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  4. The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to :

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Q. The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to :

JEE MainJEE Main 2019Electromagnetic Induction

Solution:

$\Phi \, = \, NBA = LI$
$N \mu_0 \, nI \pi R^2 \, LI$
$N \mu_0 \frac{N}{\ell} I \pi R^2 = LI$
N & R constant
self inductance (L) \propto $\frac{1}{\ell}$ \propto $\frac{1}{length}$
Option (2)