CBSE Class 12-science Answered

Let us suppose that q is an isolated point charge situated at centre of sphere of radius

According to Coulomb’s law electric field intensity at every point on the surface of the sphere is

where is a unit vector directed from +q to the surface element.

Consider a small area element dS represented by vector

Where is a unit vector along outdrawn normal to the area element.

Integrating over closed surface area of the sphere, we get

Hence                       

If there are point charges,, each will contribute to the electric flux.

Therefore  =   

                         =

                         =

                      where Q=

Hence total electric flux over the closed surface S in vacuum is 1/ times the total charge (Q) contained inside S.