How to use Gauss's Law to find electric field

W all know that Gauss's law is basically the relation between the charge distribution producing the electrostatic field to the behaviour of electrostatic field in space. Also Gauss's law is based on the fact that flux through any closed surface is a measure of total amount of charge inside that surface and any charge outside that surface would not contribute anything to the total flux. Now we'll go through the main steps which we can employ for applying Gauss's Law

1. First identify the symmetry properties of the charge distribution. By this we mean that the point at which the field is to be determined must lie on a surface and this surface must have enough symmetry which allows integrals involved to be evaluated properly.
2. Determine the direction of the electric field and a surface on which the magnitude of electric field is constant. 
3. Now choose the Gaussian surface accordingly for example if the problem has spherical symmetry then Gaussian surface would usually be spherical and for cylindrical symmetry problem Gaussian surface would be cylindrical.
4. Calculate the flux through the Gaussian surface.
5. Now calculate the charge enclosed inside the chosen Gaussian surface.
6. Equate the two sides of Gauss's law in order  to find the expression for the magnitude of the electric field in that region of space.

Row reduction method and rank of a matrix

1. Matrices are just a display of set of numbers and it does not have any value For example
is a 2 by 3 matrix having 2 rows and 3 columns.
Aij represents a matrix element of i’th row and jth column for example here A₁₂=6 and A₂₁=-2

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Superconductivity fact file (part 2)

• Transition between normal and superconducting state is thermodynamically reversible.
• London's equation is j=-CA/4π(λ_L)² , where λ_L is constant with dimensions of length and A is the vector potential.
• London equation accounts for Meissner effect . In a pure SC state the only field allowed is exponentially damped as we go from an external surface  B(x)=B(0)exp(-x/λ_L)  where λ_Lis the London penetration depth and is the measure of penetration of magnetic field.
• An applied magnetic field will penetrate a thin film fairly uniformly if the thickness is much less than λ_L. Thus in a thin film Meissner effect is not complete.
• Coherence length ξ is the measure of the distance within which SC electronic concentration can not change drastically in spatially varying magnetic field.
• Coherence length is a measure of the range over which we should average A to obtain j.
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