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Superconductor expels magnetic lines of force
Short answer
Below Tc, Cooper pairs form and persistent surface screening currents flow within the London penetration depth λL. These lossless currents create a magnetic field equal and opposite to the applied field, canceling flux inside (B=0). The flux decays exponentially: B(x)=B0 e^{-x/λL}.
How does a superconductor expel all the magnetic lines of force at T<Tc?
Below , a superconductor expels all magnetic flux from its interior. This is the Meissner effect, and it makes the material a perfect diamagnet ( inside, ).
How the flux is expelled
- When the material is cooled below , electrons form Cooper pairs (BCS theory). The pairs move together as one coherent quantum state, without scattering.
- When a magnetic field is present, the pairs set up persistent surface (screening) currents in a thin layer of thickness about the London penetration depth (10 to 100 nm).
- These loss-free currents produce a magnetic field equal and opposite to the applied field inside the body, so the net field inside is zero:
- The field does not stop sharply at the surface. By London's equation it decays exponentially inside:
So beyond a few from the surface, .
B
B0|\
| \
| `.
| `-._
| `--.____
+--|-------------- x (into sample)
0 λL
- Because the screening currents never decay (zero resistance), the expulsion is permanent as long as and .
The flux lines therefore bend around the sample instead of passing through it. This expulsion happens whether the field was applied before or after cooling, which shows that superconductivity is a true thermodynamic state and not just perfect conduction.
✓ Answer checked by Claude Opus 5.5 (high effort)
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