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A quasi-three-dimensional (3-D) analytical model of the magnetic field in an axial flux permanent-magnet synchronous machine is presented. This model is derived from an exact two-dimensional analytical solution of the magnetic field extended to the 3-D case by a simple and effective radial dependence modeling of the magnetic field. The obtained quasi-3-D solution allows rapid parametric studies of the air-gap magnetic field. Then, analytical modeling of the cogging torque is presented. It is based on the obtained quasi-3-D analytical solution. Results issued from the proposed model in the air gap are compared with those stemming from a 3-D finite-element method simulation as well as with prototype measured values.