$A$ 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 ...... $mH$.

$A$ solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, will the current increase or decrease? Explain.

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.

$A$ $10\, V$ battery connected to $5\,\Omega$ resistance coil having inductance $10\, H$ through a switch drives a constant current in the circuit. The switch is suddenly opened and the time taken to open it is $2\, ms$. The average $emf$ induced across the coil is

$A$ circuit having a self-inductance of $1 \text{ H}$ carries a current of $1 \text{ A}$. To prevent sparking when the circuit is broken,a capacitor which can withstand $500 \text{ V}$ is connected across the switch. What is the minimum value of the capacitance of the capacitor (in $\mu \text{ F}$)?

$A$ long solenoid of $N$ turns has a self-inductance $L$ and area of cross-section $A$. When a current $i$ flows through the solenoid,the magnetic field inside it has magnitude $B$. The current $i$ is equal to: