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(B) The self-inductance $L$ of a solenoid is given by the formula $L = \mu_0 n^2 A l$, where $n$ is the number of turns per unit length, $A$ is the cr

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$8$

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(B) The self-inductance $L$ of a solenoid is given by the formula $L = \mu_0 n^2 A l$, where $n$ is the number of turns per unit length, $A$ is the cross-sectional area, and $l$ is the length of the coil.Given that the linear dimensions are increased by a factor of $2$, the new length $l' = 2l$ and the new area $A' = (2)^2 A = 4A$.The number of turns per unit length $n$ remains constant.Substituting these values into the formula for the new inductance $L'$:$L' = \mu_0 n^2 (4A) (2l) = 8 (\mu_0 n^2 A l) = 8L$.Therefore, the self-inductance increases by a factor of $8$.

$A$ coil is wound on a core of rectangular cross-section. If all the linear dimensions of the core are increased by a factor of $2$ and the number of turns per unit length of the coil remains the same, the self-inductance increases by a factor of (Assume, permeability is same).

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