The self-inductance $L$ of a solenoid of length $l$ and area of cross-section $A$,with a fixed number of turns $N$,increases as:

Find out the $e.m.f.$ produced when the current changes from $0$ to $1 \, A$ in $10 \, s$,given $L = 10 \, \mu H$.

The network shown in the figure is a part of a circuit. (The battery has negligible internal resistance). At a certain instant,the current is $2 \ A$ and it is decreasing at the rate of $10^2 \ A \ s^{-1}$. What is the potential difference between the points $B$ and $A$ (in $V$)?

In an inductor,the current $I$ varies with time $t$ as $I = 5 \,A + 16 \,(A/s) \,t$. If the induced emf in the inductor is $5 \,mV$,the self-inductance of the inductor is .............. $\times 10^{-4} \,H$.

Write down the formula for the self-inductance of a very long solenoid.

$A$ solenoid with an air core has length $48 \pi \ cm$,area of cross section $12 \ cm^2$ and $1200$ turns. The self-inductance of the solenoid is: (in $mH$)