$A$ coil having an inductance of $0.5\, H$ carries a current which is uniformly varying from zero to $10\, A$ in $2\, s$. The $e.m.f.$ (in volts) generated in the coil is

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.

When the current changes from $+2 \, A$ to $-2 \, A$ in $0.05 \, s$,an $e.m.f.$ of $8 \, V$ is induced in a coil. The coefficient of self-induction of the coil is ... $H$.

$A$ toroid is a long coil of wire ($N$ turns) wound over a circular core. The coefficient of self-induction of the toroid is [The magnetic field in it is uniform and $R >> r$,where $r=$ radius of wire,$R=$ radius of coil] ($\mu_0=$ permeability of free space).

The current in a coil decreases from $1 \, A$ to $0.2 \, A$ in $10 \, s$. Calculate the coefficient of self-inductance if the induced $e.m.f.$ is $0.4 \, V$. (in $, H$)

The self-inductance of a coil is $50 mH$. When a current of $1 A$ passing through the coil reduces to zero at a steady rate in $0.1 s$,find the self-induced emf. (in $V$)