---
title: "Superconducting limits and applications"
subject: "Electrical Engineering Material"
chapter: 5
key: "semester_3/electrical_engineering_material:superconductor-limits-applications"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/superconductor-limits-applications
site: BCT Engineering
---

# Superconducting limits and applications

Electrical Engineering Material · Chapter 5: Superconductivity

- Asked in: 2078 Kartik, 4 marks
- Video: [Practical Application of Superconductivity|Limitations#applicationofsuperconductor#bscfinalphysics](https://www.youtube.com/watch?v=_qR88zGvG4g) — Physics by Amandeep Kaur Hunjra
- 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-limits-applications
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-5

## Question

What are the different limiting factors for a superconductor to remain in its superconducting state? Write some applications where superconductors are used.

## Short answer

A superconductor remains superconducting only below three critical values: critical temperature T_c, critical magnetic field H_c and critical current density J_c. Exceeding any one returns it to normal state. Applications include MRI and NMR magnets, particle accelerator magnets, maglev trains, SQUIDs for sensitive magnetometry, and superconducting power cables.

## Answer

A material stays superconducting only while three quantities are below their critical values. Exceeding any one of them returns it to the normal state.

#### Limiting factors
1. **Critical temperature $T_c$:** above $T_c$ thermal energy breaks the Cooper pairs (e.g. Hg 4.2 K, Nb$_3$Sn 18 K, YBCO 92 K).
2. **Critical magnetic field $H_c$:** a field above $H_c$ destroys superconductivity. It depends on temperature: $H_c(T) = H_0[1 - (T/T_c)^2]$.
3. **Critical current density $J_c$:** a current produces its own field; when this field at the surface reaches $H_c$, superconductivity is lost. For a wire of radius $r$: $I_c = 2\pi r H_c$.

The three form a critical surface; the material is superconducting only inside it.

#### Applications
- **MRI and NMR magnets:** NbTi coils give strong, stable fields with no power loss.
- **Maglev trains:** superconducting magnets for levitation (e.g. Japan's SCMaglev).
- **Particle accelerators:** bending magnets in the LHC.
- **SQUIDs:** extremely sensitive magnetometers (brain and heart signals).
- **Power cables and fault current limiters:** low-loss transmission and fast fault limiting.
- **SMES:** superconducting magnetic energy storage.
- **Josephson junction devices:** fast switching and quantum computing qubits.

## Check yourself

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

1. Which three quantities limit the superconducting state?
   A. Critical temperature, critical field and critical current density
   B. Critical voltage, pressure and frequency
   C. Only Tc and Hc
   D. Critical resistance, mass and length
   Answer: A. Exceeding any one returns the material to normal. (Key point: Three limits)

2. Why does heating above Tc destroy superconductivity?
   A. It melts the lattice at once
   B. Thermal energy breaks the Cooper pairs
   C. It creates extra vortices
   D. It increases Hc
   Answer: B. Above Tc thermal energy exceeds the pair binding. (Key point: Why Tc limits)

3. How does the current destroy superconductivity?
   A. It heats the wire through resistance
   B. It increases Tc
   C. Its own surface field reaches Hc
   D. It forms a Meissner state
   Answer: C. Silsbee's rule: Ic = 2 pi r Hc. (Key point: Current limit)

4. Which is a typical use of superconductors?
   A. Heating elements in toasters
   B. Insulating cable covers
   C. Incandescent lamp filaments
   D. NbTi coils for MRI magnets
   Answer: D. Superconducting magnets give strong, stable fields with no power loss. (Key point: Applications)

## Related in Electrical Engineering Material

- [Meissner effect and hard superconductors](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Ameissner-hard-superconductor) — Electrical Engineering Material, chapter 5
- [Meissner effect; type I vs type II superconductors](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Ameissner-type-i-ii) — Electrical Engineering Material, chapter 5, asked 8×

## Related in other subjects

- [Factors for limiting fire spread](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Afire-spread-factors) — Building Technology, chapter 12
- [Stability limits and factors affecting transient stability](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Astability-limits-factors) — Power System Analysis II, chapter 6, asked 2×
- [Solar intensity factors and applications](https://www.bctengineer.com/question.md?key=semester_7%2Fenergy_environment_and_society%3Asolar-intensity-factors-applications) — Energy Environment and Society, chapter 3
- [Factors affecting heat transfer and its applications](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Afactors-applications-heat-transfer) — Heat Transfer, chapter 1