What is the magnetic susceptibility of an ideal superconductor?

Superconductor:

A superconductor is a material that achieves superconductivity, which is a state of matter that has no electrical resistance and does not allow magnetic fields to penetrate.

Properties of an ideal superconductor:

1.)  Critical temperature / Transition temperature:

• The temperature below which the material changes from conductors to superconductors is called critical temperature or transition temperature.
• The transition from conductors to superconductors is sudden and complete.

2.) Zero Electric Resistance/Infinite Conductivity:

• In the superconducting state, the material has zero resistance. When the temperature of the material is reduced below the critical temperature, its resistance suddenly reduces to zero. 

3.) Expulsion of Magnetic Field:

• ​Below the critical temperature, superconductors do not allow the magnetic field to penetrate inside them. This phenomenon is called Meisser Effect. 

4.) Critical Magnetic Field:

• The certain value of the magnetic field beyond which the superconductors return to conducting state is called the critical magnetic field.
• The value of the critical magnetic field is inversely proportional to the temperature. 
• As the temperature increases, the value of the critical magnetic field decreases.

5.) Magnetic Susceptibility:

The magnetic susceptibility of an ideal superconductor is -1.

The magnetic field of a superconductor is given by:

B = μ (1 + χ)

where, B = Magnetic field

μ = Permittivity

χ = Susceptibility

SInce, the magnetic field inside a superconductor is zero i.e.

B = 0

0 = μ (1 + χ)

χ = -1