Physics Exercises/Feynman's Paradox
Suppose we have a very long solenoid carrying some current I. Around the solenoid we have a ring which can pivot around the axis of the solenoid, onto which we have glued some positive charges. At first, the ring is motionless, but suddenly, we turn the current off. From one perspective, the changing magnetic field means there is an electric field going around the solenoid (from Faraday's law), which will push on the charges on the ring, causing it to spin. On the other hand, at first, there is no angular momentum in the system (ignoring the mass of electrons -- you may want to justify this to yourself). Afterwards, we would expect angular momentum to be conserved and so the ring will remain motionless.
The question, of course, is whether or not the ring will spin. Understanding the answer will lead you to a surprising and important feature of electromagnetic fields. But to do this problem, you will need to think creatively.