The self-inductance (L) of a long solenoid on doubling its number of turns and length, keeping other factors constant, will become
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 2L \)
The self-inductance of a long solenoid is proportional to the square of the number of turns and inversely proportional to its length.
\( \displaystyle L = \frac{\mu_0 N^{2} A}{l} \)
Doubling both \( N \) and \( l \) with the area \( A \) unchanged:
\( \displaystyle L' = \frac{\mu_0 (2N)^{2} A}{2l} = \frac{4}{2}\,\frac{\mu_0 N^{2} A}{l} = 2L \)