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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

$(a) l\; and A \; increases$
$(b) l\; decreases \; and \; A\;increases$
$(c) l\; increases \; and \; A\;decreases$
$(d) l \; and\; A \; decreases$

1 Answer

The self-inductance L of a solenoid of length $l$ and area of cross-section A with fixed number of turns is
$\; \; \; \; \; \; \; L = \frac{\mu_o N^2 A}{l}$
$\; \; \; \; \; \; L\propto A \;and \;L \propto \frac{1}{l}$
Hence as L increases ,$ l$ decreases and $A$ increases
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