Steady-state sphere-like and ring-like formations of the free electromagnetic field in vacuum

Abstract

It is shown that there are exact solutions of the free Maxwell equations in vacuum allowing and existence of closed spherical magnetic surfaces (without electric field on this surface and where magnetic field is tangential and its intensity depends on time) and ring-life formations of time-dependent electric field (without magnetic field in all points of the ring and where the electric is tangential). It is detected that a form of this spheres and rings does not change with time in vacuum. One can surmise that these electromagnetic formations correspond to Kapitsas´s hyphotesis about origin and structure of ball lightning. It is shown a simple way to solve the equation.