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Why do we have to do work to remove iron nucleus from an inductor?

Since the energy associated with the inductor is $E=\frac{Li^2}{2}$, and $L$ is proportional to relative magnetic permeability $\mu_r$, then $L=\mu_rL'$ and $E=\frac{\mu_r L'i^2}{2}$. Ok... Let say that $\mu_r > 1$ for the iron and $\mu_r = 1$ for the air, then the magnetic energy with the iron ($E_+$) is greather than the magnetic energy without the iron ($E_-$). So, if I am going from a higher energy to a lower energy state, why I should do work on the system to move from one state from another?

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