A sector-type of slim electromagnet with iron pole pieces has been fabricated to obtain some precise information about the inhomogeneities of magnetic fields. Neither the eddy-current effect nor magnetic aftereffect, which are associated with the setting procedure and setting speed of the magnetic field, are observed in the present measurements. Sources producing field inhomogeneities along a central ray in the pole pieces with a sharp-cornered profile are the local saturation and hysteresis effect. The hysteresis effect is related to the magnetization-demagnetization process and is observed under a measuring precision better than 10-4. The magnetic field distribution changes with the field strength independent of the magnetization-demagnetization process. Sources producing field inhomogeneities along a radial direction in the pole pieces with the sharp-cornered profile are the local saturation and the difference between leakage fluxes in pole-piece sides with the small and large curvature radii, which is due to the magnetic asymmetry of the pole-piece geometry along the radial direction. The B-constant design of pole pieces has excellent effects in avoiding field inhomogeneities due to the aforementioned sources, although the small cycling effect remains in field inhomogeneities along the central ray.