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 BB 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 Φtotal=constant\Phi_{\text{total}} = \text{constant} and Φ=LI\Phi = LI 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 BB 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 Φtotal=constant\Phi_{\text{total}} = \text{constant} and Φ=LI\Phi = LI to relate the current amplitude to the geometry and field strength.

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