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  4. In a solenoid, if number of turns is doubled, then self-inductance will become:

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Q. In a solenoid, if number of turns is doubled, then self-inductance will become:

AFMCAFMC 2005

Solution:

For a solenoid of length $l$, area of cross-section $A$, having $N$ closely wound turns, the self inductance of the solenoid is
$L=\frac{\mu_{0} N^{2} A}{l}$
When $N'=2 N$
$L'=\frac{\mu_{0}(2 N)^{2} A}{l}$
$=\frac{4 \mu_{0} N^{2} A}{l}=4 L$
Hence, when number of turns is doubled then self inductance becomes quadruple.