Silsbee rule and other properties in superconductors

Silsbee rule: An important result of the existence of critical magnetic field is that there is also critical strength of current Ic flowing in the superconductor. Exceeding this limit also causes the disturbance of superconductivity. To derive the relation between critical current field consider a superconductor wire of radius r carrying a current I. This current will produce a magnetic field given by:

H=I/2 π r                                  (Using Ampere’s Circuital law)

If the current through wire is such that H>Hc then Ic the superconductivity will be destroyed and material will go to normal state. Therefore if Ic is the current for which H=Hc then Ic is called critical current and is given by

Ic=2 π rHc

This is known as Silsbee’s rule. Critical current density is given by

Jc =Ic/ Area =2 π r Hc/ π r2

Or Jc=2Hc/r

Properties which change in the superconducting Transition:-

(i)      The magnetic properties in superconductors undergo change. In the pure superconducting state practically no magnetic flux is able to enter the metal which thus behaves as if it had zero permeability or strong diamagnetic susceptibility. This effect is called Meissner effect.

(ii)    The specific heat changes discontinuously at the transition temperature. There is small change of volume at transition in the presence of magnetic field.

(iii)   All the thermoelectric effects disappear in the superconducting state.

(iv)  The thermal conductivity changes discontinuously when the superconductivity is destroyed in magnetic field. It is lower in the superconducting state for pure metal but higher for certain alloys.

(v)    The entropy in the superconducting state is lesser comparative to the normal state,  that is the superconductive state is more ordered state.

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