The self-inductance $L$ of a solenoid of length $\lambda$ and area of crosssection $A$ with a fixed number…
The self-inductance $L$ of a solenoid of length $\lambda$ and area of crosssection $A$ with a fixed number of turns $N$ increases as
$\lambda$ increases and $A$ decreases
$\lambda$ decreases and $A$ increases
both $\lambda$ and $A$ increase
both $\lambda$ and $A$ decreases
Solution
The self-inductance $L$ of a solenoid of length $b$ and area of cross section $A$ with fixed number of turns $N$ is
$L=\frac{\mu_0 N^2 A}{b}$
So, L increases when $b$ decreases and $A$ increases