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Permeance variation in the air gap of the permanent-magnet synchronous machine induces eddy-current losses in its permanent magnets even in the absence of stator currents. This paper proposes a new analytical approach to analyze these losses using the permeance-variation vector function introduced for the air-gap magnetic-flux density distribution to take into account the stator teeth. The Laplace equation is employed to derive the radial dependency of the stator slotting effect on the magnetic-flux density distribution. The induced eddy currents are further calculated by using Faraday's law. The analytical results are compared with the numerical ones based on the finite-element analysis. The paper offers a faster alternative to the numerically intensive calculations of eddy-current losses, and the method is especially useful in initial design optimization of the electric machine.