Analytical solution of the shielding low-frequency magnetic field by thin spherical screens problem

O b j e c t i v e s. Construction of an analytical solution to the problem of shielding a low-frequency magnetic field by two thin non-intersecting spherical screens located on the surface of a sphere. Calculation of the shielding coefficient of the initial magnetic field by spherical screens. M e t h o d s. The method of addition theorems and the method of triple summation equations are used to solve the boundary value problem. The potential of the initial magnetic field is represented as spherical harmonic functions. The secondary potentials of the magnetic field are represented as a superposition of spherical harmonic functions in a local coordinate system in three-dimensional space. Re s u l t s. The solution of the boundary value problem is reduced to the solution of a system of Fredholm integral equations of the second kind with respect to specially introduced functions. The influence of the geometric parameters of the problem on the value of the screening coefficient is numerically investigated. The results of the calculations are presented in the form of graphs. Co n c l u s i o n. The proposed methodology and the developed software can find practical application in the development and design of screens in various fields of technology.