Question

Diamagnetic materials have:

• A. Permanent magnetic moments
• B. Magnetic susceptibility $< 0$
• C. Magnetic susceptibility $> 0$
• D. Hysteresis

Hint:

Superconductors are perfect diamagnets. They exhibit the Meissner effect, expelling all interior magnetic flux lanes completely. For a perfect superconductor, the magnetic susceptibility reaches its absolute theoretical lower bound: \[ \chi_m = -1 \]

Answer 1

The Correct Option is B

Concept: Magnetic susceptibility ($\chi_m$) is a dimensionless proportionality constant that quantifies how a material responds to an externally applied magnetic field ($H$). It is defined by the fundamental constitutive vector equation: \[ M = \chi_m H \] Where $M$ is the induced magnetization per unit volume. Diamagnetism is a universal property found in all materials where atoms contain completely filled electronic shells, resulting in zero net permanent atomic magnetic moments ($\mu_{atom} = 0$) in the absence of an external field.

Step 1: Understanding Lenz's Law at the atomic scale.
When a diamagnetic material is placed inside an external magnetic field $H$, the changing magnetic flux alters the orbital motion of the paired electrons. According to Lenz's law of electromagnetism, these induced orbital currents adjust their paths to generate a microscopic magnetic field that directly opposes the applied external field.

Step 2: Determining the mathematical sign of magnetization and susceptibility.
Because the internally induced magnetization $M$ works in direct opposition to the applied field direction $H$, the vectors point in completely opposite directions. Expressing this mathematically: \[ M \propto -H \quad \Rightarrow \quad M = \chi_m H \] This opposing behavior requires the proportionality coefficient $\chi_m$ to be strictly negative: \[ \chi_m < 0 \] Typically, for diamagnetic substances (like Copper, Water, and Bismuth), $\chi_m$ is a small, constant negative value ($\sim -10^{-5}$ to $-10^{-6}$) and is independent of temperature.

Step 3: Checking the other options.

• Option A: Diamagnets have zero permanent magnetic moments; permanent moments are characteristic of paramagnetic and ferromagnetic substances.
• Option C: Positive susceptibility ($\chi_m > 0$) is characteristic of paramagnets and ferromagnets.
• Option D: Hysteresis loops represent domain-wall friction and energy dissipation, which only occur in ferromagnetic and ferrimagnetic materials. Hence, a negative magnetic susceptibility ($\chi_m < 0$) uniquely describes diamagnetic materials.