The self-inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as(a) l and A increase. (b) l decreases and A increases. (c) l increases and A decreases. (d) both l and A decrease.

The answer is the option (b)

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

$L=\frac{\left ( \mu_ r \: \mu_0\: n^2 \right )}{I}$

So, from the equation, the inductance should increase as l decreases and A increases. As, L is inversely proportional to l and directly proportional to A.

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