If a small planar element of area `DeltaS` is place normal to `vecE` at a point, the number of field line, crossing it is proportional to `vecE.DeltavecS`.
Suppose we tilt the area element by angle `theta` , the `DeltaS` number of field lines crossing AS is proportiona to `EDeltaS cos theta`.
When `theta = 90^(@)`, field lines will be parallel tc surface and will not cross it at all.
When `theta = 0^(@)` , field lines will be normal to surface as shown in figure.
The vector associated with every area element of a closed surface is taken to be in the direction of the outward normal. Thus, the area element vector `DeltavecS` at a point on a closed surface equals `DeltaS hatn` where `DeltaS` is the magnitude of the area element and h is a unit vector in the direction of outward normal at that point.
Electric flux is no. of electric field lines passing through or associated with the surface placed in electric field.
`therefore` Electric flux `Deltaphi` through an area element `DeltavecS` is `Deltaphi = vecE.DeltavecS = E DeltaS cos theta` , the angle `theta` here is the angle between `vecE` and `vecS`.
`phi = vecE.DeltavecS`
`=EDeltaS cos theta`
where `theta` is angle between `vecE` and `DeltavecS`
SI unit of electric flux is `Nm^(2)C^(-1)` or Vm and it is a scalar quantity.
Definition of electric.flux : "Electric flux associated with any area is areal integration of vector electric field on that area".
