Savchenko Problem 11.5.8
Physics · mechanics · electromagnetism
Problem
In a constant homogeneous induction field B, a superconducting ring rotates around its diameter oriented perpendicular to the field. Inductance of the ring L, its diameter D. Determine the amplitude of the alternating current in the ring.Intuitive explanation
The key insight is that a rotating superconductor maintains constant magnetic flux through itself—any change in external flux induces a current that exactly cancels it. As the ring rotates, the component of threading through it oscillates sinusoidally, forcing the induced current to oscillate as well to keep total flux constant. You'll need to find how the flux changes with rotation angle, then use and to relate the current amplitude to the geometry and field strength.
Intuitive explanation
The key insight is that a rotating superconductor maintains constant magnetic flux through itself—any change in external flux induces a current that exactly cancels it. As the ring rotates, the component of threading through it oscillates sinusoidally, forcing the induced current to oscillate as well to keep total flux constant. You'll need to find how the flux changes with rotation angle, then use and to relate the current amplitude to the geometry and field strength.