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The force equation of a synchronous permanent-magnet planar motor (SPMPM) was investigated. The flux density distribution of a two-dimensional (2-D) magnet array for a SPMPM was obtained by solving the equations of the scalar magnetic potential. The expressions of the force and back-EMF constant were derived and examined. Using these expressions, the conditions for normal operation of the SPMPM were found and the optimal design was determined in order to maximize the force of the SPMPM.