= Orientation torque on a flux-conserving loop
{title2=$\langle\tau_\theta\rangle=A^2B_0^2\sin\theta\cos\theta/(2L)$}
For a loop of area $A$ and <self-inductance> $L$, negligible resistance conserves $LI+\Phi_{\rm ext}$. With zero trapped total flux and $\Phi_{\rm ext}=AB_0\sin(\omega t)\cos\theta$, the <electric current> is $I=-AB_0\sin(\omega t)\cos\theta/L$. The <magnetic torque> generalized to the angle between loop normal and field is $\tau_\theta=-IAB\sin\theta$. For an orientation varying slowly over a field cycle, averaging gives the displayed torque and effective potential $U_{\rm av}=A^2B_0^2\cos^2\theta/(4L)$. Its stable orientations have loop normal perpendicular to the applied field. Without <damping>, a freely released loop librates around such an orientation instead of settling there.
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