QB_PH_SEC7_026: Dielectric, Magnetic Properties & Superconductivity

Which of the following classes of magnetic materials has a small, temperature-independent negative magnetic susceptibility ($\chi < 0$) across ordinary temperatures?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Larmor Theorem & Induced Orbital Moment**: - An applied magnetic field $\vec{B}$ causes Larmor precession of atomic electron orbits with frequency $\omega_L = \frac{eB}{2m}$. - By Lenz's law, this precession produces an induced magnetic dipole moment opposing $\vec{B}$: $\mu_{\text{induced}} = -\frac{Z e^2 B}{6 m} \langle r^2 \rangle$ 2. **Langevin Diamagnetic Susceptibility**: $\chi_{\text{dia}} = \frac{\mu_0 M}{B} = -\frac{\mu_0 N Z e^2}{6 m} \langle r^2 \rangle$ 3. **Temperature Dependence**: Because the atomic electronic ground state charge distribution $\langle r^2 \rangle$ is dictated by quantum mechanics and does not change with thermal energy $k_B T \ll E_{\text{electronic}}$, $\chi_{\text{dia}}$ is virtually constant with temperature. 4. **Conclusion**: Diamagnetic materials. Option (A) is correct.