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I expanded Maxwell’s equations by adding the integral form in SI system and then a shorter version of discussion from electromagnetism for the differential form of the equations, both in 3d and 4d formulations. Note also that Ampère’s law is about producing magnetic field from current; while it is Maxwell’s equation, or Ampère-Maxwell which adds the term with the change of electric field, the main discovery of Maxwell. Some people nowdays say generalized Ampère’s law what I wrote, but I am not happy about it as the general form does not generalize it in the straightforward manner, but adds new physics what needs a separate attribution.
Needs some explanations, like why and how $D$ and $H$ come in terms of $E$, $B$ and metric. The integral form is written in terms of $E$ and $B$ only. $D$ and $H$ are usually motivated either by controlling the Hodge star operation, either by physics of materials.
Thanks, that’s good to have. I’ll try to join in later.
added pointer to
(for no particular reason, but it’s an interesting read with some history and some reflections)
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