The self-inductance $(L)$ produced by a solenoid of length '$l$' having '$N$' number of turns and cross-sectional area '$A$' is given by the formula (where $\phi$ = magnetic flux,$\mu_0$ = permeability of vacuum).

Current in a circuit falls from $5.0 \ A$ to $0.0 \ A$ in $0.1 \ s$. If an average emf of $100 \ V$ is induced,then the value of self-inductance of the circuit is . . . . . . . (in $H$)

$A$ 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.

$A$ graph of magnetic flux ( $\phi$ ) versus current $(I)$ is shown for four inductors $A, B, C, D$. The smaller value of self-inductance is for inductor:

$A$ hollow cylinder has length $l$,radius $r$,and thickness $d$,where $l >> r >> d$,and is made of a material with resistivity $\rho$. $A$ time-varying current $I$ flows through the cylinder in the tangential direction. Assume the current is always uniformly distributed along the length of the cylinder. The cylinder is fixed so that it cannot move; assume that there are no externally generated magnetic fields during the time considered for the problems below. Assume current at $t = 0$ to be $I_0$. What is the current $I(t)$ for $t > 0$?

$A$ long solenoid has $500$ turns. When a current of $2 \, A$ is passed through it,the resulting magnetic flux linked with each turn of the solenoid is $4 \times 10^{-3} \, Wb$. The self-inductance of the solenoid is ....... $H$.