The self-inductance of a solenoid of length $31.4 \ cm$,area of cross-section $10^{-3} \ m^2$ having a total number of turns $500$ will be nearly $\left[\mu_0 = 4 \pi \times 10^{-7} \ SI \ unit\right]$.

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.

If a coil is open,then its self-inductance $L$ and resistance $R$ become:

$A$ graph of magnetic flux $(\phi)$ versus current $(I)$ is plotted for four inductors $A, B, C, D$. Which inductor has the largest value of self-inductance?

Magnetic flux of $10 \mu Wb$ is linked with a coil,when a current of $2 \ mA$ flows through it. What is the self-inductance of the coil (in $mH$)?

The inductance of a coil is $60\,\mu H$. $A$ current in this coil increases from $1.0\,A$ to $1.5\,A$ in $0.1\,s$. The magnitude of the induced $e.m.f.$ is