Q 12-06-134JEE MainJEE Main 2019 (9 Apr, Shift 1)Easy
The total number of turns and cross-section area in a solenoid is fixed. However, its length $L$ is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to
Answer: (C) $\dfrac1L$
$$L_{self} = \mu_0n^2AL = \mu_0\frac{N^2}{L^2}AL = \frac{\mu_0N^2A}{L}$$
With $N$ and $A$ fixed, the inductance is proportional to $\dfrac1L$.
Solution by Sreeraj P, M.Sc Physics