--- title: "Superconductor and critical magnetic field" subject: "Engineering Physics" chapter: 8 key: "semester_1/engineering_physics:superconductor-critical-field-characteristics" source: https://www.bctengineer.com/q/semester_1/engineering_physics/superconductor-critical-field-characteristics site: BCT Engineering --- # Superconductor and critical magnetic field Engineering Physics · Chapter 8: Electromagnetism - Asked in: 2074 Asoj, 5 marks - Video: [Critical Temperature and Magnetic Field - Superconductors & Supercapacitors - Engineering Physics 1](https://www.youtube.com/watch?v=qHZuEJ-QugI) — Ekeeda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_1/engineering_physics/superconductor-critical-field-characteristics - Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-8 ## Question What is superconductor? Explain critical magnetic field. Describe the characteristics of superconductor. ## Short answer A superconductor loses all resistance below a critical temperature Tc. The critical magnetic field Bc(T) is the minimum field that restores normal resistance, varying as Bc(0)[1-(T/Tc)²]. Key characteristics: zero resistance, Meissner effect (perfect diamagnetism), critical current and field, Type I/II behaviour, isotope effect, and a jump in heat capacity at Tc. ## Answer #### Superconductor A **superconductor** is a material whose electrical resistance drops abruptly to zero when it is cooled below a certain temperature called the **critical (transition) temperature** T_c. Examples: mercury (T_c = 4.2 K), lead (7.2 K), niobium (9.2 K), YBa₂Cu₃O₇ (about 92 K). #### Critical magnetic field A strong magnetic field destroys superconductivity. The minimum field that restores the normal (resistive) state at a given temperature is the **critical field** B_c(T). It varies with temperature as B_c(T) = B_c(0) [1 − (T/T_c)²] ```text Bc | Bc(0)|* | * | * Normal state | SC * | state * |_____________________*__ T Tc ``` B_c = B_c(0) at T = 0 and falls to zero at T = T_c. Below the curve the material is superconducting. Related to this, a current above the **critical current** I_c = 2πaB_c/μ0 (Silsbee's rule, wire of radius a) also destroys superconductivity. #### Characteristics 1. **Zero resistance:** a current set up in a ring persists for years without a source. 2. **Meissner effect:** a superconductor expels magnetic flux from its interior (B = 0), i.e. perfect diamagnetism, χ = −1. This differs from a mere perfect conductor. 3. Critical temperature, field and current exist as limits. 4. **Type I** (pure metals): sharp transition at B_c. **Type II** (alloys, ceramics): mixed state between lower and upper critical fields B_c1 and B_c2; they stay superconducting to high fields. 5. Isotope effect: T_c ∝ 1/√M. 6. Heat capacity shows a jump at T_c; an energy gap appears. 7. Applications: powerful magnets (MRI, maglev), SQUIDs, lossless cables. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. A superconductor has A. Zero resistance below T_c B. Very high resistance C. Constant resistance D. Zero resistance at all T Answer: A. Resistance drops abruptly to zero below the critical temperature. (Key point: Definition) 2. B_c(T) varies as A. B_c(0)[1 − (T/Tc)^2] B. B_c(0)(T/Tc)^2 C. B_c(0)e^(−T) D. B_c(0)[1 + T/Tc] Answer: A. It is B_c(0) at T = 0 and falls to zero at T_c. (Key point: Critical field) 3. The Meissner effect is A. Perfect conductivity only B. Expulsion of magnetic flux, B = 0 inside C. Trapping of flux D. Heating by current Answer: B. This perfect diamagnetism differs from a perfect conductor. (Key point: Meissner) 4. Type II superconductors A. Have a sharp transition B. Have a mixed state between B_c1 and B_c2 C. Are pure metals only D. Show no critical field Answer: B. Type II (alloys, ceramics) stay superconducting to high fields. 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