Constitutive relation in magnetized media (SI units) Let B denote magnetic flux density (tesla), H the magnetic field intensity (A/m), and M the magnetization (A/m). Assess the validity of the statement: B = μ0 * (H + M).

Introduction / Context:
In electromagnetics (SI units), the constitutive link between the magnetic flux density B, magnetic field intensity H, and magnetization M captures how matter responds to applied magnetic fields. The compact relation B = μ0 * (H + M) is foundational for materials ranging from paramagnets and diamagnets to ferromagnets.

Given Data / Assumptions:

• SI unit system with μ0 = 4π × 10^−7 H/m.
• B is measured in tesla; H and M are in A/m.
• No specific linearity or small-signal assumption is required for the identity itself.

Concept / Approach:
Start from the macroscopic decomposition of magnetic response. Magnetization M represents dipole moment per unit volume induced or aligned in material. The total flux density B can be written as the superposition of the contribution from the applied field H and the bound currents equivalently represented by M. In SI, this yields B = μ0 * (H + M). For linear, isotropic media one may define M = χm * H to get B = μ0 * (1 + χm) * H = μ0 * μr * H, but the more general relation does not assume linearity.

Step-by-Step Solution:
Identify macroscopic fields: B, H, and magnetization M.Use the SI definition: B = μ0 * H in vacuum; matter adds μ0 * M.Therefore, B = μ0 * (H + M) holds generally in SI.

Verification / Alternative check:
In a vacuum M = 0, so B = μ0 * H, which is recovered as a special case. In a linear medium M = χm H, giving the familiar μr form. Both reduce consistently to the general identity.

Why Other Options Are Wrong:
“False” contradicts SI macroscopic EM. “True only for linear ferromagnets” is too restrictive; linearity is not required. “True only in vacuum” ignores the M term. “False unless μr appears” confuses the linear-material parameterization with the fundamental identity.

Common Pitfalls:

• Mixing CGS (Gaussian) and SI; the forms differ across systems.
• Assuming μr must appear explicitly even when writing the most general SI relation.

Final Answer:
True