The self induction ($L$) produced by solenoid of length '$l$' having '$N$' number of turns and cross sectional area '$A$' is given by the formula ($\phi = \text{magnetic flux through one turn}, \mu_0 = \text{permeability of vacuum}$)}
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Self-inductance of a solenoid is proportional to the square of the number of turns ($L \propto N^2$) and the cross-sectional area, and inversely proportional to the length.