Let P be a point very close to a charge conductor having surface charge density a near P. We have to find out electric field intensity at p.
As there is no surface current, the component of electric field along the tangent to the surface is zero. Hence vector E is normal to surface. Let us construct a small pill box as Gaussian surface, Its some part ties inside the metal surface where vector E = 0. As its thickness is very small because p is very close to surface the flux is only due to cap surface. Thus,
The electric field intensity σ/ε where σ is the surface density of charge near P.
