# When does Lorentz reciprocity not apply to an EM system?

I'm trying to understand the limits of when Lorentz reciprocity does and doesn't apply to a given system. I know that it only applies to linear systems, but based on a couple of examples I believe there might be more to it:

Example 1: DC through an inductor produces a static magnetic field. Expose that same inductor to a static magnetic field of the same magnitude, a current is not induced. This suggests to me non-reciprocity.

Example 2: near field effects in a simple transmit/receive antenna system. I have produced a simple model of 2 identical dipole antennas, with a large metal object in close proximity to one of the antennas. When I measure the received spectrum for one, and then for the other, with the other antenna transmitting the same signal, the results are similar but not identical at certain frequencies. Physical measurements seem to agree with these results. I imagine it is due to non-linear effects, but I'm interested to hear if anyone can confirm if this is likely or if there is some other way Lorentz reciprocity could be being broken?

• I do not understand your first example but regarding the second here is the answer. The most common example of bench-top linear and non-reciprocal behavior is anything involving biased ferrites (isolators, circulators). Commented Aug 10, 2023 at 14:04
• @hyportnex sorry I don't think your link answers the second question. Regarding the first question, I will try to rephrase based on my understanding: reciprocity states that fields due to a current should be the same as currents due to that same field, however this is not the case with an inductor. Commented Aug 11, 2023 at 15:30
• A static magnetic field does not generate a current, but starting with no field and then creating a static field by some means during a transition from nothing to something does induce a current, se Faraday's law. If the linked answer is not what you expect for #2 then I do not know what your question means. Anyhow, linearity is not enough for reciprocity. Commented Aug 11, 2023 at 15:54
• True going from no field to a magnetic field will induce a transient current as it would be a time varying field, however the point I'm making is that the presence of a static field on it's own is not enough to reproduce the exact same current in an inductor that would produce that static field if that current was passed through the inductor. Commented Aug 14, 2023 at 9:05
• "bias" fields are not he same as "applied" fields, see en.wikipedia.org/wiki/Reciprocity_(electromagnetism). Commented Aug 14, 2023 at 9:21