(a) Consider a semi-infinite and tightlywound solenoid with a circular cross section. Prove that the magnetic flux which passes out through the open end of the solenoid is exactly one-half the flux which passes through a cross section deep inside the solenoid.
(b) A tightly wound solenoid has length L and a circular cross section. Let L = 5R, where R is the radius of the cross section. Sketch the magnetic field lines associated with this solenoid. Take special care with the lines near the open ends. Do any field lines penetrate the walls of the solenoid? If not, explain why not. If so, discuss their behavior very near the walls.