Imagine a ferromagnetic medium shaped as a cylinder (a ferromagnetic fiber) with a magnetic relative permeability of μr, tilted with an angle a, as shown in the picture. I would like to prove analytically that the sum of the inductances measured along the x axis (angle is a) and y axis (angle is π/2 - a) is independent of the angle a. (Lsum = Lx + Ly independent of a). Each case, Lx and Ly is also the sum of the inductance of the projections of the fiber in the x and y axis. My approach consists in using Hopkinson's Law and first determining the Reluctance for each case, and then calculating the Inductance using L= N2/Reluctance, where N is a constant number of turns of a supposed magnetomotive force. Do you think it's possible? Thank you very much.