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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?

Thanks in advance for your answers!

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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.

Qualitatively speaking: even if one inductor has a core that allows it to generate more flux for a given current excitation, that same core will funnel the magnetic field made by the coreless inductor better, such that the mutual inductance remains reciprocal. I'll look around to see if I can find a more satisfactory explanation.

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  • $\begingroup$ Thanks for your answer. I was thinking about a different reluctance in the medium between both inductors, rather than the core, so you could use a complex geometry to create some sort of magnetic diode. The flux would go easily from one coil to another one, but not the other way around. Do you think this could be possible? $\endgroup$ – John Clarkson Feb 7 '17 at 14:51
  • $\begingroup$ Oh, you are wondering if there is a magnetic diode equivalent for magnetic flux? My understanding is that this is not possible. $\endgroup$ – Kthaxt Feb 12 '17 at 0:51

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