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MHT CET 2023 (12 May, Shift 2) · Self-Inductance & Energy

Self-Inductance & Energy question from MHT CET 2023 (12 May, Shift 2)

Q59MHT CET 2023 · 12 MAY · SHIFT 2Medium

Self-Inductance & Energy

Inductance per unit length near the middle of a long solenoid is $(\mu_0 =$ permeability of free space, $n =$ number of turns per unit length, $d =$ the diameter of the solenoid)

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Answer: (a)

For a long solenoid $L = \mu_0 n^2 A l$ , so $\dfrac{L}{l} = \mu_0 n^2 A$ .
$A = \dfrac{\pi d^2}{4}$ , so $\dfrac{L}{l} = \mu_0 \pi \dfrac{n^2 d^2}{4} = \mu_0 \pi \left(\dfrac{nd}{2}\right)^2$
So the answer is (a).

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