A little primer on magnetic circuits:
The classic example is an electric transformer, which you may have noticed has a central iron core surrounded by (usually) two smaller legs such that the iron laminations form two closed loops with the central core. Sort of a closed off capital H on its side. The primary coil produces a time varying magnetic field, usually given the symbol H. The presence of the iron, in turn gives a magnetic flux density B, such that B is proportional to H. B = uxH. The quantity u is called the permeability and is a property of the material. The time varying flux (BxA, A is the cross sectional area of the core) causes a voltage to appear in the secondary winding. The flux is the same everywhere in the core and divides in two for the two legs. In other words, the flux forms closed loops. If you were to take a hacksaw and cut out a section of the central core you would find that the voltage in the secondary winding would drop. This occurs because the permeability of air (or space) is less, about 1/1,000 as much as the permeability of the iron, which causes a drop in the flux everywhere in the closed loops. A similar effect exists for an alternator where the moving magnets now provide the time varying magnetic field. The voltage induced in the coils still depends on the flux through the coils, so you want to maximize that. The way to do that is to provide a iron path for the flux and to keep any air gaps as small as possible. Usually the major air gap is the stator itself.
