Question Bank MSQ • 2 Marks Section 7: Solid State Physics Dielectric, Magnetic Properties & Superconductivity

QB_PH_SEC7_003: Dielectric, Magnetic Properties & Superconductivity

Question Statement

Which of the following statements is/are CORRECT regarding superconductors in the Meissner state?
(A) The magnetic induction $\vec{B}$ inside the bulk of the superconductor is identically zero.
(B) The magnetic susceptibility $\chi_m$ is exactly $-1$ in SI units.
(C) The magnetic field decays exponentially into the superconductor with a characteristic London penetration depth $\lambda_L$.
(D) The critical temperature $T_c$ increases linearly with an applied external magnetic field.
Correct Answer
A, B, C
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Step-by-Step Multi-Select Evaluation: 1. **Statement A (Bulk Field)**: By definition of the Meissner-Ochsenfeld effect, when cooled below $T_c$ in a magnetic field, the material expels all interior magnetic flux: $\vec{B} = 0$ in the bulk. (CORRECT) 2. **Statement B (Susceptibility)**: $\vec{B} = \mu_0(\vec{H} + \vec{M}) = 0 \implies \vec{M} = -\vec{H} \implies \chi_m = \frac{M}{H} = -1$. Superconductors are ideal diamagnets. (CORRECT) 3. **Statement C (Penetration Depth)**: From the London equation $\nabla^2 \vec{B} = \vec{B}/\lambda_L^2$, the external field penetrates only a surface layer $B(x) = B_0 e^{-x/\lambda_L}$ where $\lambda_L = \sqrt{\frac{m}{\mu_0 n_s e^2}}$. (CORRECT) 4. **Statement D (Field Dependence)**: The phase boundary is $H_c(T) = H_c(0)[1 - (T/T_c)^2]$. An applied field reduces the effective transition temperature, it does not increase $T_c$. (INCORRECT) 5. **Conclusion**: Options A, B, and C are correct.
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