I may have confused after thinking too much about Faraday's law. If an emf is induced in a circuit due to some changing magnetic field, the induced current will be in a direction such that the "induced magnetic field" opposes the original magnetic field (Lenz's law).
So wouldn't the induced magnetic field also generate an induced current that opposes it, and that current would also generate a magnetic field and so on... so it seems like there would be infinitely many induced magnetic fields and currents. This is particularly true if the original magnetic field is a sinusoid so it's infinitely differentiable.
Am I misinterpreting Faraday's law? Is Faraday's law just a description of how the electric and magnetic fields can coexist, so we don't have to worry about "infinite induction"?