The self-inductance of an air-core inductor (solenoid) is $0.03 \ mH$. By introducing an iron core into the inductor, the self-inductance increases to $30 \ mH$. The relative permeability of the core used is:

The magnitude of the induced emf in a coil of inductance $30 \ mH$ in which the current changes from $6 \ A$ to $2 \ A$ in $2 \ s$ is: (in $V$)

Current in a circuit falls from $5.0\, A$ to $0\, A$ in $0.1\, s$. If an average $emf$ of $200\, V$ is induced,estimate the self-inductance of the circuit in $H$.

$A$ current vs. time graph of the current passing through a solenoid is shown in the figure. For which time is the back electromotive force $(emf)$ a maximum? If the back $emf$ at $t = 3\;s$ is $e$, find the back $emf$ at $t = 7\;s$, $15\;s$, and $40\;s$. $OA$, $AB$, and $BC$ are straight line segments.

Consider a long solenoid of length $l$ and radius $r$. If $n$ is the number of turns per unit length and $\mu_0$ is the permeability of free space, the inductance of the solenoid is:

Physically,the self-inductance plays the role of