Revealing the mystery of the cases where Nd-Fe-B magnetic like poles attract each other

This investigation reveals the mystery of the cases where magnetic like poles attract each other, and unlike poles repel one another. It is identified that for two unequally sized like poles, the pole with a higher P-c (permeance coefficient) causes a localized demagnetization (LD) to the pole with a lower P-c. If the LD is large enough, the polarity of a localized area can be reversed, resulting in an attraction between these two like poles in the LD area in a small gap. Two unusual behaviors are observed: (1) an inflection point IP appears on the force vs gap curves of all the unequally sized like poles since they have different P-c. Normally, the like poles' repelling force increases when the gap decreases, but this IP results in nonmonotonic curves, even an attractive force in a small gap; (2) for some NdFeB magnets with a low coercivity and nonlinear B-H curve in the 2nd quadrant, a repulsion can occur for these unequal sized unlike poles, after previously pairing with their like poles that left an unrecoverable LD and reversed polarity area. The relationship of the LD, the P-c ratio, and the B-H curve are also explored in this paper.