(a) Define electric flux . Write its S.I. unit.
(b) Using Gauss's law , prove that electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it.
(c ) How is the field directed if (i) the sheet is positively charged , (ii) negatively charged ?

Explanation

(a) Electric flux is defined as the number of electric field lines passing through an area normal to the surface.
Alternatively,
Surface integral of the electric field is defined as the electric flux through a closed surface
`phi=ointvecE*vecds`
SI unit : `(N.m^(2))/(C)` or volt . metre
(b)
Outward flux through the Gaussian surface , is
`2EA=sigmaA//epsilon_(0)`
`thereforeE=sigma//2epsilon_(0)`
In vector form , `vecE=(sigma)/(2epsilon_(0))hatn`
where `hatn` is a unit vector normal to the plane , away from it .
Hence electric field is independent of the distance from the sheet.
(c ) For positively charged sheet the electric field is directed away from the sheet.
For negatively charged sheet the electric field is directed towards the plane of sheet.
For positively charged sheet the electric field is directed towards the plane of sheet.