Self-inductance of a solenoid is

directly proportional to its area of cross-section

The correct answer is Option (3) → directly proportional to its area of cross-section

The self-inductance of a solenoid is given by:

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

where:

$N$ = total number of turns, $A$ = area of cross-section, $l$ = length of the solenoid

This shows that self-inductance is:

— Independent of the current

— Not directly proportional to number of turns per unit length (since $N / l$)

— Directly proportional to area of cross-section

— Not inversely proportional to area