## Superconductors, critical temperature, critical magnetic field and Meissner effect

Superconductors:

Superconductors are the materials whose conductivity tends to infinite as resistivity tends to zero at critical temperature (transition temperature).

Critical temperature (Tc): The temperature at which a conductor becomes a superconductor is known as critical temperature.

Critical Magnetic Field (Hc): The magnetic field required to convert the superconductor into a conductor is known as critical magnetic field.

Critical magnetic field is related with critical temperature as:

Hc(T) = Hc(0)[1 – T2/Tc2]

Meissner Effect:

Suppose there is a conductor placed in a magnetic field at temperature T (refer figure). Then the temperature is decreased till the critical temperature. See what happened (figure). Lines of force are expelled from the superconductor. This is called Meissner effect.

B is not 0 at T > Tc                  B=0 at T < Tc

Definition Meissner Effect: The expulsion of magnetic lines of force from a superconducting specimen when it is cooled below the critical temperature is called Meissner effect.

To prove that superconductors are diamagnetic by nature:

B is not 0 at T > Tc                  B=0 at T < Tc

As B = µ0 (H +M)

Where B is magnetic induction or magnetic flux density,

H is applied magnetic field or magnetic field intensity

And M is intensity of magnetization.

For superconductors B = 0

Thus either µ0 = 0 or H + M = 0

But µ0 can not be zero,

Thus H + M =0

Or M = -H                               (1)

By definition of magnetic susceptibility

X = M/H

Put equation (1)

Thus X = -1

But magnetic susceptibility is negative for diamagnetic materials, thus it proves that superconductors are diamagnetic by nature.