The famous Chapman-Ferraro problem for the determination of the magnetospheric cavity is elucidated for its two-dimensional solutions in mathematical detail. The general solution presented in this paper amounts to a complex variable extension of the well-known Poisson's integral formula for the Dirichlet problem for a half-plane or a circle domain. It provides the needed methodology for obtaining desirable solutions that avoid the defects inherent in the Dungey-Hurley solution, which uses Ferraro's approximation of pressure balance as the boundary condition.
