# Mutual Inductance with non-homogeneous magnetic reluctance medium

Given two inductive circuit elements, it can be shown that the inductance coefficient between the first one and the second one is the same as the inductance coefficient between the second one and the first one.

$$M_{21}=M_{12}=M$$

My question is: does this equality hold even if the magnetic reluctance of the medium is not homogeneous, but a function of position?

Yes, this relationship should always hold. Mutual inductance is defined as: $$M_{21} = \frac{\phi_{21}}{I_2}$$ In words: the flux generated by current 2 integrated over the surface of circuit 1.