In this study, ball lightning (BL) is assumed to have a solid, positively-charged core. According to this underlying assumption, the core is surrounded by a thin electron layer with a charge nearly equal in magnitude to that of the core. A vacuum exists between the core and the electron layer containing an intense electromagnetic (EM) field which is reflected and guided by the electron layer. The microwave EM field applies a ponderomotive force (radiation pressure) to the electrons preventing them from falling into the core. The energetic electrons ionize the air next to the electron layer forming a neutral plasma layer. The electric-field distributions and their associated frequencies in the ball are determined by applying boundary conditions to a differential equation given by Stratton (1941). It is then shown that the electron and plasma layers are sufficiently thick and dense to completely trap and guide the EM field. This model of BL is exceptional in that it can explain all or nearly all of the peculiar characteristics of BL. The ES energy associated with the core charge can be extremely large which can explain the observations that occasionally BL contains enormous energy. The mass of the core prevents the BL from rising like a helium-filled balloon - a problem with most plasma and burning-gas models. The positively charged core keeps the negatively charged electron layer from diffusing away, i.e. it holds the ball together; other models do not have a mechanism to do this. The high electrical charges on the core and in the electron layer explains why some people have been electrocuted by BL. Experiments indicate that BL radiates microwaves upon exploding and this is consistent with the model. The fact that this novel model of BL can explain these and other observations is strong evidence that the model should be taken seriously.