The self inductance L of a solenoid of length l and area of...

The self-inductance of a long solenoid is given by the formula:

$L = \dfrac{\mu_0 N^2 A}{l}$

where $N$ is the total number of turns, $A$ is the cross-sectional area, and $l$ is the length of the solenoid.

Since the number of turns $N$ is fixed, the self-inductance $L$ is directly proportional to the area of cross-section $A$ and inversely proportional to the length $l$.

$L \propto \dfrac{A}{l}$

Thus, to increase the self-inductance $L$, the area $A$ must increase and the length $l$ must decrease.

Answer: $l$ decreases and A increases.