(a) Use superposition and the magnetic field on the symmetry axis of a current ring to find the magnetic field at the midpoint of the symmetry axis of a cylindrical solenoid. The solenoid has radius R, length L, and is wound with n turns per unit length of a wire that carries a current I.
(b) Assume that L >> R and use the results of part (a) and Amp`ere’s law to estimate the magnetic field Bout just outside the solenoid walls (but far from its edges).