Maxwell's electromagnetic theory of light.

[copernicus1234]

Maxwell's theory of light is based on Faraday's induction experiment yet Faraday's induction effect is not emitting light. Also, Poynting's energy equation of light is based on a conduction wire that is not emitting light. Can someone please explain this to me. Thank you.

 

[steveB]

Maxwell's Theory of light is not based only on Faraday's Law, but also on a modified version of Ampere's Law. The modification of Ampere's Law was figured out by Maxwell himself. In a sense, he provided the last piece of the puzzle and formulated all the known laws into one consistent set of equations that we call Maxwell's Equations. Without this last piece, electromagnetic theory would not predict electromagnetic waves (radio and light etc.).

However, this is not the crux of the answer. The basic answer to both your questions is that Maxwell's Equations describe all macroscopic and free space electromagnetic phenomena that do not enter the domain of needing quantum theory. Light is only one aspect of all possible electromagnetic phenomena. Poynting's energy/power flow equation is general and applies to all electromagnetic field effects, which includes light and conducting wires and a myriad of other cases.

 

[copernicus1234]

"Maxwell's Theory of light is not based only on Faraday's Law"

I don't understand this statement, perhaps you made a miss spelling or something.

 

[steveB]

"Maxwell's Theory of light is not based only on Faraday's Law"

I don't understand this statement, perhaps you made a miss spelling or something.

What I mean is that Maxwell's theory of light is based on more than just Faraday's Law. Yes, Fardaday's Law of induction is critical to the classical theory of light, but that alone does not predict electromagnetic radiation, or light as the special case of that.

You need to combine Faraday's Law of Induction with the modified version of Ampere's Law to show that electromagnetic radiation in the form of waves is possible. This was one of Maxwell's (not Faraday's) great discoveries.

If you still think I've made a mistake of some type, then I'm probably not understanding your question and I would ask that you provide a link or reference to indicate why Maxwell's Theory of light is based on Faraday's induction experiment. Perhaps, you are referring to an experiment that is different than the one I'm thinking of.

 

[nsaspook]

"Maxwell's Theory of light is not based only on Faraday's Law"

I don't understand this statement, perhaps you made a miss spelling or something.

The key to Maxwells theory of light is the relationship of the electric and magnetic forces in the dual entity of electromagnetic energy. His great discovery wasn't that one causes the other, he showed how the simultaneous change in charge and current density in matter (cause) results in a wavefront that can move and regenerate itself in the absence of matter (effect). What he proved whats that space was in effect a transmission line with the equivalent inductance and capacitance values derived from the intrinsic measured properties of static/moving electric and magnetic fields using existing and modified versions of Gauss/Ampere/Faraday laws into four modern equations (due to https://en.wikipedia.org/wiki/Oliver_Heaviside , who really should get more credit) to create a wave equation that showed the speed of that wave is the same as light and the information speed limit c.

The general equations are next applied to the case of a magnetic disturbance propagated through a non-conductive field, and it is shown that the only disturbances which can be so propagated are those which are transverse to the direction of propagation, and that the velocity of propagation is the velocity v, found from experiments such as those of Weber, which expresses the number of electrostatic units of electricity which are contained in one electromagnetic unit. This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.

https://en.wikisource.org/wiki/A_Dynamical_Theory_of_the_Electromagnetic_Field

That had twenty equations and luminiferous mediums but was mathematically correct.

Heaviside did much to develop and advocate vector methods and the vector calculus. Maxwell's formulation of electromagnetism consisted of 20 equations in 20 variables. Heaviside employed the curl and divergence operators of the vector calculus to reformulate 12 of these 20 equations into four equations in four variables (B, E, J, and ρ), the form by which they have been known ever since (see Maxwell's equations).

From his link:

 

[copernicus1234]

SteveB...........We seem to agree that Maxwell's electromagnetic theory of light is based on induction, right. Therefore, how do you justify using induction, that is not optical, to represent the electromagnetic field structure of light, in Maxwell's electromagnetic theory of light?

 

[nsaspook]

I don't understand your question either but steveB in the post below has a great response.

Almost everyone else in the field of focused ion beams uses the term 'optics' to refer to systems of electrostatic/electromagnetic lenses and other devices that manipulate beams of matter so it's not a term used just for light. Polished optical surfaces of metal (good conductors like silver) reflect the light of various electromagnetic wavelengths (light 'rays' are used because of the law of reflection makes things much easier at boundary conditions) because of the effects of https://en.wikipedia.org/wiki/Electromagnetic_induction#Maxwell.E2.80.93Faraday_equation that generate EM fields inside the surface of that conductor that effect how energy flows into the surface, is reflected or absorbed.
https://www.physicsclassroom.com/mmedia/optics/lr.cfm

 

[steveB]

SteveB...........We seem to agree that Maxwell's electromagnetic theory of light is based on induction, right. Therefore, how do you justify using induction, that is not optical, to represent the electromagnetic field structure of light, in Maxwell's electromagnetic theory of light?

Well, yes, that is quite a big step logically and mentally. That's an indication of what a genius Maxwell was.

First of all, you are partially asking the important question of why is light electromagnetic in nature. Well, that's just the way it is. It's a great discovery made by Maxwell. So, how do I justify it? I don't have to justify experimentally confirmed facts. So, justifying it is the wrong angle to take. However, trying to understand it at a lower level is a useful exercise, and I can comment on that.

