Intuition of Maxwell's Equations Is there an intuitive explanation for Maxwell's equations?
I know they are axioms but is there a logical understanding of why instead of mathematical. Both forms don't explicate the scientific reasoning behind them to me.
I would appreciate a non- or minimally mathematical approach to them.
 A: The two equations involving the divergence aren't dynamical (they have no time derivatives), and if they're satisfied initially, they're automatically satisfied at all later times. They tell us about the sources and sinks of the fields.
The two equations involving the curl have time-derivative terms and a current term.
The time-derivative terms describe electromagnetic induction. Their signs are opposite, which is what allows negative feedback so we can have oscillating electromagnetic waves.
The current term describes how moving charges create magnetic fields. It has to be there because of Lorentz invariance, i.e., if we had known about electric fields but not about magnetic fields, relativity would have forced us to invent magnetism.
A: They’re not axioms: They’re experimental results. 
Coulomb, Faraday, etc did a lot of experimental work to observe and systematize the underlying phenomena. Maxwell then reformulated them (though not in the modern form) and added the displacement current term which itself was later confirmed experimentally. 
So the “why” historically comes down to “because people observed this”
Today, the underlying “why” is “because these emerge from the quantum field theory of QED” and even fro electroweak interactions. But that’s a very long leap to make intuitive. 
So if you want an intuitive understanding of Maxwell’s equations themselves, the best place to look is at the experiments that underlies them. It’s a lot to put in an Answer, because it’s a lot of physics. 
For example, forces on small charges led to Coulomb’s law, which led to the idea of an electric potential hence electric field and Gauss’ law. 
