In class, we calculated the magnetic field along the axis of a circular loop of wire of radius a carrying a current I as a function of the distance x from the center.

(i) Use this result to derive the magnetic field along the axis of a cylindrical solenoid with (finite) length L, radius a, and n turns of wire per unit length.

(ii) Determine the field at the ends of the solenoid.

(iii) Use a computer to plot the magnetic field strength as a function of the position along the axis. Use L = 2.0m, a = 0.2 m, n = 1000 m^-1, and I = 1 A.

(iv) Show that for L >> a the field near the center of the solenoid is nearly constant and is nearly equal to the field inside an infinite solenoid.