There is something particularly special about Faraday's law of induction. Basically, it relates fields and not sources. In EM theory, currents and charges are the sources of fields, but induction does not relate the sources, but only the fields. That is a clue because electromagnetic waves (which includes light) is "the fields" taking on a life of it's own. In other words, " a changing field over here, can create a changing field over there", so to speak.

So, induction is all about how a time changing magnetic field and a spatially changing electric field go hand in hand. This relationship may not be all that obvious if you just think of induction as voltage being equal the the rate of change of flux. But, if you remember that electric field is a result of a changing voltage in space, and flux is magnetic field integrated over an area, then you can see that induction is telling you half of what you need to have wave propagation of electromagnetic fields.

But, that is not enough. You have to add the other part that Maxwell discovered. Maxwell realized that it is also true that a spatially changing magnetic field goes hand in hand with a time varying electric field. And presto, wave propagation naturally follows from that. To see this clearly, you need to work out the derivations mathematically. When you do so, and when you calculate the speed of such electromagnetic waves, you find that the speed of those waves is that of light. If the frequency gets high enough, then those waves are optical waves which we call light. This last sentence is something that needs to be proved experimentally, which has been done. There are other waves that travel at the speed of light that are not electromagnetic, so the fact that light, which is photons, and electromagnetic forces are intimately related is an important discovery in physics.

 

[copernicus1234]

steveB..............."There is something particularly special about Faraday's law of induction. Basically, it relates fields and not sources."

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Maxwell's electromagnetic theory of light is based on Ampere and Faraday induction experiments, that are the source the Maxwell's electromagnetic induction field, but induction is not optical. In addition, the derivation of the EM wave equations of light, using Maxwell's equations, is patently incorrect.

 

[steveB]

I doubt that we will see eye to eye on many things in this area, but I probably agree somewhat with your statement, but maybe for different reasons.

First, Maxwell's equations are based on Ampere's and Faraday's experiments, - that's true. But Maxwell did modify Ampere's law, so we have to add that piece to your description. As I mentioned, electromagnetic fields and photons have been scientifically shown to be intimately linked, and so electromagnetic effects can be optical in nature. That's just scientific fact.

I would not say that the derivation of the EM wave equation of light, via Maxwell's equations is incorrect. The derivation is mathematically correct. As to whether it is correct physics, that is always a difficult thing to comment on. In a sense, all of our physics theories are approximations and models of the physical world. In a sense, the mathematics we write is our best language to express many of the scientific facts we have learned, and we can learn even more by manipulating those equations. For example, Maxwell showed, mathematically, that EM waves might very well exist and might also be the basic nature of light. He turned out to be correct, but perhaps he did not really prove it. Other scientists proved that radio waves exist experimentally, and showed that light is electromagnetic.

But, we know Maxwell's equations are approximations to reality because they do not include quantum effects (it does include relativity and Lorentz invariance). However, we can make the same criticism of Newton's Laws of mechanics and gravity (which are not Lorentz invariant). They are approximate and essentially wrong, and have been replaced by relativity theory. Even relativity theory does not include quantum effects an hence is also an approximation. We do have quantum electrodynamics field theory which does include both relativity and quantum mechanics and intimately shows the real connection between photons, electromagnetic fields and particle production. Maxwell's equations are only an approximate classical level theory of this more fundamental theory.

 

[copernicus1234]

The derivation of the EM wave equations of light, using Maxwell's equations, cannot be justified since the expansion method directly contradicts the divergent method.

 

[nsaspook]

The derivation of the EM wave equations of light, using Maxwell's equations, cannot be justified since the expansion method directly contradicts the divergent method.

https://coub.com/view/qzxv

 

[copernicus1234]

unit vector

 

[nsaspook]

unit vector

I'll make it easy for you. Look at the FLP and find where he is wrong. Some of it is a little dense for me but I will try to follow.
https://www.feynmanlectures.caltech.edu/II_toc.html

 

[steveB]

unit vector

unit troll

 

[steveB]

For anyone interested, a live lecture is sometimes easier to follow than a book.

https://theoreticalminimum.com/cour...-classical-field-theory/2012/spring/lecture-9

 

[nsaspook]

For anyone interested, a live lecture is sometimes easier to follow than a book.

https://theoreticalminimum.com/cour...-classical-field-theory/2012/spring/lecture-9

Note to self, don't eat cookies while talking.

Lagrangians are a a powerful way of looking at dynamic systems. He lost me at about 30 into the lecture so now I have some summer reading tasks to learn the basics and build a good mental picture of what's important in my narrow field.

 

[steveB]

Yes, the first 30 minutes is what I intended to be of interest. You may have noticed the sign error in Maxwell's equation. He picks up on this at the end of the lecture, but it does not affect the basics of the wave equation discussion.

 

[nsaspook]

Yes, the first 30 minutes is what I intended to be of interest. You may have noticed the sign error in Maxwell's equation. He picks up on this at the end of the lecture, but it does not affect the basics of the wave equation discussion.

I can also see how using geometrized units (like c=1) simplifies calculations in this context. It 'almost' makes me wish I had taken more math in school.

 

[copernicus1234]

In the gradient method https://en.wikipedia.org/wiki/Electromagnetic_wave_equation ,
forms a horizontal wave.

In the expansion method (Jenkins, Francis and White, Harvy. Fundamentals of Optics. 3rd ed. McGraw-Hill. 1957) just after Maxwell's equations are expanded, produces first order differential equations (that are used in the derivation of the EM wave equations of light) produces the unit vector catastrophe, when the electromagnetic wave equations, are used with Bo = Eo, in the said equations.