Do not solve with AI$.$

$$A conductor having radius of $5$ cm and resistance of $10$ Ohm is placed perpendicularly within a varying magnetic field with $1$ mT$/$s$.$ a$)$ What is the current induced in the conductor. b$)$ If the conductor suddenly becomes superconducting $($zero resistance$)$ the current in the superconductor varies $2$ A$/$s response to same varying field. What is the inductance of the coil? c$)$ If the energy loss in conductor were to be stored in the ring what would be the circulating persistent current in the superconductor after the external field is removed?$$