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(C) The self-inductance $L$ of a solenoid is given by the formula $L = \frac{\mu_0 N^2 A}{l}$,where $N$ is the total number of turns,$A$ is the cross-

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(C) The self-inductance $L$ of a solenoid is given by the formula $L = \frac{\mu_0 N^2 A}{l}$,where $N$ is the total number of turns,$A$ is the cross-sectional area,and $l$ is the length of the solenoid.Since the number of turns per unit length $n = \frac{N}{l}$,we can write $L = \mu_0 n^2 A l$.From this expression,it is clear that $L \propto n^2$ (or $L \propto N^2$ if length $l$ is constant).Given that the number of turns $N$ is doubled $(N' = 2N)$ while the length $l$ remains unchanged,the new self-inductance $L'$ is:$L' = \mu_0 (2N)^2 \frac{A}{l} = 4 \left( \frac{\mu_0 N^2 A}{l} \right) = 4L$.Therefore,the self-inductance becomes four times the original value.

When the number of turns in a solenoid are doubled without any change in the length of the solenoid,its self-inductance becomes

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