Modeling the electrostatic field of a charged ring located inside an infinite cylinder in the presence of a torus

Abstract

Objectives. Analytical solution of the boundary value problem of electrostatics for modeling the electrostatic field of a charged ring located inside a grounded infinite circular cylinder in the presence of a perfectly conducting torus is considered. The field source is a thin charged ring located on a plane perpendicular to the axis of the cylindrical screen.Methods. To solve the problem, the method of addition theorems is used. The potential of the initial electrostatic field is presented in the form of spherical harmonic functions and in the form of a superposition of cylindrical and toroidal harmonic functions, using addition theorems relating spherical, cylindrical and toroidal harmonic functions. The secondary potential of the electrostatic field is also represented as a superposition of cylindrical and toroidal harmonic functions.Results. The solution of the formulated boundary problem is reduced to the solution of an infinite system of linear algebraic equations of the second kind with respect to the coefficients included in the representation of the secondary field. The influence of some parameters of the problem on the value of the electrostatic potential inside a grounded cylindrical shield in the presence of a toroidal inclusion is numerically studied. The calculation results are presented in the form of graphs.Conclusion. The proposed technique and the developed software can find practical application in the development and design of screens in various fields of technology.

Keywords

• boundary value problem
• electrostatic field
• potential
• addition theorems
• harmonic functions