QB_PH_SEC7_016: Dielectric, Magnetic Properties & Superconductivity

A Type-I superconductor has a critical magnetic field of $B_c(0) = 0.080\text{ T}$ at $T = 0\text{ K}$ and a critical temperature of $T_c = 4.0\text{ K}$. What is its critical magnetic field $B_c(T)$ in Tesla at $T = 2.0\text{ K}$?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Empirical Parabolic Critical Field Relation**: $B_c(T) = B_c(0) \left[1 - \left(\frac{T}{T_c}\right)^2\right]$ 2. **Parameter Substitution**: - $B_c(0) = 0.080\text{ T}$ - $T_c = 4.0\text{ K}$ - $T = 2.0\text{ K}$ 3. **Evaluation**: $\frac{T}{T_c} = \frac{2.0\text{ K}}{4.0\text{ K}} = 0.5$ $\left(\frac{T}{T_c}\right)^2 = (0.5)^2 = 0.25$ $B_c(2.0\text{ K}) = 0.080 \times (1 - 0.25) = 0.080 \times 0.75 = 0.060\text{ T}$ 4. **Official Value**: 0.060 T.