Question

A given superconductor has a critical field of 2.3 x 10 5 and 6.8 x 10 5 A/m at 10 K and 8 K, respectively. Calculate its transition temperature and critical field for 4.2 K.

Answer 1

The critical field:

$$H_{1}=H_0\bigg(1-\frac{T_1^2}{T_{c}^2}\bigg),\\\space\\ H_{2}=H_0\bigg(1-\frac{T_2^2}{T_{c}^2}\bigg),\\\space\\ \frac{H_{1}}{H_{2}}=\frac{1-T_1^2/T_c^2}{1-T_2^2/T_c^2},\\\space\\ T_c=122.8\text{ K}.\\\space\\ H_0=6.83·10^5\text{ A/m}.$$

The field at 4.2 K:

$$H_3=6.83·10^5\bigg(1-\frac{4.2^2}{122.8^2}\bigg)=6.82·10^5\text{ A/m}.$$