Abstract and Applied Analysis
Volume 2004 (2004), Issue 4, Pages 307-314
On the exterior magnetic field and silent sources in
1Division of Applied Mathematics, Department of Chemical Engineering, University of Patras, Patras 26504, Greece
2Institute of Chemical Engineering and High Temperature Chemical Processes
(ICE/HT), Foundation for Research Technology-Hellas (FORTH), Patras 26504, Greece
Received 27 September 2002
Copyright © 2004 George Dassios and Fotini Kariotou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Two main results are included in this
paper. The first one
deals with the leading asymptotic term of the magnetic field
outside any conductive medium. In accord with physical reality,
it is proved mathematically that the leading approximation is
a quadrupole term which means that the conductive brain tissue
weakens the intensity of the magnetic field outside the head.
The second one concerns the orientation of the silent sources
when the geometry of the brain model is not a sphere but an
ellipsoid which provides the best possible mathematical
approximation of the human brain. It is shown that what
characterizes a dipole source as silent is not the collinearity
of the dipole moment with its position vector, but the fact that
the dipole moment lives in the Gaussian image space at the point
where the position vector meets the surface of the ellipsoid.
The appropriate representation for the spheroidal case is also