What is electriG flux ? Explain how the electric flux through a surface is related to electric field intensity, when the surface is heldinside the electric field.

Explanation

Electric flux : It is defined as the total number of electric field lines passing through the given surface area normally.
Relation between electric field intensity and electric flux :
1. Let a closed surface of area S is held inside the electric field intensity E. If E is perpendicular to the given surface the `phi = ES`
2. If electric field is not perpendicular to the given surface : Let a surface having area S is held inside the electric field intensity E.
Consider the small are element dS of the surface S.
The elementary area dS can be represented by vec(dS) which is perpendicular to area element dS. Area vector `vec(dS)` is directed along normal to the area element dS.
Let `theta` = Angle which electric field makes with the area vector `vec(dS)`.

`E_(n) = E cos theta` = Component of electric field perpendicular to the area element dS. The electric field associated the area element dS is given as
`d phi = E_(n) dS`
`d phi = (E cos theta) dS = E dS cos theta = vec(E). vec(dS)`
Electric flux associated with the whole surface is given as
`oint d phi = oint vec(E). vec(dS) = oint E_(n) dS`