for superconductors we have a phase transition diagram. according to that phase diagram in a temperature below Tc, we can only increase the applied magnetic field to make a superconductor a normal. but when i ask it from a prof. he said that we can not do that just by increasing the applied magnetic field because the applied magnetic field does not increase the velocity and so the copper pairs can not be broken. so is his reasoning right or wrong?
Superconductors have both a critical temperature, at which they transition to the normal phase, and a critical applied magnetic field value. Once the applied magnetic field is at the critical value, a transition to normal occurs, regardless of the fact that the superconductor is below its critical temperature.
The critical value of the applied magnetic field varies with temperature, from a maximum at absolute zero temperature, to lower values as the critical temperature for superconductivity is approached.
If an applied magnetic field is above the critical value, the Meissner effect no longer functions to exclude the magnetic field from the superconductor. A magnetic field stronger than the critical value induces a high electric current that breaks superconductivity. The energy of electron interaction which forms Cooper pairs is quite weak, and can be broken either by high temperature or by a strong magnetic field.
See this summary: http://hyperphysics.phy-astr.gsu.edu/hbase/solids/scbc.html.