# gauss law in electrostatics is true for any closed surface ,no matter wat its shape or size is.justify this statement with an example

Gauss law is true for any closed surface as the electric flux does not depend on the area , size,etc.
Flux only depends on the charge enclosed by surface as :
​Flux=Charge/permittivity of vacumn
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Gauss's Law :
The total electric  flux over a closed surface in vacuum is equal to 1/ε₀ the total charge enclosed by the surface.
if q is the charge enclosed by surface S, The total electric flux through the surface S is Φ=q/ε₀
while measuring the electric flux, surface area is more important than its volume or  its size.
Example:
let us consider a closed surface S encloses a point charges +q1,-q2,+q3 and -q4, the total charge enclosed is q= q1-q2+q3-q4
∴electric flux across S will be Φ=q/ε₀=(q1-q2+q3-q4)/ε₀
The total electric flux is zero if no charge is enclosed by the surface.
conclusion:
The closed surface chosen for application of Gauss's law is called as Gaussian surface. It can be of any shape or size
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According to Gauss's law, the electric flux through a closed surface depends on the net charge enclosed by the surface and not upon the size of the surface. For any closed surface of arbitrary shape enclosing a charge, the outward flux is same as that due to a spherical Gaussian surface enclosing the same charge. This is because of the fact that: (a) electric field is radial, and (b) the electric field, E directly proportional to 1/r²
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Here, size or shape is not matter net charge is not what is inside the surface. this proves that gaussian surface is my depends on shape and size of the surface.

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