The total number of turns and cross-section area in a solenoid are fixed. However,its length $L$ is varied by adjusting the separation between windings. The inductance of the solenoid will be proportional to

$A$ long solenoid has $1000$ turns. When a current of $4\, A$ flows through it,the magnetic flux linked with each turn of the solenoid is $4 \times 10^{-3}\, Wb$. The self-inductance of the solenoid is......$H$

When the current through an inductor is changed from $2 \,A$ to $6 \,A$ in time $2 \,s$, the emf induced in it is $3 \,V$. Then the inductance of the inductor is (in $\,H$)

$A$ coil of self-inductance $L$ is connected in series with a bulb and an a.c. source. Brightness of the bulb decreases when

An $e.m.f.$ of $5 \,V$ is produced by a self-inductance when the current changes at a steady rate from $3 \,A$ to $2 \,A$ in $1 \,ms$. The value of self-inductance 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.