Effect of Removing an Iron Core from a Coil An iron-cored inductive coil is converted into an air-cored coil by removing the iron core (geometry unchanged). How does its inductance change?

Introduction / Context:
Inductance quantifies the magnetic flux linkage produced per unit current. Core materials with high relative permeability dramatically boost flux for a given current and geometry, increasing inductance. Removing such a core leaves only air (or vacuum), whose permeability is much smaller, so the flux and inductance drop accordingly.

Given Data / Assumptions:

• Same number of turns, dimensions, and current.
• Core is changed from high-μ (iron/steel) to μ ≈ μ0 (air).
• Linear operation (no core saturation assumed).

Concept / Approach:

For a solenoid-like coil, L ∝ μ N^2 A / l, where μ is the core permeability, N is turns, A is cross-sectional area, and l is magnetic path length. Replacing μ by μ0 (air) reduces L roughly by the factor μr (relative permeability), which for iron can be hundreds to thousands in the unsaturated region.

Step-by-Step Solution:

Verification / Alternative check:

Measured inductance of transformer coils plummets when the laminated core is removed, which is why air-core inductors require many more turns for the same L.

Why Other Options Are Wrong:

• Increase or remain same contradicts L ∝ μ for fixed geometry.
• “May increase or decrease” is not applicable here; the trend is unambiguous.

Common Pitfalls:

Confusing Q-factor (which can improve without core losses) with inductance value; overlooking saturation or hysteresis effects, which are separate issues.

Final Answer:

Decreases