A solenoid has n turns per unit length, radius R1, and carries a current I.

(a) A large circular loop of radius R2 > R1 and N turns encircles the solenoid at a point far away from the ends of the solenoid. Find the magnetic flux through the loop.

(b) A small circular loop of N turns and radius R3 < R1 is completely inside the solenoid, far from its ends, with its axis parallel to that of the solenoid. Find the magnetic flux through this small loop.