Field Expulsion and the Critical Field

Cool a superconductor below $T_c$ in a magnetic field and it does not merely become a perfect conductor: it actively expels the field. A superconducting sphere is a perfect diamagnet, screening currents flowing so that $B=0$ inside and the normal field vanishes at the surface, which forces the field lines to bend around it and crowd to $\tfrac32 B_0$ at the equator. The state survives only while $B_0\lt B_c(T)=B_{c0}(1-(T/T_c)^2)$ ; raise the temperature or the field past that parabola and the flux floods back in. A type-II superconductor instead admits the field as a triangular Abrikosov lattice of vortices, each carrying one flux quantum $\Phi_0=h/2e$ .

Figure 1. Field-intensity map of a superconducting sphere expelling the applied field, with the Bc(T) phase diagram and the surface-field profile crowding to (3/2) B0 at the equator. Method: closed-form perfect-diamagnet sphere field; critical-field parabola; Abrikosov lattice spacing. Reference: Tinkham, Introduction to Superconductivity, Ch. 1-5.

temperature T/Tc0.40

applied B00.030

type

Bc00.080

WHAT TO TRY

Cool below T/Tc = 1: the intensity map goes dark inside the sphere (B = 0) and the field lines bend out around it. The Meissner effect is active expulsion, not just zero resistance, so the field is pushed out, not merely frozen.
Watch the bright lobes on the flanks: the expelled flux crowds against the equator and the surface field climbs to (3/2) B0 there while it vanishes at the poles. The bottom-right profile plots exactly that |B(theta)|/B0 against the flat normal-state reference at 1.
Raise the applied field B0 past the critical field Bc(T): superconductivity is quenched and the flux floods back in. The operating dot crosses the Bc(T) parabola in the phase diagram, the boundary you are stepping over.
Switch to type II: now the field threads through as a triangular lattice of quantized vortices instead of being fully expelled, the mixed state between Bc1 and Bc2 that lets type-II magnets carry huge fields.