Concerning Structure of Simultaneous Equations of the Classical Electrodynamics

Arbitrary vector field in unfirmamented space is completely determined by the distribution of scalar and vector field sources. Volumetric density of the scalar source is divergence, whereas the volumetric density of the vector source is the curl of the considered vector field. The electromagnetic field represents a set of electric and magnetic vector fields (vector field of electrical intensity and vector field of magnetic induction). This predetermines the composition and structure of classical electrodynamics equations: two scalar equations for volumetric densities of scalar field sources and two vector equations for volumetric densities of vector field sources. The hidden symmetry of simultaneous equations of electrostatics and magnetostatics in a part of the physical content of scalar and vector field sources becomes apparent with the formal use of concepts of physically non-existent "magnetic charge" and "magnetic currents". The specificity of the equations of electrostatics and magnetostatics and also hidden symmetry of vectorfield sources of electrical intensity and vector field of magnetic induction in conjunction with the charge conservation law and the law of conservation of electromagnetic energy can form the basis of simultaneous equations design of classical electrodynamics. It is shown that the Ampere's circuital law and the Faraday law of induction can be reviewed as a consequence of generalization of electrostatics and magnetostatics laws and also physical laws mentioned above.

References

[1] Kalashnikov S.G. Elektrichestvo [Electricity]. Moscow, Nauka Publ., 1985. 576 p.

[2] Matveev A.N. Elektrichestvo i magnetism [Electricity and magnetism.]. Moscow, Vyssh.shk. Publ., 1983. 463 p.

[3] Savelyev I.V. The course of general physics. In 5 volumes. Volume II. Electricity and Magnetism, Waves, Optics. Mir Publishers, 1989. 254 p. (Russ. Ed.: Savel’ev I.V. Kurs obshchey fiziki. V 5 kn. Kn. 2: Elektrichestvo i magnetizm. Moscow, AST: Astrel’ Publ., 2005. 336 p.)

[4] Irodov I.E. Elektromagnetizm. Osnovnye zakony [Electromagnetism. The basic laws]. Moscow, Laboratoriya Bazovykh Znaniy Publ., 2000. 352 p. (Russ. Ed.: Irodov I.E. Elektromagnetizm. Osnovnye zakony. Moscow, Laboratoriya Bazovykh Znaniy, 2000. 352 p.).

[5] Gershenzon E.M., Malov N.N., Mansurov A.N. Elektrodinamika [Electrodynamics]. M.: Izdatel’skiy tsentr "Akademiya" Publ., 2002. 352 p.

[6] Bessonov L.A. Teoreticheskie osnovy elektrotekhniki. Elektromagnitnoe pole. [Theory of electrotechnics. Electromagnetic field]. Moscow, Gardariki Publ., 2001. 317 p.

[7] Matveev A.N. Elektrodinamika [Electrodynamics]. Moscow, Vyssh.shk. Publ., 1980. 383 p.

[8] Kugushev A.M., Golubeva N.S., Mitrokhin V.N. Osnovy radioelektroniki. Elektrodinamika i rasprostranenie radiovoln [Radioelectronics basis. Electrodynamics and radiowave propagation] Moscow, MGTU im. N.E. Baumana Publ., 2001. 368 p.

[9] Golubeva N.S., Mitrokhin V.N. Osnovy radioelektroniki sverkhvysokikh chastot [Basis of radioelectronics of superhigh frequency]. Moscow, MGTU im. N.E. Baumana Publ., 2006. 488 p.

[10] Novozhilov Yu.V., Yappa Yu.A. Elektrodinamika [Electrodynamics]. Moscow, Nauka Publ., 1978. 352 p.

[11] Makarov A.M., Luneva L.A., Makarov K.A. Integral equation of electrostatics. Рroc. 6 Vseross. Konf. "Neobratimye protsessy v prirode i tekhnike". V 3 ch.) [Summ. Rep. 6th All-Russ. Conf. "Irreversible processes in the Nature and Technology". In 3 parts], Moscow, 26-28 January 2011, MGTU im. N.E. Baumana, 2011, part 1, pp. 207-210 (in Russ.).

[12] Makarov A.M., Luneva L.A., Makarov K.A. Substantiation of the equations of isotropic dielectric electrostatics. Рroc. 6 Vseross. Konf. "Neobratimye protsessy v prirode i tekhnike". V3 ch.) [Summ. Rep. 6th All-Russ. Conf. "Irreversible processes in the Nature and Technology". In 3 parts], Moscow, 26-28 January 2011, MGTU im. N.E. Baumana, 2011, part 1, pp. 211-214 (in Russ.).

