Homopolar disc dynamo
= Homopolar disc dynamo
{title2=$L\dot I=(C\omega-R)I$}
Connect a <homopolar generator> to a <solenoid> producing its own axial field. Reinforcing winding and rotation give $C=\mu_0Na^2/(2l)$ and $L\dot I=(C\omega-R)I$. A seed field grows for $\omega>R/C$, is marginal at equality, and decays below threshold. An identically zero initial field remains zero in this homogeneous ideal model; startup requires a seed or perturbation.