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The number of turns, cross- sectional area and length for four solenoids are given in the following table
Solenoid Total turns Area Length
1 2N 2A $l$
2 2N A $l$
3 3N 3A $2 l$
4 2N 2A $l / 2$
The solenoid with maximum self-inductance is

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answer is D.

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Detailed Solution

$L = μ_{0} n^{2} π r^{2} l A = π r^{2} n = \frac{N}{l} \Rightarrow L = μ_{0} \frac{N^{2}}{l} A$

By putting the given values, it can be seen that it is maximum for solenoid no. 4

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