effect of field on superconductivity critical

Question

EFFECT OF FIELD ON SUPERCONDUCTIVITY: Critical Magnetic field, H_c is the maximum field that can be applied to a superconductor without destroying the superconducting behaviour. It decreases from its maximum value at absolute zero to zero at the critical temperature T_c. On the other hand, Critical Temperature T_{c, ­}is a temperature that separates superconducting states from the normal state. Above T_c the substance is the normal state whit a finite resistivity but below T_c it is in super conducting state whit zero resistivity. The transition temperature of a superconductor can be reduced by the application of a magnetic field. Whit reference to suppose a superconductor has a temperature Tc. If magnetic field H is applied, the material remains super conducting until a critical field H_c is reached such that for H >H_c, the material is in the normal state. The transition from the superconducting to the normal state under influence of a magnetic field is reversible. The function H_c (T) follows with good accuracy a formula from here h_o is the critical field at 0K, T_c is the critical temperature for a given specimen.

MEISSNER EFFECT: The Meissner effect (or Meissner-Ochsenfeld Effect) is the total exclusion of any magnetic flux from the interior of a superconductor. A superconductor below its critical temperature expels all the magnetic field from the bulk of the sample as if it were a perfectly diamagnetic substance. This phenomenon is known as the Meissner effect. Suppose that we place a super conducting material in a magnetic field above T_c. The magnetic field lines will penetrate the sample. However, when the as depicted in fig. 6.3(a). The super conductor develops a magnetization M by developing surface currents, such that M and the applied field cancel everywhere inside the sample. Thus, below T_c a superconductor is a perfectly diamagnetic substance (χ_m= -1). Now for the case of a perfect conductor in a magnetic field and then cool it below. The magnetic field is not rejected. These two types of behaviour are identified. If we switch off the field, the field around the super conductor simply disappears. But switching off the field means there is a decreasing applied field. This change in the field induces current in the perfect conductor by virtue of Faraday’s law of induction.