The gradient descent method in the problem of charge distribution over the surfaces of three concentric tori
Sakharov V. Yu.1, Tikhonov A. A.1
1St. Petersburg State University, St. Petersburg, Russia
Email: v.sakharov@spbu.ru, a.tikhonov@spbu.ru
A system of three 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 by the method of successive approximations based on the fact that in the static case, at each of the points on the surface of each of the tori, the total tangential strength of the Coulomb forces is zero. The corresponding functional is constructed, the problem of numerical minimization of which is solved by the gradient descent method. Keywords: torus, electrostatic charge, surface density, gradient descent method.
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