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.

Proof:

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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