Exact Expression of Corner Reluctances in a Magnetic Circuit of Rectangular Section

We provide an exact, simple and explicit analytical expression of corner reluctances for magnetic circuits of rectangular section. Obtained values are appreciably different from those obtained by making usual approximations. Besides, due to a decomposition of the solution in two terms which can be interpreted as an lengthening of the adjacent rectilinear legs, our expressions are very easy to use in order to compute reluctance of magnetic circuits, and thus also inductances and forces in magnetic devices, as well as magnetic losses. The present study applies also to electric and thermal resistances calculation. Although obtained expressions are rigorously exact only in the case of linear materials, this study allows also for flux and magnetic losses simplified calculation in the case of saturable materials. The accuracy of this simplified calculation is examined on a test structure by comparison with finite elements computation results