Heaviside's version of Maxwell's equations are missing one equation. Either that or the equation has to be inferred.
Maxwell's first two equation known as the Gauss equations of electricity and magnetism define static electric and magnetic fields. Ampere and Faraday have equations that follow Gauss' to define magnetic fields and currents and currents in the presence of changing magnetic fields.
The missing equation would be based on the simple electromagnet. A curling electron or current field produces a magnetic field. The curl of the volume current density is equal to the magnetic field vector with a proportionality constant. Now Gauss' equation for magnetism breaks down into the divergence of a curl which by vector calculus identities is just an identity.
Faraday's law ends up being a result of Lenz' law. A tight magnetic field (spin of electrons) will cause a larger counter-spin of electrons due to the conservation of angular momentum.
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