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How long does it take for the current induced in a shorted superconducting solenoidal coil to reach its maximum value when a permanent bar magnet rotates inside that coil by $180^\circ$ in time $t$ ?

Assume that before the magnet is rotated, the current in the coil is zero.

Assume that initially the axis of the magnet is aligned with the axis of the coil as depicted below and all of the flux threading that coil ($\Phi_0$) comes from the magnet and none from the current flowing in the coil (because initially this current is zero).

It is OK to assume that the magnet rotates at constant angular velocity through the $180^\circ$ and the sum of the magnet's flux threading the coil varies as $\Phi=\Phi_0 cos(t)$.

enter image description here

The pivot of the magnet's rotation is depicted by the white dot in the center of the magnet.

FOR EXAMPLE:
Supposing that the magnet is rotated $180^\circ$ in 100 ms and the coil has an inductance of 10 H, how long will it take for the current induced in that coil to reach its maximum value?

Will the delay, if any, between the change of external flux (generated by the magnet) and the induced current be altered if the magnet is rotated faster, e.g. in 1 ms?

Will this delay change if the inductance of the coil is increased?

P.S.
The answer to a related question states that the maximum magnitude of current induced in such coil is INDEPENDENT of the speed of the flux change $d\Phi/dt$.

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It will induce a current such as in an electric motor/generator. While the speed increases, the amount of voltage also increases, but for a shorter amount of time, the amount it takes to move to its final position.

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  • $\begingroup$ I did not ask about voltage. I asked only about the induced current. More specifically, how long will it take for the current induced in a shorted superconducting coil to reach its maximum value, when the bar magnet rotates 180º in time t. To answer this question properly you must provide a mathematical expression which defines how long that takes in terms of t and/or in terms of other variables. $\endgroup$ Oct 22 '20 at 20:37
  • $\begingroup$ Also, the following fragment of your sentence is not constructed grammatically: "...but for a shorter amount of time, the amount it takes to move to its final position.". As such, it is not understandable. Did you forget to add the word "than" after the comma ? $\endgroup$ Oct 23 '20 at 9:02

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