# Solution of Superconductivity Numericals

1. Lead has a superconducting transition temperature of 7.26 K. If initial field at 0 K is 50 ×
103 Am−1, calculate the critical field at 6 K. If the lead is in the form of a wire with diameter
1 mm, then calculate the critical current it can carry.

2. The critical field for niobium is 1 × 105 A/m at 8 K and 2 × 105 A/m at 0 K. Calculate the
transition temperature of the element.

3. A superconducting material has a critical temperature of 3.7 K in zero magnetic field and a
critical field of 0.02 T at 0 K. Find the critical field at 3 K.

4. The critical field for lead is 1.2 × 105 A/m at 8 K and 2.4 × 105 A/m at 0 K. Find the critical
temperature of the material.

5. The critical fields for lead are 1.2 × 105 A/m and 3.6 × 105 A/m at 12 K and 10 K, respectively. Find its critical temperature and critical field at 0 K and 3.2 K.

6. Determine the temperature at which the critical field becomes half of its value at 0 K, if
critical temperature of a superconductor when no magnetic field present is Tc.

7. A superconducting sample has a critical temperature of 3.722 K in zero magnetic field and a
critical field of 0.0305 T at 0 K. Evaluate the critical field at 2 K.

8. Determine the transition temperature and critical field at 4.2 K for a given specimen of a
superconductor if the critical fields are 1.41 × 105 and 4.205 × 105 A/m at 14.1 K and 12.9 K, respectively.

9. The material lead (Pb) behaves as a superconductor at a temperature of Tc = 7.26 K. If the
value of critical magnetic field of lead at T = 0 K is Hc = 8 × 105 A/m, find the critical magnetic field of lead at 4 K.

10. The critical temperature of a given superconducting sample is 1.19 K with mass 26.91. Find
the critical temperature when the isotope mass changes to 32.13.
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