$A$ 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 self-inductance of a solenoid is:

In an induction coil with resistance,the induced emf will be maximum when

In a circular conducting coil,when current increases from $2 \,A$ to $18 \,A$ in $0.05 \,s$,the induced $e.m.f.$ is $20 \,V$. The self-inductance of the coil is.....$mH$.

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.

$A$ solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, then the current in the coil