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## The Integral Theorem of the Field Energy

#### Sergey G. FEDOSIN [1]

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 four-potential of the field and the four-current 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 energy-momentum 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 non-rotating 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.

Vector field, Acceleration field, Pressure field, Relativistic uniform system
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Primary Language en Engineering Physics Orcid: 0000-0003-3627-2369Author: Sergey G. FEDOSIN (Primary Author)Institution: Perm scientific siteCountry: Russian Federation Publication Date : June 1, 2019
 Bibtex @research article { gujs435567, journal = {Gazi University Journal of Science}, issn = {}, eissn = {2147-1762}, 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) , 686-703 . 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 ): 686-703 Chicago Fedosın, S . "The Integral Theorem of the Field Energy". Gazi University Journal of Science 32 (2019 ): 686-703 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 - -2147-1762 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 -2147-1762 %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): 686-703 . AMA Fedosın S . The Integral Theorem of the Field Energy. Gazi University Journal of Science. 2019; 32(2): 686-703. Vancouver Fedosın S . The Integral Theorem of the Field Energy. Gazi University Journal of Science. 2019; 32(2): 686-703. IEEE S. Fedosın , "The Integral Theorem of the Field Energy", Gazi University Journal of Science, vol. 32, no. 2, pp. 686-703, Jun. 2019

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