Gauss’ Theorem

Chapter-1|Electric Charges and Fields | NCERT 12th Physics:

Gauss’ Theorem:

This theorem gives a relationship between the total flux passing through any closed surface and the net charge enclosed within the surface.

”Gauss’ theorem state that the total flux through any closed surface is 1/ε₀ times the net charge enclosed by the closed surface”.

Mathematically, it can be expressed as-


Gaussian Surface:

A closed surface around a charge distribution is such that the electric field intensity has a single fixed value at every point on the surface and the electric flux through the surface is normal to the surface.


To prove Gauss Theorem we will take an isolated positive charge inside a surface at its Centre. let S be the surface area and r be the radius of the sphere.

Since every point on surface is equidistant from its centre so its surface is a Gaussian surface.





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