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Introduction to induction - class-XII
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QuestionClick to flip
A solenoid coil is wound on a frame of rectangular cross section. If all the linear dimension of the frame are increased by a factor of two and the number of turns per unit length of the coil remains the same, the self-inductance increases by a factor of
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A
$8$
💡 Explanation:
Self inductance, $L = \dfrac{\mu _0 N^2 A}{l}$ __(1)
where N = total number of turns
$n = \dfrac{N}{l}$, where n = number of turns per unit length
$N = nl$ put it in (1)
$L = \dfrac{\mu _0 (n l )^2 A}{l} = \mu _0 n^2 l A$
In the given question n is same
Area will increase by $4$ times
length will increase by $2$ times
$L' = \mu _0 n^2 (2l) (4A) = 8 \mu _0 n^2 lA$
$L' = 8L$ inductance will increased by $8$ times.