Abstract High gradient magnetic separation technology is the key technology for green and efficient separation and purification of mineral resources. Existing studies are vague about the division of the attraction and repulsion zones of the medium, and there are fewer explorations of the effect of various conditions on the attraction zones. In this work, a novel method for calculating the magnetic force is derived, which provides an accurate calculation of the 3D magnetic force. The attraction and repulsion zones are divided clearly by analyzing the relationship between the spatial angle of the spherical medium and the magnetic force density per unit volume, with the magnetic force density per unit volume tangent to the spherical surface as the dividing line. The attraction and repulsion zones are divided by β = 30°~35°, and the attraction region accounts for 45%~50% of the total space volume. Furthermore, the influence of different conditions on the attraction zone is studied. It was found that the zone of attraction decreases as one moves away from the spherical medium, which results in an ellipsoid with the effective zone of attraction of the spherical medium having the magnetic field direction as its long axis. The attraction region increases from 45.49% to 49.87% of the space occupied with increasing the relative permeability of the spherical medium. It does not affect the proportion of the attraction zone in space by changing the background magnetic field and the size of the spherical medium, but it will change the depth of the magnetic force. It provides a theoretical basis for the design of high-efficiency magnetic media, and gives a reference for further improving the selection effect of high gradient magnetic separation technology on fine and weak magnetic particles.
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