The reduced scalar potential in regions with permeable materials : reasons for loss of accuracy and cancellation

Stéphane Balac
MAPLY, INSA de Lyon
20 Av. Albert Einstein
69621 Villeurbanne, France
Stephane.Balac@insa-lyon.fr

Gabriel Caloz
IRMAR, Université de Rennes 1
Campus de Beaulieu
35042 Rennes Cedex, France
Gabriel.Caloz@univ-rennes1.fr

Abstract

Practical three-dimensional magnetic field problems usually involve regions containing current sources as well as regions with permeable materials. Then the use of both the reduced scalar potential (RSP) and the total scalar potential is recommended since the use of the RSP alone usually gives severe loss in accuracy in permeable regions. Using an asymptotic expansion, we investigate the reasons for this lack of accuracy in permeable regions when using the RSP as a single potential. Finally we show that the use of two potentials is not necessarily required if the RSP is used in an adequate manner.

Keywords

magnetostatic field, reduced scalar potential, total scalar potential, asymptotic expansion.