Gauss's Law of Electric Field how it actually works? & How Gauss derived it? 
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*I want to know how Gauss derived his equation of Electric Field. Did he derive it from Coulomb's law? I don't think so. 

*Please tell me some details about how this law works? 

*inside a Gaussian surface neat $E = 0$ and why it doesn't depend on the shape of the Gaussian surface? (I know, the electric field goes in the Gaussian surface is canceled by those going out of it, but how come it doesn't depend on the shape of that surface?)
 A: The radiant flux model can actually be used to explain the inverse square law, and in modern theories, it is one of the founding equations $\nabla\cdot D = \rho $.
Suppose you have a point charge $Q$.  It emits flux $\Psi$ which radiates outwards.  Since Q has no way to add to the flux once it has left it, the same flux is spread over increasing spheres $S=4\pi r^2$, and thus the density of flux $D = \Psi/S = Q/4\pi r^2$.
Flux is a vector.  Specifically one can consider the electric field not as the action of remote charges, but local fluxkins buffeting another charge in the same way that waves, rather than what caused them, make a boat rock.
To evaluate the flux density at a point, one has to calculate the flux produced by each point of charge, and then consider the permittivity or the 'permission that space gives fluxkins to become fieldkins' ($\epsilon$), and then the nature of the field it is being acted on $F = qE$.
The total flux inside a space then depends simply on the solid angle the element of space occupies relative to each point (negative if the charge is 'outside' the element), and the charge the solid angle is measured from.
Since for any closed space, the total solid angle is 1 sphere, the total measure of flux is a direct measure of the charge contained inside the surface.  In SI, charge = flux, in CGS, flux = charge * steradians = $4\pi Q$.
Because the total flux through a surface is directly dependent on the charge, one can use symmetry to find the field (flux density at the surface).  One devises surfaces where symmetry says as much flux is coming in as out (the ends of a cylinder surrounding a long wire, for example), or are net equidistant from the charge (the curved walls of the cylinder), and because symmetry tells that the density on the non-zero surfaces are equal, it is simple to derive the flux at a distance $r$ from a wire of charge $Q/l$ is $S = 2\pi r l$ (the area active area), and thus $D=Q/S = Q/2\pi r l$.  But since we have $Q/l$, we write $D = (Q/L)/(2\pi r)$.  
It does not depend on surface, because the flux is actually counting 'lines of force'.  One might suppose that a charge has say 120 lines of force.  Regardless of the shape you draw around the charge, you have to cross all 120 lines of force going outwards, and any number of lines of force that cross inwards and outwards.  That is, the can be any number of lines of force through a surface, but except for the 120 that start at the charge, all other segments of lines enter the volume, and then depart it.  And it is that we can see that there are 120 more exits than entrances that the is that charge inside it.
The maxwell equation $\nabla\cdot D = \rho$ is a point-wise differential form of the gaussian surface.  What it means is that each element of space can be treated as a gaussian box, and the amount of flux produced by that box is directly dependent on the density of charge inside the box.  
