An innovative approach, named topology exploration, is introduced in this paper. The aim of this approach is to help in the creation of electromagnetic devices, and to explore a priori unknown structures. In so doing, a general analytical solution of the magnetic field in static-excited cylindrical machines is developed, and then coupled to a stochastic procedure to determine if some structures are viable. The analytical model can account for variable boundary conditions, and hence, is suitable to determine electromagnetic performances of any structures. After 3 months of calculations, the topology exploration approach revealed interesting results showing the validity of the method.