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We present an analytical solution for the magnetic field, induced eddy currents, and the corresponding losses generated in the rotor of a slotless permanent-magnet (PM) motor. The field excitation is a current sheet placed at the stator interior surface. The solution is based on an analytical solution of the diffusion equation using double Fourier series and in the complex domain. The first and the second Fourier series correspond to the time and space harmonics, respectively. We have analyzed the effect of each time harmonic in detail, and verified the results with FEM software.