Current in a circuit falls from $5.0 \, A$ to $0.0 \, A$ in $0.1 \, s$. If an average $emf$ of $200 \, V$ is induced,give an estimate of the self-inductance of the circuit in $H$.

$A$ coil of $N = 100$ turns carries a current $I = 5 \, A$ and creates a magnetic flux $\phi = 10^{-5} \, Wb$ per turn. The value of its inductance $L$ will be ...... $mH$.

The following figure represents two bulbs $B_1$ and $B_2$, a resistor $R$, and an inductor $L$. When the switch $S$ is turned off, which of the following statements is true?

The self-inductance of an air-cored solenoid of length $40 \ cm$,diameter $7 \ cm$ having $200$ turns is nearly: (in $\mu H$)

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

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.