Two solenoids have identical geometrical construction and the same number of turns,but one is made of thick wire and the other of thin wire. Which of the following quantities are different for the two solenoids?
$(a)$ Self-inductance.
$(b)$ Rate of Joule heating if the same current flows through them.
$(c)$ Magnetic potential energy if the same current flows through them.
$(d)$ Time constant.

$A$ copper wire is wound on a wooden frame,whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of $3$,keeping the number of turns of the coil per unit length of the frame the same,then the self-inductance of the coil:

The current in self-inductance $L=40\; mH$ is to be increased uniformly from $1\; A$ to $11\; A$ in $4\; ms$. The $e.m.f.$ induced in the inductor during this process is ..... $V$.

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 self-induced $emf$ of a coil is $25\,V$. When the current in it is changed at a uniform rate from $10\,A$ to $25\,A$ in $1\,s$,the change in the energy stored in the inductor is......$J$.

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.