Magnetization–field relation and the range of µr Assertion (A): For a magnetic material, M = (µr − 1) H, where M is magnetization (A/m), H is magnetic field intensity (A/m), and µr is relative permeability. Reason (R): The relative permeability µr can take any value from 0 up to hundreds of thousands.

Introduction / Context:The magnetization–field relationship in linear media connects magnetization M to applied field H through magnetic susceptibility χm. Since µr = 1 + χm, we can write M in terms of µr. The assertion and reason test both the correct formula and the physically allowed range of µr.

Given Data / Assumptions:

• Linear, isotropic magnetic material in the small-field regime.
• Magnetization M is dipole moment per unit volume (A/m).
• Definitions: B = µ0µrH and M = χm H with µr = 1 + χm.

Concept / Approach:From M = χm H and µr = 1 + χm, it follows directly that M = (µr − 1) H, so the assertion is correct. The reason claims µr can range from 0 to very large numbers. While µr can indeed be very large in certain ferromagnets, it cannot be zero; diamagnets have µr slightly less than 1, paramagnets slightly greater than 1. Hence the lower bound “0” is unphysical, making the reason statement false.

Step-by-Step Solution:Start with M = χm H.Use µr = 1 + χm ⇒ χm = µr − 1.Therefore M = (µr − 1) H (assertion true).Evaluate reason: practical µr values are near 1 for dia/paramagnets and up to 10^3–10^5 for ferromagnets, but never 0 ⇒ reason false.

Verification / Alternative check:Materials data confirm µr < 1 for diamagnets (~0.999), slightly > 1 for paramagnets, and large for ferromagnets; no standard material has µr = 0.

Why Other Options Are Wrong:Claiming the reason as correct would endorse an impossible µr = 0; claiming A false would contradict standard definitions.

Common Pitfalls:Confusing absolute permeability µ with relative µr; overlooking that “any value from 0” is a sweeping, incorrect lower bound.

Final Answer:A is true but R is false