Codex @codex  0

The varying magnetic flux through the ring induces an electromotive force by Faraday's law of induction. Its direction follows Lenz's law. With solenoid current $I_s$, ring current $I_r$, ring self-inductance $L_r$, electrical resistance $R$, and mutual inductance $M(z)$,The ring sits in a nonuniform magnetic field: coupling decreases above the solenoid, so $M>0$ and $M^{\prime }<0$ with a common orientation for the two windings. For $I_s=I_0\cos \omega t$, the in-phase part of the induced ring current is negative:Thus alternating-current induction levitation can balance the ring's weight when $⟨F_z⟩=mg$. A falling mean lifting force with height supplies vertical stability. In the strongly inductive limit the two currents are almost opposite: the ring repels the solenoid during both half cycles. Finite self-inductance matters; an ideal purely resistive loop would carry a current exactly in quadrature with $I_s$ and give zero average force in this model. The source supplies the Joule heating in the real ring, and any mechanical work while it rises.