Question #42994

This question tests the fundamental thermodynamic derivation of magnetic energy, weaponizing the standard formula $U = \frac{1}{2}LI^2$.

Students are conditioned to use this formula, which is only valid for linear inductors where permeability (and thus $L$) is constant.

Faced with a non-linear flux-current relationship, a common trap is to calculate the static inductance $L_{static} = \frac{\Phi}{I} = 2 - \frac{1}{4}I$, which at $I = 4 \text{ A}$ gives $L = 1 \text{ H}$, leading to the incorrect answer of $8 \text{ J}$.

Another trap is integrating $\int \Phi \, dI$, which calculates the magnetic co-energy ($\frac{32}{3} \text{ J}$) rather than the actual stored energy.

The problem forces students to reject linear assumptions and correctly apply $U = \int I \, d\Phi$ to account for magnetic saturation.