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  4. A long solenoid has self inductance L. If its length is doubled keeping total number of turns constant then its new self inductance will be

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Q. A long solenoid has self inductance $L$. If its length is doubled keeping total number of turns constant then its new self inductance will be

Electromagnetic Induction

Solution:

$L=\mu_{0} n^{2} A l$
$L=\mu_{0}\left(\frac{N}{I}\right)^{2} A l$
$L=\frac{\mu_{0} N^{2}}{l} A $
$\Rightarrow L \propto \frac{1}{l}$
$\Rightarrow L'=\frac{L}{2}$