Faraday induction law:
The amount of EMF has been determined empirically in the days of Faraday.
What I am wondering about, has there ever been an explanation as of why this EMF is induced?
For example, the voltage induced in the PN junction of a solar panel can perfectly be explained by the band gap, fermi level etc.
I am a bit surprised that I cannot find any explanation for the Faraday effect, neither classical, not quantum mechanial.

jlinkels

Dear jlinkels,
Faraday's Law is one of the basic law of Electromagnetism. It is one of the four Maxwell Equations of Electromagnetism.
So it is like postulate of Electromagnetism, rather than a derived one.
But there is Lorentz Force concept which is more explanatory than Faraday's Law particularly in case of homopolar motor.

So it is like Newtons' Law of Gravitation. It explains there is gravitation between two massive particles but doesn't say why this force is generated. (Although Einstein tried to explain the geometrical concept of it, but that is different theory).

That was exactly my question. In all publications I have at hand it is stated what Faraday's law is, and what phenomenon it describes.

But I have not seen stated "the cause why an EMF is induced is not understood".

Unlike as in gravity theory by the way. It is often stated that the cause for gravity is not known, but that it is suspected that it is caused by the Higgs boson. At least in that field it becomes clear what is understood and what not.

I need this knowledge for a lecture I have to give on electromagnetic induction. And I expect the question why a voltage is developed. I am happy to say that it is unknown. But that should be a true statement of course.

Thanks for replying.
jlinkels

I think that statements like "'why' is not understood" are, well, understood. Faraday didn't know why electromagnetism occurred. But he did know enough to describe it and to measure it, based upon what he could and did observe.

E=Electric Field (Electric Field Intensity)
B=Magnetic Field (Magnetic Flux Density)
V=Voltage/EMF

E=-(grad V)

Hence EMF induced means Electric Field generation,
So actually your question is "Why Electric Field is generated when Magnetic Field changes with time?"
or why Faraday's Law exists in nature?

Some philosophy:
Whenever we humans start to reason logically, scientifically, mathematically etc. we start with some Axioms/Postulates etc. So let's e.g.
Marcus is a Man. (Postulate) (We have taken this as truth.)
All men are mortals. (Postulate) (We have taken this as truth.)
=> Marcus is a mortal.
So asking Why Marcus is a mortal? has above two postulates as answer.
But asking Why Marcus is a Man? or Why all men are mortals? is answerless at least in this logic. Because we have to start our logic from some basic truths or something which is assumed to be a truth by observations etc.
e.g. Einstein Special Theory of Relativity has got two postulates. Now asking
"Why laws of nature must be the same in all inertial frame of reference?"
or
"Why speed of light is constant in every inertial reference frame?
or "Why Einstein and others assume Universe to be Homogeneous, Isotropic etc.?"

"Why Newton's Gravitation was assumed to be a universal Law, though we humans weren't been able to travel in the entire universe (Even we hadn't reached at Moon at that time)?"

Euclid gives 5 postulates for Geometry. All other theorems took these as base.
Hence Faraday's Law works (or EMF induces) because we have seen it in nature without exception.

Epilogue:
Although Classical Electromagnetism consists Faradays' Law as a fundamental Law.

But your question is somehow correct and enlightening in terms of looking deep inside the Law.
Hence I am not saying that there can not be other answer to your question in entire Universe.
e.g. Maxwell equation Div B=0 is fundamental but can be turned to more appropriate physical explanation that "Magnetic Monopoles doesn't exist in nature".
Now "Why magnetic monopoles doesn't exist in nature?" has got answer, "..because we haven't seen any until now."

Similarly Conservation of Energy exist because of Symmetry in time (Ref. Noether's Theorem).
(Again someone may ask "Why time is symmetrical?..because it is observed, so we take it for granted.")

But these are precisely not answers/reasons/causes, but alternative form of the same thing.