Electromagnetic Induction

JEE Main level, single correct, medium

134 of 153

Question 134 of 153

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

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Answer: (C) 1L\dfrac{1}{L}

Self-Inductance =μ0n2πr2L={\mu }_{0}{n}^{2}\pi {r}^{2}L (n = number of turns per unit length)
=μ0(NL)2πr2L={\mu }_{0}{\left(\dfrac{N}{L}\right)}^{2}\pi {r}^{2}L
=μ0N2πr2L=\dfrac{{\mu }_{0}{N}^{2}\pi {r}^{2}}{L}
Self-Inductance ∝1L\propto \dfrac{1}{L}

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