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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 number of turns, $A$ is the area of cr

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Is doubled

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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 number of turns, $A$ is the area of cross-section, and $l$ is the length of the solenoid.Given that the new number of turns $N' = 2N$ and the new length $l' = 2l$, while the area $A$ remains constant.The new inductance $L'$ is given by:$L' = \frac{\mu_0 (N')^2 A}{l'} = \frac{\mu_0 (2N)^2 A}{2l} = \frac{\mu_0 (4N^2) A}{2l} = 2 \left( \frac{\mu_0 N^2 A}{l} \right) = 2L$.Therefore, the inductance is doubled.

When the number of turns and the length of the solenoid are doubled keeping the area of cross-section same, the inductance

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