When current $I$ passes through an inductor having self-inductance of $4 \ H$. If the current is made double,what will be the new self-inductance of the inductor?

In an inductor of self-inductance $L = 2 \, mH$,current changes with time according to the relation $i = t^2 e^{-t}$. At what time is the $emf$ zero? (in seconds)

Explain self-induction and obtain the equation for the self-induced $emf$ in a coil.

$A$ long coaxial cable carries current $I$ along its surface. The current flows down the surface of the inner cylinder of radius $a$ and back along the outer cylinder of radius $b$.

An air-cored solenoid with length $30 \ cm$,area of cross-section $25 \ cm^2$ and number of turns $500$ carries a current of $2.5 \ A$. The current is suddenly switched off for a brief time of $10^{-3} \ s$. How much is the (nearly) average back e.m.f. induced across the ends of the open switch in the circuit (in $V$)? (Ignore the variation of magnetic field near the ends of solenoid)

$A$ magnetic flux of $5 \mu Wb$ is linked with a coil when a current of $1 \ mA$ flows through it. Calculate the self inductance of the coil.