |
| _version_ | 1819131113571876864 |
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| author | A.A. Ashour M.S. Abou-Dina A.F. Ghaleb |
| author_facet | A.A. Ashour M.S. Abou-Dina A.F. Ghaleb |
| author_sort | A.A. Ashour |
| collection | DOAJ |
| description | The objective is to introduce a semi-analytical method for solving axisymmetric problems of electromagnetic induction in thin spherical caps placed in a time-varying magnetic field due to an axial magnetic dipole or in a time-varying uniform axial magnetic field. This method provides approximate solutions to mathematically difficult mixed boundary-value problems governing the induction of electric currents in thin sheets, for arbitrary angles of the cap. Numerical results are given and discussed. The best approximations were obtained for sheets with integrated conductivity decreasing to zero towards the edge of the sheet. The case of uniform conductivity, characterized by weak singularities of the induced magnetic vector potential at the rim of the cap, yielded relatively large errors and is dealt with separately within an improved model. The method may be adequately extended to deal with other problems involving more complicated geometries, arbitrary electric conductivity distributions and inducing magnetic fields, in two or three dimensions, for various geophysical applications. |
| first_indexed | 2024-12-22T09:10:21Z |
| format | Article |
| id | doaj.art-dc0fb18435534d0f9367577fffa4cc98 |
| institution | Directory Open Access Journal |
| issn | 1027-524X 2414-536X |
| language | English |
| last_indexed | 2024-12-22T09:10:21Z |
| publishDate | 2012-12-01 |
| publisher | Sultan Qaboos University |
| record_format | Article |
| series | Sultan Qaboos University Journal for Science |
| spelling | doaj.art-dc0fb18435534d0f9367577fffa4cc982022-12-21T18:31:28ZengSultan Qaboos UniversitySultan Qaboos University Journal for Science1027-524X2414-536X2012-12-0117217018610.24200/squjs.vol17iss2pp170-186398The Induction of Electric Currents in a Conducting Spherical Cap with Geomagnetic Applications: A Semi-analytical Approach for the Axisymmetric CaseA.A. Ashour0M.S. Abou-Dina1A.F. Ghaleb2Department of Mathematics, Faculty of Science, Cairo University, Giza, EgyptDepartment of Mathematics, Faculty of Science, Cairo University, Giza, EgyptDepartment of Mathematics, Faculty of Science, Cairo University, Giza, EgyptThe objective is to introduce a semi-analytical method for solving axisymmetric problems of electromagnetic induction in thin spherical caps placed in a time-varying magnetic field due to an axial magnetic dipole or in a time-varying uniform axial magnetic field. This method provides approximate solutions to mathematically difficult mixed boundary-value problems governing the induction of electric currents in thin sheets, for arbitrary angles of the cap. Numerical results are given and discussed. The best approximations were obtained for sheets with integrated conductivity decreasing to zero towards the edge of the sheet. The case of uniform conductivity, characterized by weak singularities of the induced magnetic vector potential at the rim of the cap, yielded relatively large errors and is dealt with separately within an improved model. The method may be adequately extended to deal with other problems involving more complicated geometries, arbitrary electric conductivity distributions and inducing magnetic fields, in two or three dimensions, for various geophysical applications.https://journals.squ.edu.om/index.php/squjs/article/view/401Spherical cap, Geomagnetic applications, Axisymmetric case. |
| spellingShingle | A.A. Ashour M.S. Abou-Dina A.F. Ghaleb The Induction of Electric Currents in a Conducting Spherical Cap with Geomagnetic Applications: A Semi-analytical Approach for the Axisymmetric Case Sultan Qaboos University Journal for Science Spherical cap, Geomagnetic applications, Axisymmetric case. |
| title | The Induction of Electric Currents in a Conducting Spherical Cap with Geomagnetic Applications: A Semi-analytical Approach for the Axisymmetric Case |
| title_full | The Induction of Electric Currents in a Conducting Spherical Cap with Geomagnetic Applications: A Semi-analytical Approach for the Axisymmetric Case |
| title_fullStr | The Induction of Electric Currents in a Conducting Spherical Cap with Geomagnetic Applications: A Semi-analytical Approach for the Axisymmetric Case |
| title_full_unstemmed | The Induction of Electric Currents in a Conducting Spherical Cap with Geomagnetic Applications: A Semi-analytical Approach for the Axisymmetric Case |
| title_short | The Induction of Electric Currents in a Conducting Spherical Cap with Geomagnetic Applications: A Semi-analytical Approach for the Axisymmetric Case |
| title_sort | induction of electric currents in a conducting spherical cap with geomagnetic applications a semi analytical approach for the axisymmetric case |
| topic | Spherical cap, Geomagnetic applications, Axisymmetric case. |
| url | https://journals.squ.edu.om/index.php/squjs/article/view/401 |
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