The integral theorem of the vector field energy is derived in a covariant way, according to which under certain conditions the potential energy of the system’s field turns out to be half as large in the absolute value as the field’s kinetic energy associated with the fourpotential of the field and the fourcurrent of the system’s particles. Thus, the integral theorem turns out to be the analogue of the virial theorem, but with respect to the field rather than to the particles. Using this theorem, it becomes possible to substantiate the fact that electrostatic energy can be calculated by two seemingly unrelated ways, either through the scalar potential of the field or through the stres energymomentum tensor of the field. In closed systems, the theorem formulation is simplified for the electromagnetic and gravitational fields, which can act at a distance up to infinity. At the same time for the fields acting locally in the matter, such as the acceleration field and the pressure field, in the theorem formulation it is necessary to take into account the additional term with integral taken over the system’s surface. The proof of the theorem for an ideal relativistic uniform system containing nonrotating and randomly moving particles shows full coincidence in all significant terms, particularly for the electromagnetic and gravitational fields, the acceleration field and the vector pressure field.
Primary Language  en 

Subjects  Engineering 
Journal Section  Physics 
Authors 

Dates 
Publication Date : June 1, 2019 
Bibtex  @research article { gujs435567,
journal = {Gazi University Journal of Science},
issn = {},
eissn = {21471762},
address = {},
publisher = {Gazi University},
year = {2019},
volume = {32},
pages = {686  703},
doi = {},
title = {The Integral Theorem of the Field Energy},
key = {cite},
author = {Fedosın, Sergey G.}
} 
APA  Fedosın, S . (2019). The Integral Theorem of the Field Energy . Gazi University Journal of Science , 32 (2) , 686703 . Retrieved from https://dergipark.org.tr/en/pub/gujs/issue/45480/435567 
MLA  Fedosın, S . "The Integral Theorem of the Field Energy" . Gazi University Journal of Science 32 (2019 ): 686703 <https://dergipark.org.tr/en/pub/gujs/issue/45480/435567> 
Chicago  Fedosın, S . "The Integral Theorem of the Field Energy". Gazi University Journal of Science 32 (2019 ): 686703 
RIS  TY  JOUR T1  The Integral Theorem of the Field Energy AU  Sergey G. Fedosın Y1  2019 PY  2019 N1  DO  T2  Gazi University Journal of Science JF  Journal JO  JOR SP  686 EP  703 VL  32 IS  2 SN  21471762 M3  UR  Y2  2019 ER  
EndNote  %0 Gazi University Journal of Science The Integral Theorem of the Field Energy %A Sergey G. Fedosın %T The Integral Theorem of the Field Energy %D 2019 %J Gazi University Journal of Science %P 21471762 %V 32 %N 2 %R %U 
ISNAD  Fedosın, Sergey G. . "The Integral Theorem of the Field Energy". Gazi University Journal of Science 32 / 2 (June 2019): 686703 . 
AMA  Fedosın S . The Integral Theorem of the Field Energy. Gazi University Journal of Science. 2019; 32(2): 686703. 
Vancouver  Fedosın S . The Integral Theorem of the Field Energy. Gazi University Journal of Science. 2019; 32(2): 686703. 
IEEE  S. Fedosın , "The Integral Theorem of the Field Energy", Gazi University Journal of Science, vol. 32, no. 2, pp. 686703, Jun. 2019 