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