If both the physical length and the total number of turns of an air-cored solenoid are doubled, whil

Question

If both the physical length and the total number of turns of an air-cored solenoid are doubled, while its cross-sectional area remains completely unchanged, its self-inductance will

Professor PC Thomas Classes · Answer

(b) : The self-inductance of a long solenoid is given by $L = \frac{\mu_0 N^2 A}{l}$, where $N$ is the total number of turns and $l$ is the length. If $N$ becomes $2N$ and $l$ becomes $2l$, the new self-inductance is $L' = \frac{\mu_0 (2N)^2 A}{2l} = \frac{\mu_0 (4N^2) A}{2l} = 2 \left( \frac{\mu_0 N^2 A}{l} \right) = 2L$. Therefore, the self-inductance is doubled.