Question #43003

This question tests the misapplication of Faraday's law and Kirchhoff's loop rule in circuits with time-varying inductance.

A common trap is assuming that zero resistance implies $L \frac{di}{dt} = 0$, leading students to incorrectly believe the current $I_0$ remains constant.

If they assume constant current, they calculate the work done by the magnetic torque $\tau = \frac{1}{2}I^2 \frac{dL}{d\theta}$ as $\int_0^{\pi/2} \frac{1}{2}I_0^2 (2L_0\cos\theta) d\theta = I_0^2 L_0$, yielding an incorrect angular velocity of $I_0 \sqrt{2L_0/J}$ (Option B).

The correct physical principle is that the total magnetic flux $\Phi = L(\theta)I$ is conserved.

The product rule $\frac{d}{dt}(L i) = L \frac{di}{dt} + i \frac{dL}{dt} = 0$ dictates that the current must decrease as the inductance increases, fundamentally altering the energy transfer.