The field diffraction of current ring on a spiral conductive sphere with a hole

The problem of the field diffraction of radial electrical current ring on a spiral conductive sphere with a hole has been solved. The current ring is placed outside the supplement of a sphere with a hole to a closed hollow sphere. The method of operator semi-inversion of the problem, the method of separation of variables in the spherical system coordinates and of the solution of Abel integral equations are used. The infinite system of linear algebraic equations of the second kind with a compact operator in a Hilbert space is obtained. Efficient solvability of algebraic equations of the problem is justified. Some limiting variants of the problem are investigated. Some resonant frequencies of the structure are considered.