Inductance Dependence on Geometry and Material Assess the statement: “Inductance is indirectly (inversely) proportional to the square of the number of turns, the permeability, and the core cross-sectional area.”

Introduction / Context:
Coil inductance depends on physical geometry and magnetic properties. Designers adjust turns, core area, path length, and permeability to set target inductance in chokes, filters, resonators, and transformers. This item challenges a common misconception about the direction of proportionality.

Given Data / Assumptions:

• Solenoidal coil approximation with uniform core.
• Magnetic path length l, cross-sectional area A, relative permeability μ_r, vacuum permeability μ_0, number of turns N.
• Linear, unsaturated magnetic material (no hysteresis nonlinearity considered).

Concept / Approach:

For a typical coil, an approximate formula is L ∝ μ * N^2 * A / l, where μ = μ_0 * μ_r. That is, inductance increases with the square of turns, increases with permeability, increases with cross-sectional area, and decreases with magnetic path length. The prompt claims the opposite sign (indirectly proportional) with respect to N^2, μ, and A, which is incorrect.

Step-by-Step Solution:

Verification / Alternative check:

Magnetic circuit analogy: Reluctance ℜ = l / (μ A). Inductance L = N^2 / ℜ = μ N^2 A / l. Physical intuition agrees: more turns or higher permeability gives stronger flux linkage for the same current, producing higher inductance.

Why Other Options Are Wrong:

“True”, “True only for air-core”, and “True only at very high frequency” contradict the governing proportionality. “Indeterminate without wire gauge” is irrelevant to the fundamental geometric/material dependence (wire gauge mainly affects resistance and current handling, not the primary L proportionality in first order).

Common Pitfalls:

Confusing inductance L with stored energy or with copper loss. Also, mixing up the inverse proportionality to path length l with the direct proportionalities to N^2, μ, and A leads to errors in preliminary designs.

Final Answer:

False