Factors that decrease inductance of an iron-core coil: Which action will definitely reduce the inductance value of a given coil (all else equal)?

Introduction / Context:
The inductance L of a coil depends on geometry (number of turns, cross-sectional area, length) and core permeability. Designers adjust these parameters to reach target L-values for filters, chokes, and transformers. Knowing how each factor influences L prevents trial-and-error mistakes.

Given Data / Assumptions:

• Iron-core coil; compare the effect of changing geometry or core material.
• Standard approximate relation: L ∝ μ * N^2 * A / l, where μ is core permeability, N is turns, A is core area, and l is magnetic path length.
• All else (unlisted variables) held constant when evaluating each option independently.

Concept / Approach:
From L ∝ μ * N^2 * A / l, increasing μ, increasing N, or increasing A will increase inductance; increasing l will decrease inductance. Removing the iron core effectively reduces μ toward μ0 (air), which substantially decreases L compared to iron-core values.

Step-by-Step Solution:

Verification / Alternative check:
Common lab observation: swapping an iron core for air reduces measured inductance dramatically, confirming μ’s dominant influence on L.

Why Other Options Are Wrong:

• increasing number of turns: Raises inductance via N^2 scaling.
• inserting higher-permeability core: Raises μ, thus increases L.
• increasing cross-sectional area: Increases A, raising L.

Common Pitfalls:

• Thinking that shortening length always decreases L; here length is not the option. The presented incorrect options all increase L.

Final Answer:
removing the iron core from the coil