Problem 3.325

A ring of radius $a=50 \mathrm{~mm}$ made of thin wire of radius $b=1.0 \mathrm{~mm}$ was located in a uniform magnetic field with induction $B=0.50 \mathrm{mT}$ so that the ring plane was perpendicular to the vector $\mathrm{B}$ Then the ring was cooled down to a superconducting state, and the magnetic field was switched off. Find the ring current after that. Note that the inductance of a thin ring along which the surface current flows is equal to $L=\mu_{0} a\left(\ln \frac{8 a}{b}-2\right)$