Four primary factors determine the inductance of a coil: number of turns, coil length, coil cross-sectional area, and which material property of the core?

Introduction / Context:
Inductance quantifies a coil's ability to store magnetic energy. For a single-layer solenoid-style inductor, physical dimensions and core material dominate L. Understanding which parameters matter most helps when adjusting inductance for filters, chokes, and transformers.

Given Data / Assumptions:

• Single coil with a magnetic path that largely follows the core.
• Quasi-static magnetic behavior without strong leakage.
• Classical approximation for solenoid inductance applies.

Concept / Approach:
Approximate inductance for a solenoid: L ∝ (μ * N^2 * A) / l, where μ is permeability of the core material, N is the number of turns, A is cross-sectional area, and l is magnetic path length. Thus, in addition to turns, length, and area, the key independent material property is permeability μ = μ0 * μr.

Step-by-Step Explanation:
Identify geometric factors: N (turns), A (area), l (length).Include material factor: μ, which scales magnetic flux density for a given H.Increasing μ (e.g., adding an iron or ferrite core) increases L dramatically.Hence, the fourth factor is permeability.

Verification / Alternative check:
Empirical measurements show that swapping an air core (μr ≈ 1) for a ferrite core (μr >> 1) increases inductance by roughly μr times, aligning with the proportional relation above.

Why Other Options Are Wrong:

• Reluctance: Inversely related to μ and geometry; not an independent design parameter of the coil itself.
• Counter emf: A result of inductance (L * di/dt), not a determining factor.
• Coefficient of coupling: Pertains to mutual inductance between coils, not self-inductance of a single coil.
• Wire resistivity: Affects losses, not L directly.

Common Pitfalls:

• Confusing permeability (material property) with reluctance (circuit property).
• Overlooking air gaps that reduce effective μ and L.

Final Answer:
permeability