In this paper, we present an improved Coulombianbased analytical calculation of magnetic fields created by permanentmagnetic rings. The 3 dimensional (3D) components of two types of magnetized rings (axially and radially) were analytically evaluated. The obtained components of the magnetic field are expressed over complete elliptical integrals of the first and second kind, as well as by Heuman's Lambda function. These expressions permit fast and accurate calculations of the magnetic field at any point of interest, for both regular and singular cases. The presented method gives an improvement of already known expressions for calculating the magnetic fields of the aforementioned magnetized rings, and we consider that these improved analytical expressions are more extendable to numerical applications.
1. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "Analytical calculation of the magnetic field created by permanent-magnet rings," IEEE Trans. Magn. , Vol. 44, No. 8, 1982-1989, Aug. 2008. doi:10.1109/TMAG.2008.923096
2. Rakotoarison, H., J. Yonnet, and B. Delinchant, "Using coulombian approach for modelling scalar potential and magnetic field of a permanent magnet with radial polarization," IEEE Trans. Magn., Vol. 43, No. 4, 1261-1264, Apr. 2007. doi:10.1109/TMAG.2007.892316
3. Zhilichev, Y., "Calculation of magnetic field of tubular permanent magnet assemblies in cylindrical bipolar coordinates," IEEE Trans. Magn., Vol. 43, No. 7, 3189-3195, Jul. 2007. doi:10.1109/TMAG.2007.894636
4. Lindell, I. V., "Electromagnetic field in self-dual media in different-form representation," Progress In Electromagnetics Research, Vol. 58, 319-333, 2006. doi:10.2528/PIER05072201
5. Lemarquand, G. and V. Lemarquand, "Annular magnet position sensor," IEEE. Trans. Magn., Vol. 26, No. 5, 2041-2043, Sep. 1990. doi:10.1109/20.104612
6. Lemarquand, G. and V. Lemarquand, "Variable magnetic torque sensor," J. Appl. Phys., Vol. 70, No. 10, 6630-6632, 1991. doi:10.1063/1.349880
7. Pulyer, Y. and M. Hrovat, "Generation of remote homogeneous magnetic field," IEEE Trans. Magn., Vol. 38, No. 3, 1553-1563, May 2002. doi:10.1109/20.999131
8. Berkouk, M., V. Lemarquand, and G. Lemarquand, "Analytical calculation of ironless loudspeaker motors," IEEE Trans. Magn., Vol. 37, No. 2, 1011-1014, Mar. 2001. doi:10.1109/20.917185
9. Furlani, E. P., S. Reznik, and A. Kroll, "A three-dimensonal field solution for radially polarized cylinders," IEEE Trans. Magn., Vol. 31, No. 1, 844-851, Jan. 1995. doi:10.1109/20.364587
10. Durand, E., Electrostatique, Vol. 1, 248-251, Masson Editeur, Paris, France, 1964.
11. Dehghan, M. and F. Shakeri, "Solution of an integral-differential equation arising oscillating magnetic fields using He's homotopy peturbation method ," Progress In Electromagnetics Research, Vol. 78, 361-376, 2008. doi:10.2528/PIER07090403
12. D'Agostino, F., F. Ferrara, C. Gennarelli, R. Guerriero, and G. Riccio, "An effective technique for reducing the truncation error in the near-field-far-field transformation with plane-polar scanning," Progress In Electromagnetics Research, Vol. 73, 213-238, 2007. doi:10.2528/PIER07032202
13. Furlani, E. P., "A 3-dimensional field solution for axially polarized multipole disks," J. Magn. Magn. Mat., Vol. 135, No. 2, 205-214, 1994. doi:10.1016/0304-8853(94)90347-6
14. Furlani, E. P., Permanent Magnet & Electromechanical Devices: Materials, A nalysis, and Applications, Academic Press, 2001.
15. Azzerboni, B. and E. Cardelli, "Magnetic field evaluation for disk conductors," IEEE Trans. Magn., Vol. 29, No. 6, 2419-2421, 1993. doi:10.1109/20.280997
16. Xu, X. B. and L. Zeng, "Ferromagnetic cylinders in earth's magnetic field: A two-dimentional model of magnetization of submarine," Progress In Electromagnetics Research, Vol. 19, 319-335, 1998. doi:10.2528/PIER97120100
17. Babic, S. I. and C. Akyel, "New mutual inductance calculation of the magnetically coupled coils: Thin disk coil-thin wall solenoid," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 10, 1661-1669, 2006. doi:10.1163/156939306779276794
18. Babic, S., C. Akyel, S. Salon, and S. Kincic, "New expressions for calculating the magnetic field created by radial current in massive disks," IEEE Trans. Magn., Vol. 38, No. 2, 497-500, Mar. 2002. doi:10.1109/20.996131
19. Babic, S. and M. Gavrilovic, "New expression for calculating magnetic fields due to current-carrying solid conductors," IEEE Trans. Magn., Vol. 33, No. 5, 4134-4136, Sep. 1997. doi:10.1109/20.619687
20. Babic, S., et al., "Analytical magnetostatic field calculation for the conductor carrying constant current in the longitudinal diretion," J. Appl. Phys., Vol. 67, 5827-5829, May 1990. doi:10.1063/1.345977
21. Blache, C. and G. Lemarquand, "High magnetic field gradients in flux confining permanent magnet structures," J. Magn. Magn. Mater., Vol. 104–107, 1111-1112, 1992. doi:10.1016/0304-8853(92)90510-U
22. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics, Series 55, Washington DC, Dec. 1972.
23. Gradshteyn, I. S. and I. M. Rhyzik, Tables of Integrals, Series and Products, Dover, New York, 1972.