The Method of Zero Tangential Strengths in the Problem of Charge Distribution over the Surfaces of Two Interacting Tori

Document Type : Research Paper

Authors
Nikita N. Dmitriev
Vadim Yu. Sakharov
Alexey A. Tikhonov
Saint Petersburg State University, 7-9 Universitetskaya nab., Saint Petersburg, 199034, Russia
10.22055/jacm.2025.48138.5009
Abstract
In this paper, a system of two circular concentric non-touching tori is considered. An electrostatic charge can be applied to each of the tori. The problem is to find the density of charge distribution over the surfaces of the tori, taking into account the Coulomb interaction between the surfaces. The required density is found numerically by the method of successive approximations based on the fact that in the static case, the total tangential strength of the Coulomb forces is zero at each of the points on the surface of each of the tori. The corresponding functional is constructed, the problem of numerical minimization of which is solved by the gradient descent method.
Keywords
Torus
electrostatic charge
charge distribution
tangential stresses
surface density
gradient descent method
Subjects

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Journal of Applied and Computational Mechanics
Volume 11, Issue 4
Autumn 2025
Pages 1196-1206