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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 TcT_c, a superconductor expels all magnetic flux from its interior. This is the Meissner effect, and it makes the material a perfect diamagnet (B=0B = 0 inside, χm=−1\chi_m = -1).

How the flux is expelled

  1. When the material is cooled below TcT_c, electrons form Cooper pairs (BCS theory). The pairs move together as one coherent quantum state, without scattering.
  2. 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 λL\lambda_L (10 to 100 nm).
  3. 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:
B=μ0(H+M)=0  ⇒  M=−HB = \mu_0(H + M) = 0 \;\Rightarrow\; M = -H
  1. The field does not stop sharply at the surface. By London's equation it decays exponentially inside:
B(x)=B0 e−x/λLB(x) = B_0\,e^{-x/\lambda_L}

So beyond a few λL\lambda_L from the surface, B≈0B \approx 0.

  B
 B0|\
   | \
   |  `.
   |    `-._
   |        `--.____
   +--|-------------- x (into sample)
   0  λL
  1. Because the screening currents never decay (zero resistance), the expulsion is permanent as long as T<TcT < T_c and H<HcH < H_c.

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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