Question

The critical magnetic fields of a super-conductor at temperatures 4K and 8K are 11 mA/m and 5.5 mA/m respectively. The transition
temperature is approximately?
a.8.4 K
b.10.6 K
c.12.9 K
d.15.0 K

Answer 1

The critical magnetic field in the superconductor is related to the temperature by equation

$$H_c(T)=H_c(0)\left[1-\left(\frac{T}{T_c}\right)^2\right]$$

Hence

$$T_c=\sqrt{\frac{H_{c1}T_2^2-H_{c2}T_1^2}{H_{c1}-H_{c2}}}$$

$$T_c=\sqrt{\frac{11*8^2-5.5*4^2}{11-5.5}}=10.6\:\rm K$$

Answer: b