DocumentCode :
762134
Title :
Electromagnetic quantities in 3-space and the dual Hodge operator
Author :
Fournet, G.
Author_Institution :
Lab. de Genie Electrique de Paris, Ecole Superieure d´´Electr., Gif-sur-Yvette, France
Volume :
149
Issue :
3
fYear :
2002
fDate :
5/1/2002 12:00:00 AM
Firstpage :
138
Lastpage :
146
Abstract :
In 3-space, polar vectors (such as a force F) must be distinguished from axial vectors (such as a torque C). A more detailed analysis shows that ´axial vector´ C is an antisymmetric tensor of the second order. In 3-space, its 9 (= 32) components Cij are grouped together in a 3×3 square. In presentations of electromagnetism, taking account of the existence of these two types of vector, two options exist (α and β), vectors E and B being associated either with group DαHαjα or with group DβHβjβ. Option α (developed in the book Global Geometry of Electromagnetic Systems by Baldomir and Hammond, Clarendon press, 1996) is based on the use of differential forms: magnitudes in m-1 lead to the polar nature of E and Hα while magnitudes in m-2 correspond to B, Dα and jα. The * Hodge operator then becomes necessary allowing, in particular, the forms *E→EH (the H suffix indicating the role of the Hodge operator), to be able to write Dα0E H in the case of the vacuum. This operator is also vital for linking B to Hα, and jα to E. In this paper, we defend option β, showing that the choice of Dβ , Hβ, jβ is justified by purely geometrical arguments; no special operator is then required to establish links between E and Dβ, E and jβ, B and Hβ
Keywords :
computational geometry; electromagnetic field theory; mathematical operators; vectors; Hodge operator role; antisymmetric tensor; axial vectors; differential forms; dual Hodge operator; electromagnetic quantities; electromagnetism; force vector; global electromagnetic systems geometry; polar nature; polar vectors; three-space; three-space components; torque vector;
fLanguage :
English
Journal_Title :
Science, Measurement and Technology, IEE Proceedings -
Publisher :
iet
ISSN :
1350-2344
Type :
jour
DOI :
10.1049/ip-smt:20020192
Filename :
1009376
Link To Document :
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