Contents
Following the approach of Neumann and Lindell [1] we derive an image line source that produces in a homogeneous medium the same electric field as a point charge inside a layered dielectric sphere. The image charge density function for the sphere with two interfaces is solved analytically, and approximations are derived in the case of a thin layer and a low-contrast layer. An image expression for the thin-layered sphere with three interfaces is developed. We suggest that point charge approximations of the image charge may be used to speed up computations of the electric potential on the scalp due to sources in the brain.
Übersicht
Basierend auf dem Ansatz von Neumann und Lindell [1] wird eine scheinbare Linienladung abgeleitet, die in einem homogenen Medium das gleiche elektrische Feld hervorruft wie eine Punktladung innerhalb einer geschichteten dielektrischen Kugel. Die Dichtefunktion der Bildladung für eine Kugel mit zwei Trennflächen wird analytisch bestimmt, und Näherungen für den Fall einer dünnen Schicht und einer nur kleinen Änderung der Permittivität werden abgeleitet. Eine Abbildung für eine Kugel aus dünnen Schichten mit drei Trennflächen wird entwickelt. Die Punktladungsnäherungen der Bildladungen können verwendet werden, um die Berechnung des elektrischen Potentials auf der Kopfhaut aufgrund von Qellen im Gehirn zu beschleunigen.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Lindell, I. V.: Electrostatic image theory for the dielectric sphere. Radio Sci. 27 (1992) 1–8
Dassios, G.;Kleinman, R. E.: On Kelvin inversion and low-frequency scattering. SIAM Review 31 (1989) 565–585
Neumann, C.: Hydrodynamische Untersuchungen: Leipzig, Teubner, 1883
Sten, J. C.-E.;Lindell, I. V.: Electrostatic image theory for the dielectric sphere with an internal source. Microwave and Optical Tech. Lett. 5 (1992) 579–602
Lindell, I. V.;Ermutlu, M. E.;Sihvola, A. H.: Electrostatic image theory for the layered dielectric sphere. IEEE Proc. H 139 (1992) 186–192
Lindell, I. V.;Sten, J. C.-E.;Nikoskinen, K. I.: Electrostatic image solution for the interaction of two dielectric spheres. Radio Sci. 28 (1993) 319–329
Lindell, I. V.;Sten, J. C.-E.;Kleinmann, R. E.: Low-frequency image theory for the dielectric sphere. J. Electro. Waves Applic., Vol. 8, No. 3, 295–313, 1994
Lindell, I. V.;Lehtola, E. A.: Magnetostatic image theory for the permeable sphere. IEEE Trans. Magn. 28 (1992) 1930–1934
Hosek, R. S.;Sances Jr., A.;Jodat, R. W.;Larson, S. J.: The contributions of intracerebral currents to the EEG and evoked potentials. IEEE Trans. Biomed. Eng. BME-25 (1978) 405–413
Cuffin, B. N.;Cohen, D.: Comparison of the magnetoencephalogram and electroencephalogram. Electroenceph. Clin Neurophysiol. 47 (1979) 132–146
Ary, J. P.;Klein, S. A.;Fender, D. H.: Location of sources of evoked scalp potentials: Corrections for skull and scalp thicknesses. IEEE Trans. Biomed. Eng. BME-28 (1981) 447–452
de Munck, J. C.;van Dijk, B. V.;Spekreijse, H.: An analytic method to determine the effect of source modeling errors on the apparent location and direction of biological sources. J. Appl. Phys. 63 (1988) 944–956
Uzunoglu, N. K.;Ventouras, E.;Papageorgiou, C.;Rabavilas, A.;Stefanis, C.: Inversion of simulated evoked potentials to charge distribution inside the human brain using an algebraic reconstruction technique. IEEE Trans. Med. Imaging 10 (1991) 479–484
Stratton, J. A.: Electromagnetic Theory: New York, McGraw-Hill, 1941
Gradshteyn, I. S.;Ryzhik, I. M.: Table of Integrals, Series, and Products: New York, Academic, Press, 1980
Author information
Authors and Affiliations
Additional information
This study was supported in part by the Academy of Finland. We thank Ismo V. Lindell, Olli V. Lounasmaa and Seppo Ahlfors for criticsm and comments.
Rights and permissions
About this article
Cite this article
Sten, J.C.E., Ilmoniemi, R. Image theory for a point charge inside a layered dielectric sphere. Archiv f. Elektrotechnik 77, 327–335 (1994). https://doi.org/10.1007/BF01574678
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01574678