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Question:

The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of the solenoid will be proportional to:

1/L

L2

1/L2

L

Solution:

Φ=NBA=LI
μ₀nIπR²=LI
μ₀NlIπR²=LI
and R constant
self inductance(L) ∝ 1/l ∝ 1/length