Electrical Engineering ⇒ Topic : Proof of Gausss Law

Proof of Gauss's Law

Consider a positive charge + Q located at point 0 as shown in Fig. (a). We draw a sphere of radius r with charge + Q as its centre. We now show that total electric flux (i.e. total number of electric lines of force) passing through the closed surface is Q/ε_o. The magnitude of electric field at any point on the spherical surface is given by 

                                                          figure (a)

The electric field is directed radially outward from + Q. The spherical surface is only imaginar and is called Gaussian surface.

Consider a small elementary area dS on the surface of sphere as shown in Fig.(a). It is clear that E is* parallel to dS i. e. angle between E and dS is zero. Therefore, electric flux through the entire closed spherical surface is