The self-inductance of a solenoid is $L$, which is made by a wire of length $l_w$. What is the length of the solenoid?

In a circular conducting coil,when current increases from $2 \,A$ to $18 \,A$ in $0.05 \,s$,the induced $e.m.f.$ is $20 \,V$. The self-inductance of the coil is.....$mH$.

Regarding self-inductance:
$A:$ The self-inductance of the coil depends on its geometry.
$B:$ Self-inductance does not depend on the permeability of the medium.
$C:$ Self-induced e.m.f. opposes any change in the current in a circuit.
$D:$ Self-inductance is the electromagnetic analogue of mass in mechanics.
$E:$ Work needs to be done against self-induced e.m.f. in establishing the current.
Choose the correct answer from the options given below:

The inductance of a close-packed coil of $400$ turns is $8 \, mH$. $A$ current of $5 \, mA$ is passed through it. The magnetic flux through each turn of the coil is

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 in a brief time of $10^{-3} \; s$. How much is the average back $emf$ induced (in $V$) across the ends of the open switch in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.

The self-induced $e.m.f.$ in a $0.1 \, H$ coil when the current in it is changing at the rate of $200 \, A/s$ is......$V$