To deliberately decrease the inductance of an existing coil (without changing core material), which geometric change would be effective?

Introduction / Context:
Adjusting a coil's inductance can be done by altering geometry or materials. When core material must remain unchanged, geometric manipulations are the lever. This question checks which change specifically reduces L for a given coil and core material.

Given Data / Assumptions:

• Core material is fixed (permeability unchanged).
• We can modify turn spacing, area, or number of turns.
• Quasi-static solenoid approximations apply.

Concept / Approach:
For a solenoid-like coil, L ∝ (μ * N^2 * A) / l and is also influenced by turn proximity and leakage. Increasing spacing between turns reduces mutual coupling between adjacent turns and can effectively lower the coil's inductance compared to tightly wound turns. Increasing N or A would increase L; increasing μ would also increase L.

Step-by-Step Explanation:
Hold μ constant; consider geometry effects.Increase turn spacing → reduce effective coupling and increase mean length → lower L.Contrast with other changes: more turns (N↑) or larger area (A↑) both raise L.Therefore, increasing spacing between turns decreases inductance.

Verification / Alternative check:
Practical RF inductors use spaced turns or basket weave to reduce self-capacitance and inductance; simulations and measurements confirm reduced L versus tightly wound coils with the same N.

Why Other Options Are Wrong:

• Increase turns: L rises approximately with N^2.
• Increase permeability: L increases in proportion to μ.
• Increase area: L increases in proportion to A.
• Remove the core: While this can reduce L, it violates the stated constraint of not changing the core material; the most direct geometric change among the listed options is spacing.

Common Pitfalls:

• Assuming all geometric enlargements increase L; spacing reduces coupling and can lower L.
• Overlooking that core changes dominate L; here core is held constant by assumption.

Final Answer:
increase the spacing between turns