There is a famous law which says that a potential difference is produced across a conductor when it is exposed to a varying MF. But, how do you measure it to prove? It is quite practical.
Particularly, I had once a problem developing a power supply. When transistor rapidly opened a loop of powerful current, I had very strange effects and discovered that there is a voltage difference across the same wire, without any resistor between the probing points! The longer was the distance between probes, the higher was the voltage. Then I have realized how the real the law is. But, what I could not understand if the voltage were spikes induced in the wire indeed or they were purely fictional, induced right in the oscilloscope probes. I expected that voltage drop must be across the loop-breaking transistor but why was it rather distributed along the resistance-free wire?
Look at dr. Levin's voltmeter. What does it measure? I ask this question partially because he tells about non-conservative measurements, which depends on the path, but does not explain how to set up the paths to measure -0.1 v in one case and +0.9 v in the other, between the same points.
How the typical voltmeter works? There should be some known high resistance and small current through it shows how large the voltage is. But here, in addition to the D-A induced voltage, the EMF may be added because the is also induced current flowing through the voltmeter. How much is the effect?
In school I also had a problem with understanding what if the loop is open? You have a wire. The law will induce potential difference at its ends. But how do you measure the difference? Created such voltage in a short wire, we can be sure that closing the ends with voltmeter probes will not create any current in the voltmeter (just because magnetic field supports the difference. If it just created it then why should it let the polarized charges reunite when a parallel wire is connected?). So, no current and the voltmeter will show 0 voltage despite we know that Faraday law says that must be some. Do you understand what I am talking about? The field creates the potential difference that cannot be measured. It is like gravity stretches a spring but we cannot measure the force created because spring contraction force is balanced by gravity and your dynamometer shows 0. This is my concern that I cannot understand. How do you measure voltage difference when Faraday law precludes the polarized charges from the opposite ends of the wire to come together?
Best Answer
I'm not sure I understood all your points. I suggest you to read this beautifull paper
if you can find it. It's seems it's exactly what Prof. Levin is doing in his lecture. The proof is clear. If you have some difficulties to obtain this paper, I have some notes about this paper that I can share on SE too.
Edit: If you can find this reference, you will see that the only thing which matters is the position of the circuitry relative to the solenoid. More explicitly, this is the topology of the circuit which matters. It will then be clear for you that
Now, some of your questions:
You have two ways to see induction, as clearly discuss in the Feynman lecture. To be honest, I do not know a better book to start with.
you close a loop with a moving bar, whereas a coil was previously inside the loop. Then you record a voltage drop through Faraday's law because the circuit is moving (if you prefer, the path you calculate your integral with).
you close a loop and encapsulate a time dependent magnetic field via time dependent current passing through the coil. Then you record a voltage drop because of the time variation of the magnetic field itself.
In both case you have a time varying flux. As Prof. Levin says: "Misterrr Farrraday is happy with that !"
Yes he does ! It is always from top to bottom (A to D point if I remember correctly), first passing on the left, second time passing on the right. Edit: The previous statement was confusing. When discussing magnetic flux, you need to define convention for following the circuit path, i.e. rotation direction. The path for -0.1 V is the counterclockwise path from A to D, the path giving +0.9 V is the clockwise path from A to D. That explain the signs also.
I suggest you to read the wikipedia page http://en.wikipedia.org/wiki/Voltmeter. A perfect voltmeter has no EMF. (Edit: see also http://en.wikipedia.org/wiki/Electromotive_force for the definition(s) of an EMF and its different interpretations.)
For me your last paragraph is incomprehensible. Faraday's law relates voltage drop to time varying magnetic flux, so it doesn't apply to open circuit.
Final edit: A way to avoid the flux drop: From http://dx.doi.org/10.1119/1.12923, see http://i.stack.imgur.com/X5qPb.png.