Question

4. Superposition: Show that the field on the axis at the end of a semi-infinte solenoid is half of the field well inside of the solenoid. Then show that half of the flux inside the solenoid leaves through the walls, and half leaves through the open end.

Answer 1

Suppose we have two long solenoid each of them have magnetic field B at the end. Now we join them as their magnetic fields are in some direction. B_net = B + B = 2B hence magnetic field inside solenoid is twice the magnetic field at the end on its axis. I as B is half at ends flux will also be half that of inside, hence half of the flux will leave through ends (because there are two ends)