The Interaction Force between the Halves of a Uniformly Polarized Ellipsoidal Dielectric

  • Oleg P. POLYAKOV
  • Petr A. POLYAKOV
DOI: https://doi.org/10.24160/0013-5380-2025-7-66-70
Keywords: electrostatics of dielectrics, Maxwell tension tensor, interaction forces between polarized bodies

Abstract

The article deals with a theoretical study of the ponderomotive coupling force between the components of uniformly polarized ellipsoid-shaped dielectric bodies. A new analytical solution to the problem of the interaction between two halves of a uniformly polarized dielectric ellipsoid of revolution has been found. In the special case of a uniformly polarized ball, the obtained solution coincides with the well-known Landau solution for the attraction force between the halves of a polarized ball. The dependence of the interaction force between the halves of a polarized ellipsoid on the ratio of its semi-axes is constructed. It is shown, within the framework of the Maxwell tension tensor method, that the main contribution to the coupling force is introduced by the tension of electric field lines in the virtual gap between the ellipsoid halves. When taking into account only the tension of the electric field lines, the deviation from the interaction force exact value is no more than 20%. The dependence of the attraction force between the halves of a polarized ellipsoid of a fixed volume on the ratio of its semi-axes is found. It has been established that this force has a maximum value for the case of a spherical ellipsoid. It is shown that when the ratio of the semi-axes tends to an infinitely large value (an elongated ellipsoid), the interaction force between its halves tends to zero. The same interaction force value is also achieved in the case of an infinitesimal ratio of the semi-axes, i.e., for an ellipsoid having an oblate shape.

Author Biographies

Oleg P. POLYAKOV

(M.V. Lomonosov Moscow State University, Moscow, Russia) – Docent of the General Physics Dept., Faculty of Physics, Cand. Sci. (Phis.-Math.).

Petr A. POLYAKOV

(M.V. Lomonosov Moscow State University, Moscow, Russia) – Professor of the General Physics Dept., Faculty of Physics, Dr. Sci. (Phis.-Math.), Professor.

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Published
2025-05-29
Issue
No 7 (2025): Issue № 7
Section
Article