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For part (c) I need to find the time taken for the solenoid to gain maximum magnetic field strength. However, since it uses superconducting wires, the total resistance is zero, so how would I be able to calculate the duration before the current is steady using $I(t) = I_0(1-e^{-t/\tau})$ for $\tau = L/R$? Since the limit as $R$ goes to zero implies the limit of $I(t)$ as $R$ goes to zero is $I_0$, should we conclude that and initial $I_0 = 0$ implies that you can never add current since the inductance will be infinite or something? I know this is not the case but what is the alternative? Should I try to leave a small $\delta$ of resistance?

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    $\begingroup$ While your question is interesting, I think you're misinterpreting what the exercise is asking. It's not asking about the behavior of the superconducting material, but just a $P = E/t$ question based on the power of the supply. $\endgroup$ – BowlOfRed Oct 1 at 20:39

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