$A$ coil of $Cu$ wire (radius $r$,self-inductance $L$) is bent into two concentric turns,each having a radius of $r/2$. What is the new self-inductance?

The total number of turns and cross-section area in a solenoid are fixed. However,its length $L$ is varied by adjusting the separation between windings. The inductance of the solenoid will be proportional to

$A$ solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, will the current increase or decrease? Explain.

Define the unit of self-inductance. On which factors does self-inductance depend?

In the given circuit, if $dI/dt = -1 \text{ A/s}$, then the value of $V_{AB}$ at this instant will be: (in $\text{ V}$)

An air-cored solenoid with length $30 \ cm$,area of cross-section $25 \ cm^2$ and number of turns $500$ carries a current of $2.5 \ A$. The current is suddenly switched off for a brief time of $10^{-3} \ s$. How much is the (nearly) average back e.m.f. induced across the ends of the open switch in the circuit (in $V$)? (Ignore the variation of magnetic field near the ends of solenoid)