A N=200-turn solenoid having a length of l=25 cm and a diameter of 10 cm (R=5 cm) carries a current of I= 0.30 amp. (a) What is the magnetic field near the center of the solenoid? (b) What is the magnetic flux through an annular ring having an inside diameter of d=2.0 cm and an outside diameter of D=8.0 cm if the plane of the ring is perpendicular to the axis of the solenoid? Solve using variables first and plug numbers at the end. Hint: calculate the field of one loop as a function of Z and then add up all the loops.