350 rub
Journal Electromagnetic Waves and Electronic Systems №1 for 2018 г.
Article in number:
Application of Gibbs variational principle and Lagrange multiplier method to problems of electrostatics. Part 1. Calculation of variation of electrostatic field energy
Type of article: scientific article
UDC: 517.9:537.2
Keywords: variation energy of electrostatic field Gibbs principle variational principles
Authors:

I.N. Aliev – Dr.Sc.(Phys.-Math.), Professor, Department «Physics», Bauman Moscow State Technical University

Z.A. Samedova – Post-graduate Student, Lecturer, Department «Physics», Bauman Moscow State Technical University

Abstract:

In this paper, we analyzed the calculation of the energy of an electrostatic field and its variation using the Gibbs variational principle and the Lagrange multiplier method. In addition, results were obtained that are the basis for subsequent research in this field of physics, in view of the insufficiently detailed consideration of variational principles in the solution of magnetostatic and electrostatic problems. This paper reflects a completely new method for calculating the energy of an electrostatic field and its variation.

References
  1. Polak L.S. Variaczionny’e princzipy’ mexaniki. Sb. statej klassikov nauki. Fizmatlit. M.: 1959. 930 s.                                Variaczionny’e princzipy’ mexaniki. Ix razvitie i primenenie v fizike. M.: URSS. 2010. 600 s.
  2. Gibbs Dzh. Termodinamicheskie raboty’: Per. s angl. M.-L.: Gostexizdat. 1950. 492 s.
  3. Aliev I.N., Kopy’lov I.S. Primenenie metoda mnozhitelej Lagranzha k vy’chisleniyu magnitnogo polya postoyannogo toka // Dinamika slozhny’x sistem. 2015. № 4. S. 3−10.
  4. Meissner W., Ochsenfeld R. Ein neurer effekt bei eintritt der supraleitfähigkeit // Naturwissenschaften. 1933. V. 21. № 44. P. 787−788.
  5. Fiolhais M.C.N, Essen H., Providenxcia C., Nordmark A.B. Magnetic field and current are zero inside ideal conductors // Progress in electromagnetic research B. 2011. V. 27. P. 187−212.
  6. Fiolhais M.C.N, Essen H. Magnetic field expulsion in perfect conductors-The Magnetic equivalent of Thomson`s theorem // Progress in electromagnetic research symposium proceedings. Stockholm (Sweden). 12−15 August 2013. P. 1193.
  7. Erkovich O.S, Ivliev P.A. Raschet magnitny’x svojstv odnoslojny’x uglerodny’x nanotrubok v ramkax metoda funkczionalov plotnosti // Vestnik MGTU im. Baumana. Ser. Estestvenny’e nauki. 2016. № 4(67). doi 10.186.98/1812-3368-2016-4-56-64.
  8. Yurchenko S.O.,Kryuchkov N.P.,Ivlev A.V. Interpolation method for pair correlations in classical crystals // Journal of Physics. Condensed Matter. 2016. 28. P. 235401.7. doi 1088/0953-8984/28/23/235401.
  9. Kazanczev V.P. Primer, demonstriruyushhij vozmozhnosti i osobennosti variaczionnogo podxoda k zadacham e’lektrostatiki // UFN. 2002. T. 172. № 3. S. 357−362. doi:10.3367/UFNr.0172.200203g.0357.
  10. Maksvell D.K. Traktat ob e’lektrichestve i magnetizme. T. 1. M.: Nauka. 1989. 416 s.
  11. 11. Landau L.D., Lifshicz E.M. E’lektrodinamika sploshny’x sred. M.: Nauka. 1982. 620 s.
  12. Zommerfel’d A. E’lektrodinamika. M.: Izd-vo inostrannoj literatury’. 1958. 501 s.
  13. Aliev I.N., Kopy’lov I.S. Ob e’lektrodinamicheskoj modeli Londonov i teorii Gortera–Kazimira // Poverxnost’. Rentgenovskie, sinxrotronny’e i nejtronny’e issledovaniya. 2017. № 2. S. 64. doi10.7868/S0207352816120040.
Date of receipt: 20 сентября 2017 г.