Problem $2$ A long solenoid, of radius $a,$ is driven by an alternating current, $s0$ that the field inside is sinusoidal: $B(t)=B_{0}cos(t)hat(z).$ A circular loop of wire, of radius $\frac{a}{2}$ and resistance $R,$ is placed inside the solenoid, and coaxial with it$.$ Find the current induced in the loop, as a function of time.