0Here is an intuitive explanation of Gauss Law:
Pre-requisites: Electric field, Area Vector, Dot Product of Vectors
There are two concepts crucial to understanding the Gauss Law, first of which is the concept of electric flux. Now electric flux through any surface can be thought of as liquid flowing through an area. Gauss Law in basic terms, helps evaluate the total flow passing through a closed surface.
We begin by breaking down the entire surface into smaller sections (dA). Now the dot product of the 'flow' of electric field through this small area's vector gives the total electric flux. We add up all such dot products to arrive the net flux through the surface. Gauss Law gives a simplified relation between this 'sum of flux' and the charge enclosed as:
∫ E.dA = Total Charge Enclosed in the Surface / ε
Solved Example
The law finds its best application for symmetrical surfaces with difficult surface integrals. For instance, what would be the net flux through a square surface kept at a distance s from a charge particle Q.
You can start by imagining a cube around the charge, one of the faces of which is represented by the square in consideration. Gauss Law states that the net flux through the closed cube would be Q/ε. Now we shift our focus to the one square surface, given that all the surfaces are symmetrical, we can argue that the flux through each of the 6 faces should be same and must add up to Q/ε as suggested by Gauss Law. Therefore, the net flux through each one of the surfaces should be Q/6ε. Hence we arrive at the final answer. The net flux through a square surface kept near a charge Q is Q/6ε.
