Basic Statistics

## Why curl of coservative fields is zero

If earth is a big magnet, then why does not all the iron stick to it?

## BCS theory

At sufficiently low temperatures, electrons near the Fermi surface become unstable against the formation of Cooper pairs. Cooper showed such binding will occur in the presence of an attractive potential, no matter how weak. In conventional superconductors, an attraction is generally attributed to an electron-lattice interaction. The BCS theory, however, requires only that the potential be attractive, regardless of its origin. In the BCS framework, superconductivity is a macroscopic effect which results from “condensation” of Cooper pairs. These have some bosonic properties, while bosons, at sufficiently low temperature, can form a large Bose-Einstein condensate. Superconductivity was simultaneously explained by Nikolay Bogoliubov, by means of the so-called Bogoliubov transformations.

In many superconductors, the attractive interaction between electrons (necessary for pairing) is brought about indirectly by the interaction between the electrons and the vibrating crystal lattice (the phonons). Roughly speaking the picture is the following:

An electron moving through a conductor will attract nearby positive charges in the lattice. This deformation of the lattice causes another electron, with opposite “spin”, to move into the region of higher positive charge density. The two electrons then become correlated. There are a lot of such electron pairs in a superconductor, so that they overlap very strongly, forming a highly collective “condensate”. Breaking of one pair results in changing of energies of remained macroscopic number of pairs. If the required energy is higher than the energy provided by kicks from oscillating atoms in the conductor (which is true at low temperatures), then the electrons will stay paired and resist all kicks, thus not experiencing resistance. Thus, the collective behaviour of “condensate” is a crucial ingredient of superconductors.

## skin effect

skin effect is ac flows on the surface of conductor or upto a certain depth.

but why so?  flow of current is due to movement or moment of electron… is there no free electron in bulk of conductor,  if no then why ,  if yes then why ac can’t flow there and what about dc , can it flow in bulk of conductor..

what is the difference in flow of electron in ac and dc

## BCS Theory of Superconductivity

A qualitative discussion of a successful theory of superconductivity was given by Bardeen, Copper and Schrieffer, known as BCS theory after the initials of their names. This theory accounts for all properties of superconductors.

(a)    Electron –phonon Interaction. Continue reading “BCS Theory of Superconductivity”

## Assignment-I (b)

Assignment-I (b)

Electrostatics and Electrodynamics

1. Write Maxwell’s equations both in integral and differential forms. Also give their physical significance.
2. What is Equation of continuity? Explain. How could Maxwell correct and present Ampere’s law in its generalized form?
3. Using Ampere law obtain an expression for the magnetic field due to a current carrying straight conductor of infinite length.
4. State Gauss theorem. Derive the differential form of Gauss Theorem.
5. Show that Coulomb’s Law can be deduced from Gauss Law.
6. Using Gauss Theorem calculate the electric field due to a uniformly charged non conducting solid sphere at a point (i) Outside the sphere (ii) On the surface of sphere (iii) Inside the sphere.
7. Show that the Electric field is conservative and Prove curl E =0.
8. Given A=y2x i + (y-x) k , find divergence and curl of A.