How does the self-inductance of an air core coil change, when an iron rod is introduced in the coil?

A copper coil $L$ wound on a soft iron core and a lamp $B$ are connected to a battery $E$ through a tapping key $K$. When the key is closed, the lamp glows dimly. But when the key is suddenly opened, the lamp flashes for an instant to much greater brightness. Explain.

 

In which of the cases shown in Fig. 6.70, will the mutual inductance of two coils be maximum, if the number of turns remains the same in each case?

In which of the cases shown in Fig. 6.70, will the mutual inductance of two coils be minimum, if the number of turns remains the same in each case?

The circuit arrangement given in Fig. 6.71 shows that when an a.c. passes through the coil $A$, the current starts flowing in the coil $B$. Name the underlying principle involved.