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.
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Is it possible to describe the physical meaning of  and show how they lead to electromagnetic wave, with little involvement of mathematics ?
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If there is no source then also there is electromagnetic waves described by Maxwell equation. how if there is no source then existence of EM waves. What gives energy to this EM  waves. Is it vacuum fluctuation or something else?
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Assume I want to learn math and physics enough to reach a level where I understand Maxwell's equations (The terms and reasoning in the equations I.e. why they "work"). What would I have to learn in order to have the tools I need to make sense out of it?  I'm kindof looking for a road map which I can use to get started and know what to focus on. The fields are pretty big so some pruning would be very helpful (if possible)
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So, as your usual physics undergrad, I read Griffiths's derivation of the general   uncertainty principle. I understood it but there was no physical intuition given behind it in the book. It was basically a bunch of manipulations and inequalities used to get just the right result.  Other than "It's because of the statistical interpretation." is there a more intuitive reasoning behind uncertainty. Like commutators, behavior of particles, etc.  Thank you for the replies and as always, much obliged.
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So I know that for an electromagnetic field in a vacuum the Lagrangian is $$\mathcal L=-\frac 1 4 F^{\mu\nu} F_{\mu\nu},$$ the standard model tells me this. What I want to know is if there is an elementary argument (based on symmetry perhaps) as to why it has this form. I have done some searching/reading on this, but have only ever found authors jumping straight to the expression and sometimes saying something to the effect that it is the "simplest possible".
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I was curious if anyone could give me an example of the use of  in physics and explain what they offer that "conventional" mathematics does not (in terms of new physics and not just another method to work the problem)?   If you look at the conservation of mass example on the wikipedia page they cite the paper  they derive a general equation for conservation of mass in equation 13. It seems like the fractional derivative is then used as a method to approach their problem, but I dont think it includes new physics (correct me if I'm wrong on this). Is there anything gained by stating that fractional conservation of mass holds in this case (apart from gaining another way to approach the problem)?    Any thoughts on this example or others would be appreciated!
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Do we have any experimental evidence to confirm that light is an electromagnetic wave? Or is it confirmed simply by Maxwell's equations showing a similarity in speed?
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Most of us have heard of Einstein's amazing equations which describe the universe around us, yet only some of us understand what the equations are actually saying.      What are these equations actually saying, and is there a simple (relatively) way to derive them?   Here they are, from :  $$R_{\mu\nu}-\dfrac{1}{2}g_{\mu\nu}R+g_{\mu\nu}\Lambda=\dfrac{8\pi G}{c^4}T_{\mu\nu}$$  I have a vague notion of what a tensor is (it describes things as an array and higher orders define more complex transformations), but I don't understand what all of these tensors are doing. And why is there a $c^{4}$  in the equation!?
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As I understand it, electromagnetic waves have two components which are the result of each other, i.e., when a moving electric charge creates a changing magnetic field at point X then a changing electric field is created at point Y and this repeating process is what creates EM waves, so therefore, it requires no medium. Is my understanding correct?  One thing that I'm surprised to know is that light is also called an electromagnetic wave.  Does this include light of any kind, for example: light from a bulb, a tube, and also from the Sun? How do they contain electric and magnetic fields?
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I've read and heard that quantum electrodynamics is more fundamental than maxwells equations. How do you go from quantum electrodynamics to Maxwell's equations?
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Given that:  1) virtual photons mediate the electric and magnetic force fields  2) the magnetic field is the curl of the magnetic vector potential  3) the electric field is the negative gradient of the electric scalar potential  How do we understand the vector and scalar potentials in terms of virtual photons?   Specifically, I mean curl-free magnetic vector and gradient-free electric scalar potential fields, where no electromagnetic waves or physical forces are present.   For instance, what's actually happening outside of the solenoid in the Aharonov-Bohm experiment that alters the phase of the passing electron? Are virtual particles involved there? This question has really stumped me because I only have an undergrad level of understanding in physics. Thanks for any help.
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In my quantum field theory class we have been told to use this Lagrangian for the photon field  $$\mathcal{L}=-\frac{1}{4}F_{\alpha\beta}F^{\alpha\beta} -\frac{1}{2}(\partial_{\rho}A^{\rho})^2.$$  but the reasons have been kept quite obscure. Why do we do this? We don't we stick with the good old Maxwell Lagrangian? Doesn't this extra term change things? and if not (as I suppose it is) why not?
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Why does light have the speed it does? why is it not considerably faster or slower than it is?  I can't imagine science, being what it is, not pursuing a rational scientific explanation for the speed of light.  Just saying "it is what it is" or being satisfied saying it is 1 ($c=1$), does not sound like science.
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me and my friend has a discussion last night, and he argued that both an electromagnetic field and gravititonal field are infinite in their area of effect, but with diminishing effects as you get farther away from the object.  I argued that only gravity field is infinite in range.  So which one of us is correct, and please explain in laymen's terms, as we're not physicists :)
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There's already a question like this  so that my question could be considered duplicate, but I'll try to make my point clear that this is a different question.   Is there a way to derive  from the Lorentz' Force law or just from Maxwell's Equations?   The point is that we usually define, based on experiments, that the force felt by a moving charge on the presence of a magnetic field is $\mathbf {F} = q\mathbf{v}\times \mathbf{B}$, but in that case the magnetic field is usually left to be defined later.   Now can that force law be used in some way to obtain Biot-Savart law like we obtain the equation for the electric field directly from Coulomb's Force law?  I wanted to know that because as pointed out in the question I've mentioned, although Maxwell's Equations can be considered more fundamental, those equations are obtained after we know Coulomb's and Biot-Savart's laws, so if we start with Maxwell's Equations to obtain Biot-Savart's having use it to find Maxwell's Equations then I think we'll fall into a circular argument.   In that case, without recoursing to Maxwell's Equations the only way to obtain Biot-Savart's law is through observations or can it be derived somehow?
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What was Newton's own explanation of ? Newton advocated a corpuscular theory of light, but his rings would most conveniently be explained by a wave theory. How did he explain his own discovery?
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At the end of this nice video (), she says that  is a chain reaction of electric and magnetic fields creating each other so the chain of wave moves forward.  I wonder where the  is in this explanation. What is the relation between electromagnetic wave and photon?