Question

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

• A. $\frac{1}{L^2}$
• B. $L^2$
• C. $\frac{1}{L}$
• D. $L$

Answer 1

The correct option is C $\frac{1}{L}$

We know that the self-inductance of the solenoid is given as
Inductance $=\frac{{\mu }_0{N}^{2}A}{L}$
$\Rightarrow$ Inductance $\propto \frac{1}{L}$
As ${\mu }_0,A\text{and}N$ are constant here.
Hence option $\left(D\right)$ is correct.