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 transition temperature can be found from the critical magnetic fields. Write the critical field for the given temperature for both cases:

$$H_{cT1}=H_{c0}\bigg(1-\bigg(\frac {T_1}{T_c}\bigg)^2\bigg),\\\space\\ H_{cT2}=H_{c0}\bigg(1-\bigg(\frac {T_2}{T_c}\bigg)^2\bigg).$$

The ratio is

$$\frac{H_{cT1}}{H_{cT2}}=\frac{T_c^2-T_1^2}{T_c^2-T_2^2},\\\space\\ T_c=10.6\text{ K}.$$