volume | PIER Journals

Abstract

The aim of this paper is to show the interest of using equivalence models for calculating the electric field produced by cylindrical capacitors with dielectrics. To do so, we use an equivalent model, based on the dual Maxwell's Equations for calculating the two electric field components created inside the capacitor and outside it. This equivalent model uses fictitious currents generating a electric vector potential that allows us to determine the electric field components in all points in space. The electric field produced by charge distributions as capacitor with dielectrics is generally determined by using the coulombian model. Indeed, it is well known that the electric field derives from a scalar potential. By using the Maxwell's equations, this scalar potential is in fact linked to the existence of charge distributions that are generally located on the faces of the capacitors. However, this last model does not allow us to obtain reduced analytical expressions since it involves the calculation of charge volume density appearing in the dielectric material for arcshaped cylindrical topologies. Consequently, it is interesting to look for another approach that gives analytical expressions with a lower computational cost. In this paper, we show that the use of fictitious currents instead of charges allow us to obtain 3D analytical reduced expressions with a lower computational cost. This analytical approach is compared to the coulombian model for showing the equivalence between the two approaches.

1. Durand, E., Magnetostatique, Masson Editeur, 1968.

2. Akyel, C., S. I. Babic, and M. M. Mahmoudi, "Mutual inductance calculation for non-coaxial circular air coils with parallel axes," Progress In Electromagnetics Research, Vol. 91, 287-301, 2009.
doi:10.2528/PIER09021907

3. Babic, S. I., F. Sirois, and C. Akyel, "Validity check of mutual inductance formulas for circular filaments with lateral and angular misalignments," Progress In Electromagnetics Research M, Vol. 8, 15-26, 2009.
doi:10.2528/PIERM09060105

4. 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, 1995.
doi:10.1109/20.364587

5. Furlani, E. P. and M. Knewston, "A three-dimensional field solution for permanent-magnet axial-field motors," IEEE Trans. Magn., Vol. 33, No. 3, 2322-2325, 1997.
doi:10.1109/20.573849

6. Ravaud, R., G. Lemarquand, and V. Lemarquand, "Magnetic field created by tile permanent magnets," IEEE Trans. Magn., Vol. 45, No. 7, 2920-2926, 2009.
doi:10.1109/TMAG.2009.2014752

7. Furlani, E. P., Permanent Magnet and Electromechanical Devices: Materials, Analysis and Applications, Academic Press, 2001.

8. Ravaud, R. and G. Lemarquand, "Comparison of the coulombian and amperian current models for calculating the magnetic field produced by radially magnetized arc-shaped permanent magnets," Progress In Electromagnetics Research, Vol. 95, 309-327, 2009.
doi:10.2528/PIER09042105

9. Emets, Y. P., N. V. Barabanova, Y. P. Onofrichuk, and L. Suboch, "Force on insulated wire at the interface of 2 dielectric media," IEEE Trans. Dielectrics and Electrical Insulation, Vol. 1, No. 6, 1201-1204, 1994.
doi:10.1109/94.368642

10. Emets, Y. P., "Electric field of insulated wire at the interface of two dielectric media ," IEEE Trans. Dielectrics and Electrical Insulation, Vol. 4, No. 4, 439-449, 1997.
doi:10.1109/94.625361

11. Emets, J. Y. and Y. P. Onofrichuk, "Interaction forces of dielectric cylinders in electric fields," IEEE Trans. Dielectrics and Electrical Insulation, Vol. 3, No. 1, 87-98, 1996.
doi:10.1109/94.485519

12. Emets, Y. P., "System of two dielectric cylinders involving charge sources: I. Calculation of the electric field," Technical Physics, Vol. 50, No. 11, 1391-1401, 2005.
doi:10.1134/1.2131944

13. Wu, C.-Y., Y. Wang, and C.-C. Zhu, "Effect of equivalent surface charge density on electrical field of positively beveled p-n junction," Journal of Shangai University, Vol. 12, No. 1, 43-46, 2008.
doi:10.1007/s11741-008-0109-2

14. Ye, Q. Z., J. Li, and J. C. Zhang, "A displaced dipole model for a two-cylinder system," IEEE Trans. Dielectrics and Electrical Insulation, Vol. 11, No. 3, 542-550, 2004.

15. Babic, S. I. and C. Akyel, "Improvement in the analytical calculation of the magnetic field produced by permanent magnet rings," Progress In Electromagnetics Research C, Vol. 5, 71-82, 2008.

16. Babic, S. I., C. Akyel, and M. M. Gavrilovic, "Calculation improvement of 3D linear magnetostatic field based on fictitious magnetic surface charge," IEEE Trans. Magn., Vol. 36, No. 5, 3125-3127, 2000.
doi:10.1109/20.908707

17. Lang, M., "Fast calculation method for the forces and stiffnesses of permanent-magnet bearings," 8th International Symposium on Magnetic Bearing, 533-537, 2002.

18. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "Discussion about the analytical calculation of the magnetic field created by permanent magnets," Progress In Electromagnetics Research B, Vol. 11, 281-297, 2009.
doi:10.2528/PIERB08112102

19. 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, 2008.
doi:10.1109/TMAG.2008.923096

20. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "The three exact components of the magnetic field created by a radially magnetized tile permanent magnet," Progress In Electromagnetics Research, Vol. 88, 307-319, 2008.
doi:10.2528/PIER08112708

21. Babic, S. I., 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, 2002.
doi:10.1109/20.996131

22. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "Permanent magnet couplings: Field and torque three-dimensional expressions based on the coulombian model," IEEE Trans. Magn., Vol. 45, No. 4, 1950-1958, 2009.
doi:10.1109/TMAG.2008.2010623

23. Azzerboni, B., E. Cardelli, and A. Tellini, "Computation of the magnetic field in massive conductor systems," IEEE Trans. Magn., Vol. 25, No. 6, 4462-4473, 1989.
doi:10.1109/20.45327

24. Azzerboni, B., E. Cardelli, M. Raugi, A. Tellini, and G. Tina, "Analytic expressions for magnetic field from finite curved conductors," IEEE Trans. Magn., Vol. 27, No. 2, 750-757, 1991.
doi:10.1109/20.133288

25. Azzerboni, B., G. A. Saraceno, and E. Cardelli, "Three-dimensional calculation of the magnetic field created by current-carrying massive disks," IEEE Trans. Magn., Vol. 34, No. 5, 2601-2604, 1998.
doi:10.1109/20.717601

26. Brissonneau, P., Magnetisme et Materiaux Magnetiques pour l'Electrotechnique, Hermes Ed., 1997.

Dr. Romain Ravaud

Prof. Guy Lemarquand

Dr. Slobodan Babic