Assertion–Reason (Magnetism): Diamagnetic susceptibility is much smaller in magnitude than paramagnetic susceptibility; for both classes the relative permeability μr is close to unity.
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ABoth A and R are true and R is correct explanation of A
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BBoth A and R are true but R is not correct explanation of A
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CA is true but R is false
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DA is false but R is true
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EBoth A and R are false
Answer
Correct Answer: Both A and R are true but R is not correct explanation of A
Explanation
Introduction / Context:Magnetic materials are broadly categorized by their magnetic susceptibility χ and relative permeability μr = 1 + χ. Diamagnets possess small negative χ; paramagnets have small positive χ. Knowing magnitudes and physical origins clarifies many design choices in electromagnetics.
Given Data / Assumptions:
- Diamagnetic χ typically ~ −10^-5 to −10^-6; paramagnetic χ typically ~ +10^-3 to +10^-6.
- μr = 1 + χ for linear, isotropic materials under weak fields.
- No cooperative magnetic ordering (i.e., not ferro/ferri/antiferromagnets).
Concept / Approach:The assertion states the magnitude of diamagnetic susceptibility is much smaller than that of paramagnetic susceptibility, which is generally true for most elemental and molecular solids. The reason claims μr ≈ 1 for both. While that statement is also true (since |χ| ≪ 1), it does not explain why diamagnetic |χ| is typically smaller than paramagnetic χ. The origins differ: diamagnetism arises from induced currents opposing applied fields (Lenz-like response), whereas paramagnetism arises from alignment of permanent atomic magnetic moments from unpaired spins; the latter mechanism usually yields larger χ.
Step-by-Step Solution:
Accept A: |χ_dia| ≪ χ_para in most cases.Evaluate R: μr ≈ 1 is true but merely restates small χ, not the magnitude comparison between classes.Therefore, both true, but R is not the correct explanation.Verification / Alternative check:
Tabulated values (e.g., Cu: χ ≈ −10^-5; Al: χ ≈ +2×10^-5) illustrate the stated orders of magnitude.Why Other Options Are Wrong:
Claiming R explains A confuses a mathematical identity with a physical cause.Saying A false contradicts typical magnitudes.Common Pitfalls:
Mixing up sign (negative vs positive χ) with magnitude; assuming μr close to 1 implies identical behavior.Final Answer:
Both A and R are true but R is not correct explanation of A