$A$ branch of a circuit is shown in the figure. If the current is decreasing at the rate of $10^3 \ A \ s^{-1}$, then the potential difference between $A$ and $B$ is (in $V$)

The network shown in the figure is a part of a circuit. (The battery has negligible internal resistance). At a certain instant,the current is $2 \ A$ and it is decreasing at the rate of $10^2 \ A \ s^{-1}$. What is the potential difference between the points $B$ and $A$ (in $V$)?

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1 :$ Self inductance of a long solenoid of length $L,$ total number of turns $N$ and radius $r$ is less than $\frac{{\pi {\mu _0}{N^2}{r^2}}}{L}$
Statement $2:$ The magnetic induction in the solenoid in Statement $1$ carrying current $I$ is $\frac{{{\mu _0}NI}}{L}$ in the middle of the solenoid but becomes less as we move towards its ends.

What length of a very thin wire is required to obtain a solenoid of length $l_0$ and inductance $L$?

When the current in a coil changes from $8 \ A$ to $2 \ A$ in $3 \times 10^{-3} \ s$,the induced $e.m.f.$ in the coil is $2 \ V$. The self-inductance of the coil in millihenry $(mH)$ is:

The length of a wire required to make a solenoid of length $l$ and self-induction $L$ is