[evan_au]

ε is a material bulk property and does not vary with frequency, to the best of my knowledge

Water (H₂O) and Glass (SiO₂) have a μ_r close to 1, but they are still dispersive (produce rainbows) - is this is due to variation in ε or μ with wavelength?
- There are particular wavelengths of infra-red light where optical fibers have near-zero dispersion (ie over that part of the spectrum, refractive index does not vary very much). These wavelengths are of great interest for high-speed telecommunications, since dispersion distorts optical signals - different wavelengths arrive at different times.
- The other trick used for high-speed telecommunications is to have a long length of "normal" dispersive fiber (eg 30-70km), with a short length of dispersion-compensating fiber (eg 30-70m), which has the opposite dispersion characteristic to "normal" fiber, ensuring that all wavelengths arrive simultaneously.

https://www.fiberopticsonline.com/doc/understanding-and-measuring-chromatic-dispers-0002

[hamdani yusuf]

Those exclusions would make Maxwell's equations not very useful.

Like a train timetable, eh? Or the periodic table, which doesn't predict the winner of a horse race.

So why did Kelvin confidently say that physics was almost complete back then?

Because he was wrong. Kapitza said the same thing in 1964 (I was there). As they say in aviation
after 100 hours you know everything
after 1000 hours you know you don't know everything
after 10,000 hours you know you can't know everything.

Then why did you write this statement?

Maxwell's equations have no known limitations. AFAIK they describe the propagation of EM radiation at all frequencies and in all materials.

[alancalverd]

Because it is true.

[hamdani yusuf]

Because it is true.

When two statements are contradicting each other, then at least one of them must be false.

Maxwell's equations have no known limitations.

Followed by their limitations.

They do not purport to describe attenuation, diffraction, interference, or any other interaction with anything

[alancalverd]

A bus timetable does not purport to tell you when the next train leaves. If you want to be pedantic, that is a limitation, but if you want to travel by bus, it isn't.

Maxwell's equations are intended to describe the propagation of electromagnetic radiation in a medium. As far as we know they do so for all EMR in all media. If that is what interests you, they have no limitation. If however you are interested in the color of Manchester United's 2023 away strip, they are admittedly of no use whatever.

[Bored chemist]

When two statements are contradicting each other, then at least one of them must be false.

And if they are both accurate answers to a question, (which they are) it must be a very poorly constructed question.

[hamdani yusuf]

Maxwell's equations are intended to describe the propagation of electromagnetic radiation in a medium. As far as we know they do so for all EMR in all media. If that is what interests you, they have no limitation. If however you are interested in the color of Manchester United's 2023 away strip, they are admittedly of no use whatever.

Michelson & Morley's, Fizeau's, and Sagnac's experiments showed the limitations of Maxwell's equations. There's also Faraday's paradox. They should still be within the scope of Maxwell's model.

[hamdani yusuf]

Water (H2O) and Glass (SiO2) have a μr close to 1, but they are still dispersive (produce rainbows) - is this is due to variation in ε or μ with wavelength?

Then εr is the varying factor.

[hamdani yusuf]

When two statements are contradicting each other, then at least one of them must be false.

And if they are both accurate answers to a question, (which they are) it must be a very poorly constructed question.

Which question?
Is there something you don't understand?

[alancalverd]

Michelson & Morley's, Fizeau's, and Sagnac's experiments showed the limitations of Maxwell's equations. There's also Faraday's paradox. They should still be within the scope of Maxwell's model.

M&M and Fizeau are entirely consistent with Maxwell. Faraday's paradox has nothing to do with the propagation of light. 

[Bored chemist]

Water (H2O) and Glass (SiO2) have a μr close to 1, but they are still dispersive (produce rainbows) - is this is due to variation in ε or μ with wavelength?

Then εr is the varying factor.

How did you come to that conclusion?

[Bored chemist]

Which question?

Have you forgotten what you asked?
You asked what current an electron was.

[hamdani yusuf]

M&M and Fizeau are entirely consistent with Maxwell.

If you modify Newton's framework, just like Lorentz did.

[hamdani yusuf]

Faraday's paradox has nothing to do with the propagation of light.

It has to do with generating electromagnetic field, which is what light is, according to Maxwell.

[hamdani yusuf]

Water (H2O) and Glass (SiO2) have a μr close to 1, but they are still dispersive (produce rainbows) - is this is due to variation in ε or μ with wavelength?

Then εr is the varying factor.

How did you come to that conclusion?

Because c = 1/√εμ
If c changes while μ doesn't, then ε must change.

[hamdani yusuf]

Which question?

Have you forgotten what you asked?
You asked what current an electron was.

It looks like you came late to join the party.
Here's my original question.

Maxwell treated electric charge as continuum, which can be divided infinitesimally.

No. He merely used the known phenomena of a magnetic field being induced by a moving charge and a potential being induced by a changing magnetic field. He made no assumptions about the nature of either.

What is the equation describing how a magnetic field is induced by a moving charge?

[alancalverd]

Quote from: alancalverd on 29/12/2022 10:45:12
Faraday's paradox has nothing to do with the propagation of light.
It has to do with generating electromagnetic field, which is what light is, according to Maxwell.

No, it's a misconception of Gaussian induction.

Maxwell combines two observed phenomena: an electric current generates a magnetic field, and a changing magnetic field can induce a current.

The Faraday "paradox" only involves the second phenomenon.

[hamdani yusuf]

Maxwell combines two observed phenomena: an electric current generates a magnetic field, and a changing magnetic field can induce a current.

Check again the 4th equation. Magnetic field is generated by electric current PLUS changing electric field.

[alancalverd]

Not in my textbook, but that wasn't the point I made: I quoted only Faraday's Law and Ampere's law as the observational "givens" for Maxwell.

[hamdani yusuf]

The real contribution of Maxwell in his four equations is the addition of displacement current to the fourth equation. The others are from Gauss, Ampere, and Faraday.

His addition was the critical point which led Maxwell to conclude the existence of electromagnetic waves.