Magnetization–permeability relationship In linear magnetic materials (SI units), is the magnetization given by M = (μ_r − 1) * H?

Introduction / Context:
Relating magnetization M, magnetic field strength H, and relative permeability μ_r is fundamental in electromagnetics. In linear, isotropic media, a simple proportionality connects these quantities through magnetic susceptibility χ_m.

Given Data / Assumptions:

• Linear, isotropic magnetic response.
• Definitions: B = μ0 (H + M) and μ = μ0 μ_r.
• Magnetic susceptibility χ_m = M / H.

Concept / Approach:

From B = μ0 (H + M) and B = μ H = μ0 μ_r H, equate to get μ0 μ_r H = μ0 H + μ0 M ⇒ μ_r H = H + M ⇒ M = (μ_r − 1) H. Also, since χ_m = μ_r − 1, we have the standard relation M = χ_m H. This holds for linear media (small-signal regime).

Step-by-Step Solution:

Verification / Alternative check:

In vacuum, μ_r = 1 ⇒ M = 0, consistent with no magnetization; for paramagnets/diamagnetics, |χ_m| ≪ 1, so M is small compared with H.

Why Other Options Are Wrong:

• “False” contradicts standard linear-material relations.
• Limiting to ferromagnets or vacuum is unnecessary; the relation is general for linear regimes.

Common Pitfalls:

Confusing H and B; forgetting that μ_r = 1 + χ_m in SI units.

Final Answer:

True