https://doi.org/10.1140/epjp/s13360-023-03791-y
Regular Article
The differential forms of Rumsey reaction and the corresponding reciprocal equations in the unified space and time form
1
Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing, China
2
School of Electronic Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, China
3
Institute of Electrical Engineering and Advanced Electromagnetic Drive Technology, Qilu Zhongke, China
Received:
17
November
2022
Accepted:
8
February
2023
Published online:
3
March
2023
Rumsey proposed the concept of reaction to describe the interaction between two sets of time-harmonic electromagnetic sources through the fields produced by sources, and expressed the Lorentz Reciprocity Theorem in a concise form of < 1,2 > = < 2,1 > , in 1954. Later, Lindell et al. extended the Rumsey’s reaction using the differential form, which contains two terms. The spatial term is the traditional Rumsey’s reaction term, which represents the electromagnetic power density reaction (scalar reaction), and the time-related term is the electromagnetic force density reaction (vector reaction). In this paper, the corresponding unified space and time form of the reciprocal equation is derived for Lindell’s reaction term by the differential form of the electromagnetic field equation, under the assumption that there is only electric source. However, the special form of the reciprocity equation < 1,2 > = ± < 2,1 > does not exist. Thus, we derived a new unified space and time equation of energy–momentum reciprocity and its special form. From this, a new generalized reaction is defined.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
