An eccentric position diagnosis method of static eccentricity (SE) fault of external rotor permanent magnet synchronous motor (ER‐PMSM) is presented. Firstly, an analytical model of no‐load radial magnetic field of ER‐PMSM is established. Analytical models of no‐load Back‐EMF of both unit motors and the whole motor are carried out and are verified by finite element method (FEM) and experimental measurements. Then, the influences of SE ratio, SE circumferential angle, winding distribution mode and number of parallel branches on no‐load radial magnetic field and no‐load Back‐EMF are analyzed based on these analytical models. The results show that SE does not affect the frequency characteristics of no‐load radial magnetic field, but changes space order characteristics. On one hand, for ER‐PMSM, of which the number of unit motors is equal to 1, SE causes no‐load Back‐EMF distortion. On the other hand, for ER‐PMSM, of which the number of unit motors is greater than 1, SE does not affect no‐load Back‐EMF of the whole motor, but it still leads to no‐load Back‐EMF distortion of unit motors. Therefore, based on total harmonic distortion (THD) of no‐load Back‐EMF of unit motor, a projection method of intersection lines for SE fault diagnosis of ER‐PMSM is proposed finally.