Magnetization in a solenoid core — relation between M and H in SI units In a uniform magnetic field H inside a solenoid, the magnetized core has magnetization (dipole moment per unit volume) M equal to which expression?

Introduction / Context:
In SI units, the magnetic fields are related by B, H, and M through constitutive equations. Distinguishing between absolute permeability μ, relative permeability μr, and susceptibility χ is essential for correct formulae.

Given Data / Assumptions:

• Linear, isotropic material inside the solenoid.
• SI relationships: B = μ0 (H + M) and B = μ0 μr H.
• Magnetic susceptibility defined by M = χ H.

Concept / Approach:
Equate B = μ0 (H + M) to B = μ0 μr H. Cancelling μ0 gives H + M = μr H, hence M = (μr − 1) H. Since χ = μr − 1, the expression is consistent with M = χ H. Note that μ0 H or μ0 μr H have dimensions of B, not M, and are therefore incorrect for magnetization.

Step-by-Step Solution:
Start with B = μ0 (H + M).Use B = μ0 μr H.Deduce M = (μr − 1) H.

Verification / Alternative check:
Dimensional analysis: M and H share the same units (A/m). Options containing μ0 multiply by N/A^2, giving incorrect units for M.

Why Other Options Are Wrong:
μ0 H and μ0 μr H have units of B (tesla). μr H has units A/m but equals H scaled, not M unless μr = 2; generally incorrect. H/μ0 has wrong units.

Common Pitfalls:

• Confusing B and H relationships and inserting μ0 inadvertently.
• Using cgs relations in SI contexts.

Final Answer:
(μr - 1) H