3. Superconducting quantum Interference device (SQUID)

            From the fig.2.1 you see insulators at the position YZ and XW are the superconducting material.  For applied magnetic small field B Perpendicular to the plane of the ring produces a cooper pairs of electron along the path ZXY and YWZ. Thus a small current I is induced and that induced I is sufficient enough to cancel the magnetic flux B according to the Lenz’s law but the critical current of the superconductor-insulator link prevent this.

The total magnetic flux that passes through a superconductor ring may be assumed only in quantized value, Integral multiples of the flux quantum [1]. That is the total change in phase between current I and the applied magnetic field B around the closed Loop WXYZ can be written as 

         

where

and

Where is current density, is the magnetic vector potential and  is line element along the closed loop WXYZ. By applying stokes theorem we get

 this integral gives

thus     which is equal to 2.07X10^-15Wb. There is no quantization condition from external source, so that superconducting must adjust itself appropriately in order that    assume a quantized value [1].

 is critical measuring current and  is critical current. Hence circulating supercurrent has a periodic dependence on the magnitude of the applied magnetic field, with a period of variation of .The plot describes the behavior of measuring current vs. the applied magnetic field [3].