We describe an exact 2-D analytical model for predicting the open circuit magnetic field in idealized structures of wound field and series hybrid excitation permanent-magnet synchronous machines. This technique can be used for either internal or external rotor radial-field machine topologies. It involves analytical solution of Maxwell's equations in stator and rotor slots and annular air-gap/magnet regions. We compare results from this analytical model to corresponding finite-element analyses. We then use it to estimate the cogging torque, induced back-electromotive force, and to study the effects of rotor skewing.