Discussion
The self-inductance of an air core solenoid is L. If the number of turns in the solenoid is doubled, keeping all other factors constant, then its self-inductance will be
Answer: D
The self-inductance becomes \(4L\).
For a solenoid, \(L = \frac{\mu_{0}N^{2}A}{l}\). The field inside is proportional to \(N\), and the flux links all \(N\) turns, so \(L \propto N^{2}\). Doubling \(N\) with the same length and area multiplies \(L\) by \(2^{2} = 4\).
\(2L\) assumes \(L \propto N\), counting either the field or the linkage but not both. \(8L\) would be a cube law.
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