Problem 3.314

In the middle of a long solenoid there is a coaxial ring of square cross-section, made of conducting material with resistivity \(\rho\). The thickness of the ring is equal to \(h\), its inside and outside radii are equal to \(a\) and \(b\) respectively. Find the current induced in the ring if the magnetic induction produced by the solenoid varies with time as \(B=\beta t,\) where \(\beta\) is a constant. The inductance of the ring is to be neglected.