QB_PH_SEC7_008: Dielectric, Magnetic Properties & Superconductivity

Above the Curie temperature $T_C$, the magnetic susceptibility $\chi_m$ of a ferromagnetic material in the paramagnetic regime follows the Curie-Weiss law given by

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Mean Field Approximation**: Pierre Weiss proposed that ferromagnetic coupling acts as an effective internal field proportional to magnetization: $B_{\text{int}} = \mu_0 \lambda M$. 2. **Total Effective Field**: $B_{\text{eff}} = B_{\text{ext}} + B_{\text{int}} = B_{\text{ext}} + \mu_0 \lambda M$. 3. **Paramagnetic Response ($T > T_C$)**: $M = \frac{C'}{T} B_{\text{eff}} = \frac{C'}{T}(B_{\text{ext}} + \mu_0 \lambda M)$ $M\left(1 - \frac{\mu_0 \lambda C'}{T}\right) = \frac{C'}{T} B_{\text{ext}}$ $M = \frac{C'}{T - \mu_0 \lambda C'} B_{\text{ext}}$ 4. **Curie Temperature & Susceptibility**: Defining $T_C = \mu_0 \lambda C'$: $\chi_m = \frac{C}{T - T_C}$ 5. **Conclusion**: Susceptibility diverges at $T = T_C$ according to $\frac{C}{T - T_C}$. Option (A) is correct.