Mutual inductance geometry — concept check: For mutual inductance to occur between two coils, must the coils be oriented at right angles to each other, or is coupling maximized when their magnetic axes are aligned?

Introduction / Context:
Mutual inductance quantifies how effectively a changing current in one coil induces a voltage in another. Coil orientation and core material are key design variables in transformers, inductive sensors, and wireless power systems.

Given Data / Assumptions:

• Two coils placed in proximity, potentially with a magnetic core.
• Mutual inductance M depends on flux linkage from the primary to the secondary.
• Coupling coefficient k ranges from 0 (no coupling) to 1 (perfect coupling).

Concept / Approach:
Mutual inductance M = k * sqrt(L1 * L2). The coupling coefficient k is maximized when the magnetic axes of the coils are aligned so that the primary’s flux directly links the secondary. When coils are oriented at right angles (orthogonal), the linked flux is minimized, and k trends toward zero.

Step-by-Step Solution:

Verification / Alternative check:
Transformer design universally aligns windings concentrically on a common core to maximize coupling; cross-axis placement is used when intentional low coupling is desired (e.g., some pickup coils).

Why Other Options Are Wrong:
Correct: Would assert an incorrect geometrical condition.

High-frequency or nonmagnetic qualifiers do not invert the fundamental orientation effect: aligned axes produce more coupling than orthogonal axes.

Common Pitfalls:
Confusing electromagnetic interference reduction strategies (orthogonal placement reduces coupling) with the requirement for mutual inductance. Assuming any proximity guarantees strong coupling.

Final Answer:
Incorrect