On the Time Integral of Electromagnetic Field

• Published in: Journal of experimental and theoretical physics Vol. 136; no. 4; pp. 406 - 410
• Main Author: Feshchenko, R. M.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.04.2023; Springer; Springer Nature B.V
• Subjects: Acceleration; Atoms; Charged particles; Classical and Quantum Gravitation; Electric charge; Electromagnetic fields; Electromagnetism; Elementary Particles; Fourier transforms; Magnetic fields; Molecules; Optics; Particle and Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theory; Radiation; Relativity Theory; Solid State Physics
• ISSN: 1063-7761; 1090-6509
• DOI: 10.1134/S1063776123040027

The integral over time of an electric or magnetic field in infinite limits (Bessonov integral) is considered; it is shown that it is equal to zero for any configuration of the free electromagnetic field with zero total energy. The connection between zero Bessonov integral and the impossibility of emission or absorption of a photon by a free charged particle is investigated. Exact expressions for the radiation field as well as its Fourier transform are obtained for an electric charge with an abrupt change in the velocity; it is shown that the Bessonov integral of such a radiation field equals zero as follows from the general statement. In conclusion it is shown that a nonzero Bessonov integral of the radiation field produced by an electric charge moving with acceleration, which has been reported in a number of publications, appears because of the incorrect decomposition of the total field of the accelerated charge into the radiative and nonradiative components.