Magnetic permeability of diamagnetic materials For a diamagnetic material, is the relative permeability μr exactly equal to 1?

Introduction / Context:
Diamagnetism is a weak, universal magnetic response where induced magnetic moments oppose the applied field. Understanding the sign and magnitude of susceptibility and permeability helps classify materials and anticipate their behavior in magnetic circuits and shielding applications.

Given Data / Assumptions:

• Linear, isotropic, weak-field regime.
• Relative permeability μr relates to magnetic susceptibility χm via μr = 1 + χm.
• Diamagnets have χm < 0 with small magnitude.

Concept / Approach:

Because χm is negative and small for diamagnets, μr is slightly less than 1, not exactly 1. Examples: bismuth and copper have μr marginally below unity. μr = 1 corresponds to vacuum (or an idealized non-magnetic medium with zero susceptibility), not a real diamagnetic solid.

Step-by-Step Solution:

Verification / Alternative check:

Handbook values show μr for diamagnets such as silver or gold just below 1. This confirms that the equality μr = 1 is not exact for real diamagnets.

Why Other Options Are Wrong:

(a) contradicts standard definitions; (c), (d), (e) add conditions not relevant or correct—diamagnetic χm remains negative and small over wide conditions, and μr is not exactly 1.

Common Pitfalls:

Equating “non-magnetic” colloquially with μr = 1; forgetting that both diamagnets (μr < 1) and paramagnets (μr > 1) deviate slightly from unity.

Final Answer:

False