[13] Makarov A.M., Luneva L.A., Makarov K.A. Concerning basic equations of isotropic dielectrics electrostatics. Vestn. Mosk. Gos. Tekh. Univ. im. N. E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2011, no. 2, pp. 25-40 (in Russ.).

[14] Makarov A.M., Luneva L.A., Makarov K.A. Magnetostatics of conductive medium. Рroc. 6 Vseross. Konf. "Neobratimyeprotsessy vprirode i tekhnike". V3 ch.) [Summ. Rep. 6th All-Russ. Conf. "Irreversible processes in the Nature and Technology". In 3 parts], Moscow, 26-28 January 2011, MGTU im. N.E. Baumana, 2011, part 1, pp. 215-218 (in Russ.).

[15] Makarov A.M., Luneva L.A., Makarov K.A. The statics of isotropic magnetics. Рroc. 6 Vseross. Konf. "Neobratimyeprotsessy vprirode i tekhnike". V3 ch.) [Summ. Rep. 6th All-Russ. Conf. "Irreversible processes in the Nature and Technology". In 3 parts], Moscow, 26-28 January 2011, MGTU im. N.E. Baumana, 2011, part 1, pp. 219-222 (in Russ.).

[16] Landau L.D., Lifshits E.M. Course of theoretical physics. Ten-volume set. Vol. 2 The Classical Theory of Fields,. Oxford, New York, Pergamon, 1984. 460 p. (Russ. Ed.: Landau L.D., Lifshits E.M. Teoreticheskaya fizika. V 10 t. T. 2. Teoriya polya. Moscow, Gos. izd-vo fiz.-mat. Lit. Publ., 1962. 423 p.).

[17] Savel’ev I.V. Osnovy teoreticheskoy fiziki. V 2 t. T. 1. Mekhanika i elektrodinamika. [Fundamentals of theoretical physics. Two-volume set. Vol. 1. Mechanics and electrodynamics]. Moscow, Nauka Publ., 1991. 496 p.

[18] Abraham Max, Becker Richard. The Classical Theory of Electricity and Magnetism. 2nd ed. Blackie & Son Limited, 1932. 285 p. (Russ. Ed.: Abragam M., Bekker R. Teoriya elektrichestva. L.eningrad, Moscow, ONTI: Gl. Red. Obshchetekhn. Lit. Publ., 1936. 281 p.).

[19] Panofsky W.K.H., Phillips M. Classical Electrodynamics. Second Edition. Dover Books on Physics, 2005. 512 p. (Russ. ed.: Panovskiy V., Filips M. Klassicheskaya elektrodinamika. Per. s angl. V.P. Bykova. Pod red. S.P. Kapitsy / Moscow, Fizmatgiz Publ., 1963. 432 p.).

[20] Whittaker E.R.S. A History of the Theories of Aether and Electricity. The Classical Theories. Humanities Press, 1973. 481 p. (Russ. Ed.: Uitteker E. Istoriya teorii efira i elektrichestva / per. s angl. N.A. Zubchenko. Izhevsk, NITs "Regulyarnaya i khaoticheskaya dinamika" publ., 2001. 512 p.).

[21] Makarov A.M., Luneva L.A., Makarov K.A. Teoriya i praktika klassicheskoy elektrodinamiki [Theory and practice of classical electrodynamics]. Moscow, URSS Publ., 2013. 767 p.

[22] Makarov A.M., Makarov K.A. Ampere’s circuital law as a consequence of Biot-Savart-Laplace’s law. Tezisy 3 Vseross. Konf. "Neobratimye protsessy v prirode i tekhnike" [Summ. Rep. 3th All-Russ. Conf. "Irreversible processes in the Nature and Technology"], Moscow, 24-25 January 2005, MGTU im. N.E. Baumana Publ., 2005, pp. 64-65 (in Russ.).

[23] Makarov A.M., Makarov K.A. Concerning revisiting the closed-circuit circulation of magnetic field intensity of open curve with the current. Tezisy 3 Vseross. Konf. "Neobratimye protsessy v prirode i tekhnike" [Summ. Rep. 3th All-Russ. Conf. "Irreversible processes in the Nature and Technology"], Moscow, 24-25 January 2005, MGTU im. N.E. Baumana Publ., 2005, p. 66 (in Russ.).

[24] Kochin N.E. Vektornoe ischislenie i nachala tenzornogo ischisleniya [Vectorial calculus and the onset of tenser calculus]. Moscow, Nauka Publ., 1965. 427 p.

[25] Umov N.A. Uravneniya dvizheniya energii v telakh. V kn.: "Izbrannye sochineniya" [Motion equation of energy in the bodies. In selected works]. Moscow, Leningrad, Gos. izd-vo teoreticheskoy i tekhnicheskoy lit. Publ., 1950. 575 p.