$A$ solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, then the current in the coil

Two identical inductors carry currents that vary with time according to linear laws (as shown in the figure). In which of the two inductors is the self-induced $emf$ greater?

The current in a coil of self-inductance $2.0 \, H$ is increasing according to $I = 2 \sin(t^2) \, A$. The amount of energy spent during the period when current changes from $0$ to $2 \, A$ is ...... $J$.

In a coil of self-inductance $0.5 \, H$,the current varies at a constant rate from $0 \, A$ to $10 \, A$ in $2 \, s$. The $e.m.f.$ generated in the coil is ... $V$.

$A$ coil of wire of radius $r$ has $600$ turns and self-inductance of $108 \ mH$. The self-inductance of a coil with the same radius and $500$ turns is (in $mH$)

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)