---
title: "Superconductor expels magnetic lines of force"
subject: "Electrical Engineering Material"
chapter: 5
key: "semester_3/electrical_engineering_material:superconductor-expels-field"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/superconductor-expels-field
site: BCT Engineering
---

# Superconductor expels magnetic lines of force

Electrical Engineering Material · Chapter 5: Superconductivity

- Asked in: 2076 Chaitra, 4 marks; 2074 Asoj, 6 marks (asked 2 times)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/superconductor-expels-field
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-5

## Question

How does a superconductor expel all the magnetic lines of force at T<Tc?

## 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}.

## Answer

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

#### How the flux is expelled
1. When the material is cooled below $T_c$, 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 $\lambda_L$ (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:

$$
B = \mu_0(H + M) = 0 \;\Rightarrow\; M = -H
$$

4. The field does not stop sharply at the surface. By London's equation it decays exponentially inside:

$$
B(x) = B_0\,e^{-x/\lambda_L}
$$

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

```text
  B
 B0|\
   | \
   |  `.
   |    `-._
   |        `--.____
   +--|-------------- x (into sample)
   0  λL
```

5. Because the screening currents never decay (zero resistance), the expulsion is permanent as long as $T < T_c$ and $H < H_c$.

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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What forms below Tc in the BCS explanation?
   A. Cooper pairs that move as one coherent state without scattering
   B. Free single electrons with higher mobility
   C. Magnetic monopoles that cancel the field
   D. Holes that fill the conduction band
   Answer: A. Electron pairs bound via lattice vibrations carry loss-free current. (Key point: Role of Cooper pairs)

2. How does the field inside get cancelled?
   A. The material absorbs the flux into its atoms
   B. Persistent surface screening currents create a field equal and opposite to the applied field
   C. The applied field is switched off by the cooling
   D. Eddy currents in the bulk decay and leave B = 0
   Answer: B. Loss-free screening currents in a thin layer give a cancelling field inside. (Key point: Mechanism of expulsion)

3. How does B vary inside the surface?
   A. B stays equal to B0 throughout the sample
   B. B drops to zero abruptly with no penetration at all
   C. B(x) = B0 exp(-x/lambda_L), essentially zero beyond a few lambda_L
   D. B increases exponentially with depth
   Answer: C. The field decays exponentially over the London penetration depth, about 10 to 100 nm. (Key point: London penetration depth)

4. Why is the expulsion permanent while T < Tc and H < Hc?
   A. The sample is kept refrigerated by the field
   B. The field energy is stored as heat
   C. Cooper pairs repel the field lines individually
   D. Screening currents have zero resistance and never decay
   Answer: D. Without resistance the currents persist, keeping B = 0. (Key point: Permanence)

## Related in Electrical Engineering Material

- [Superconductor, critical field and critical current density](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Adefine-critical-field-current) — Electrical Engineering Material, chapter 5
- [Strong magnetic field and critical current](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Acritical-current-strong-field) — Electrical Engineering Material, chapter 5, asked 5×
- [Field expulsion; type I vs type II](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aexpel-field-type-i-ii) — Electrical Engineering Material, chapter 5

## Related in other subjects

- [Superconductor and critical magnetic field](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Asuperconductor-critical-field-characteristics) — Engineering Physics, chapter 8