MH's ideal coil and voltage question

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The time constant is infinite.
Tau=L/R. There is no R,as it's an ideal inductor.
Tau=L/0 = infinity.

Good God, Brad!  - you are doing a mathematical analysis.  Your experimental skills mixed with that one will accomplish wonders.

Anyway,  you are correct that when R=0 then Tau=∞ , ...however Tau is not inductance.

Infinite Tau does not mean that current through an ideal inductor cannot change or that it is always constant (i.e. zero) ...like it would be with an infinite ideal inductor.
This is because if you insert R=0 into the formula for inductor's current  i(t)=(V/R)*( 1- (e^(-t*R/L)) ) you do not get a constant current function ...because there are two competing limits in this formula, one for V/R=∞ and another for (1-e^0)=0.   If you multiply them together you get ∞ * 0 ...

Which limit wins out or how the two limits combine requires higher level of math analysis.  Do you want me to go into it?

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Tau has no bearing on whether current can/will flow or not. The effect it has is how "curvy" the rise of current is, relative to the timing of your test. With an infinite tau, the curve is going to be a straight line,

That is correct.

Making the resistance R=0 "turns off" the real component of impedance but leaves the imaginary part (the inductive reactance (X) ) unaffected.
Their magnitudes combine according to SQRT(R²+X²)

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It's because the shorted single turn copper coil is producing a magnetic field that apposes that which created it.

I agree and this can be observed in this this video.

If the pipe is cooled down enough,so as it became superconductive,would the magnet still fall?

Depends how large the inner diamaeter of the pipe is compared to the magnet.  If it is small enough then the magnet would bounce forever.
This video illustrates how a falling magnet behaves when it is released from the middle of a single shorted turn that has zero resistance.



P.S.
Again, I remind everyone that the magnitude of the current induced in a perfectly conducting ring does not depend on how fast that magnet is moving.

Also copper cooled by liquid nitrogen does not become superconductive, but the YBCO ceramic does.
Niobium metal becomes superconductive when cooled by liquid helium.

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@Magneticist

You should look at that post of mine from another thread.