On a B–H (magnetization) curve, the magnetizing force H is defined as the ampere-turns per unit length of the magnetic path. Which expression correctly represents H and its SI unit?

Introduction / Context:
The B–H curve relates magnetic flux density B to magnetizing force H. Correctly defining H is fundamental in magnetic circuit analysis, core design, and understanding hysteresis. H quantifies the magnetizing effort produced by current-carrying turns along a magnetic path of a certain length.

Given Data / Assumptions:

• N turns carrying current I create magnetomotive force (MMF) equal to N * I ampere-turns.
• Magnetic path length is l (meters).
• Homogeneous path assumption for definition (local values can vary in complex cores).

Concept / Approach:
Magnetizing force H is the MMF per unit length of magnetic path: H = MMF / l = (N * I) / l. Its SI unit is A/m (ampere per meter). This field intensity is the cause, while B (flux density) is the effect through the material relationship B = μ * H (with μ = μ0 * μr).

Step-by-Step Solution:
Compute MMF: MMF = N * I (ampere-turns).Normalize by path length: H = (N * I) / l.Identify SI units: A/m.Relate to B: In free space, B = μ0 * H ⇒ H = B / μ0, consistent with units A/m.

Verification / Alternative check:
Dimensional analysis: N is dimensionless, I in A, l in m, so H has dimensions A/m, confirming the expression. Electromagnetic textbooks consistently define H using MMF per length.

Why Other Options Are Wrong:

• H = I × N (AT): That is MMF, not H; it lacks division by length.
• AT per weber: Not the definition of H; mixes unrelated quantities.
• Wb/m^2 (tesla): That is B, not H.
• H = B / μ0 (A/m): This is correct only in free space as a derived relation, not the general defining expression requested.

Common Pitfalls:

• Confusing B and H or their units (tesla vs A/m).
• Forgetting path length in practical cores; air gaps change effective l and H required.

Final Answer:
H = (N * I) / l, units A/m