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The Field-cooled Meissner experiment starts above the superconducting transition temperature with a weak, steady applied magnetic field already penetrating a solid sample. Cooling while keeping the applied magnetic field fixed tests whether the interior magnetic flux changes. This is the decisive contrast with cooling in zero magnetic field and switching the magnetic field on afterwards. The diagram shows the two histories for the same final applied magnetic field.

Meissner and Ochsenfeld reported magnetic expulsion in 1933, showing that the transition involves more than vanishing electrical resistance. A modern motivating version appears in MIT's lead-sample experiment: surround the sample with a solenoid supplying a steady magnetic field and a separate pickup coil connected to a recording instrument. Apply the magnetic field while the lead is still normal, then cool through its transition without changing the solenoid electric current. Expulsion produces a transient pickup-coil electric potential difference; warming through the transition produces the opposite sign as magnetic flux returns. MIT also checks the signal direction by switching off the applied magnetic field while the sample is normal. ^{[ref] [ref]}

Faraday's law of induction explains the readout. For a stationary $N$-turn pickup coil, with the same linked magnetic flux $\Phi$ per turn and a fixed orientation,Thus a transient measures a change in linked magnetic flux, not directly the static magnetic field at every point in the sample. For stipulated $N=100$ and $\Delta \Phi =-2\times 10^{-8}\mathrm{Wb}$ per turn, the signed pulse area is $+2\times 10^{-6}\mathrm{V}\mathrm{s}$. The apparatus geometry determines how a change in interior magnetic field contributes to that linked magnetic flux. Keeping the applied magnetic field fixed, repeating on warming, and checking a normal-state control make the expulsion interpretation testable; a stationary pickup coil has no sustained signal after the magnetic flux has stopped changing.

Why does the preparation history matter? In the stationary, ideal perfect conductor model, the interior electric field is zero. The differential form of Faraday's law of induction then givesIf the interior magnetic field was ${\mathbf{B}}_0$ when perfect conduction began, it remains ${\mathbf{B}}_0$; if it was zero, it stays zero when an external magnetic field is subsequently applied. Both a perfect conductor prepared in zero magnetic field and a sample exhibiting the Meissner effect can therefore exclude a newly applied weak magnetic field. Only the field-cooled comparison tests expulsion of an already present magnetic field. This argument concerns a stationary sample and the ideal zero-electric field model, not a moving conductor.

The equilibrium London equations supply the additional constraint. In a homogeneous region without penetrating flux tubes, they imply ${\nabla }^2\mathbf{B}=\mathbf{B}/{\lambda }_L^2$. For a half-space $z\ge 0$ with a magnetic field parallel to its flat boundary, fixed surface value $B_s$, and a bounded solution deep inside, this givesAt $z=5{\lambda }_L$ only $e^{-5}\simeq 0.00674$ of the surface magnetic field remains. The screening electric currents near the surface produce this reduction. Unlike the frozen interior magnetic field of a perfect conductor, this equilibrium profile does not retain an arbitrary initial ${\mathbf{B}}_0$. The extra constitutive relation, and not zero electrical resistance by itself, selects the screened state. Expulsion occurs during the transition, when transient electric fields can be present; the steady-state zero-electric field argument does not describe the process of establishing superconductivity. The diagram gives equilibrium end states, not transition kinetics. ^[ref]

These ideal comparisons concern a solid sample in equilibrium and a sufficiently weak magnetic field. Stronger magnetic fields can destroy superconductivity or permit magnetic flux to penetrate parts of a sample, so complete bulk expulsion is not a claim about every superconducting state. ^[ref] A hole in a superconducting loop can retain magnetic flux even while the material surrounding it screens its own interior; see flux conservation in a superconducting loop. The hole is not superconducting material, so its retained magnetic flux does not contradict the Meissner effect. ^[ref]

For a bulk type-II superconductor with negligible demagnetizing field, raising the applied magnetic field intensity past the lower critical value $H_{c1}$ favors a superconducting mixed state containing quantum vortex lines; superconductivity survives until the upper critical value $H_{c2}$. The magnetic field extends around each vortex over a penetration scale, not solely inside its core. Thus a nonzero average magnetic flux density can coexist with superconductivity. Below $H_{c1}$, a type-II superconductor also supports a Meissner state; a vortex-free state above the equilibrium entry field may instead be metastable. ^[ref]

Real preparation histories may leave quantum vortex lines held in place by material inhomogeneities, retaining magnetic flux and producing hysteresis. This flux pinning restricts access to equilibrium: it is different from the arbitrary frozen interior magnetic field of the ideal perfect conductor model. Harvard's vortex-imaging work illustrates strong pinning to bulk disorder in a type-II superconductor. ^[ref] Separately, flux conservation in a superconducting loop and fluxoid and flux quantization in a superconductor explain why a hole can retain magnetic flux. Neither bore retention, vortex penetration nor weak screening in a thin sample should be silently identified with the equilibrium Planar London screening calculation.

A superconducting persistent current is an electric current circulating in a closed path with superconductivity after the external driving electromotive force has ceased. Its associated magnetic field makes the circulation observable without inserting a measuring instrument into the path. This article concerns macroscopic circulation in superconductivity. A finite experiment establishes persistence over its observation window with a stated measurement error, rather than directly observing an infinite lifetime.

The ideal circuit connection is flux conservation in a superconducting loop. In a fixed loop with self-inductance $L$, a single circulating electric current $I$, and externally imposed linked magnetic flux ${\Phi }_{\mathrm{ext}}$, the lumped circuit approximation givesWhen the electrical resistance $R$ vanishes, integrating gives $LI+{\Phi }_{\mathrm{ext}}=\text{constant}$. Removing the external linked magnetic flux therefore changes the circulating electric current; holding it fixed afterwards preserves that electric current. This is a circuit approximation with a specified self-inductance, not a derivation of the microscopic state of superconductivity. For thin paths where the carrier contribution matters, fluxoid and flux quantization in a superconductor supplies the more careful description.

For constant $L>0$, constant effective electrical resistance $R\ge 0$, and no changing external linked magnetic flux, the RL circuit instead predictsThis exponential decay follows by separating $dI/I=-(R/L)dt$. A long relaxation time tests extremely small electrical resistance without trying to resolve an equally tiny steady electric potential difference. The stored magnetic energy is $U=L{I}^2/2$, so the same model gives $dU/dt=-R{I}^2$, exactly the Joule heating loss. The finite energy stored in the loop supplies the magnetic readout; the circulating electric current is not a continuously powered source of useful work.