Abstract
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.
Keywords
Publication details
- DOI
- 10.24200/squjs.vol17iss2pp170-186
- Journal
- Sultan Qaboos University Journal for Science, 17(2), 170
- Publisher
- Sultan Qaboos University
- Open access
- Gold open access
- License
- CC BY 4.0
Cite this article
APA 7
Ashour, A., Abou-Dina, M. S., & Ghaleb, A. F. (2012). 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, 17(2), 170. https://doi.org/10.24200/squjs.vol17iss2pp170-186
MLA 9
Ashour, A.A., et al. "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, vol. 17, no. 2, 2012, pp. 170. https://doi.org/10.24200/squjs.vol17iss2pp170-186.
Chicago (author–date)
Ashour, A.A., Moustafa Saber Abou-Dina, and Ahmed Fouad Ghaleb. 2012. "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 17 (2): 170. https://doi.org/10.24200/squjs.vol17iss2pp170-186.
Harvard
Ashour, A., Abou-Dina, M. S. and Ghaleb, A. F. (2012) '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, 17(2), pp. 170. doi:10.24200/squjs.vol17iss2pp170-186.
Vancouver
Ashour A, Abou-Dina MS, Ghaleb AF. 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. 2012;17(2):170. doi:10.24200/squjs.vol17iss2pp170-186
IEEE
A. Ashour, M. S. Abou-Dina, and 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, vol. 17, no. 2, pp. 170, 2012, doi: 10.24200/squjs.vol17iss2pp170-186.