Magnetic response of superconductors (Meissner effect) For an ideal superconductor in its superconducting state, what is the effective relative permeability μr inside the material?

Introduction / Context:Superconductors exhibit perfect diamagnetism in the Meissner state, expelling magnetic flux from their interior (except within a thin penetration depth). This behavior can be captured phenomenologically by an effective relative permeability far below unity.

Given Data / Assumptions:

• Material is below its critical temperature and field, in the superconducting state.
• Idealized bulk response ignoring finite London penetration depth.
• Linear, quasi-static viewpoint for conceptual purposes.

Concept / Approach:In the Meissner state, internal magnetic flux density B is driven to zero in the bulk. Since B = μ0 μr H for an effective linear description, achieving B ≈ 0 for finite H corresponds to μr ≈ 0. This is a way to express perfect diamagnetism (complete flux expulsion) in a simplified constitutive form.

Step-by-Step Solution:Recall Meissner effect: superconductors expel magnetic fields.Interpretation: B_inside ≈ 0 except within a thin surface layer.Linearized view: B = μ0 μr H ⇒ μr must be ≈ 0 to cancel B for finite H.Therefore, select μr ≈ 0 (“zero”).

Verification / Alternative check:London equations predict an exponential decay of magnetic field over the London penetration depth; in the bulk, B approaches zero, consistent with an effective μr near zero.

Why Other Options Are Wrong:“High” or “either low or high” contradicts perfect diamagnetism; “low” is qualitatively true but not as precise as “zero”.

Common Pitfalls:Confusing type-II mixed states (flux penetration via vortices) with the ideal Meissner state; overlooking the difference between B and H inside superconductors.

Final Answer:zero