ELECTRIC FLUX THROUGH SURFACE ENCLOSING CHARGE

Lets consider that we have to calculate electric flux of a charge "q" placed inside a spherical body since flux is calculated for a flat body so in order to convert sphere into flat body we will devide the whole sphere into small patches with area ∆A₁, ∆A₂, ∆A₃, ∆A₄----------∆A_n. There corresponding vector areas are parallel to electric field intensity or perpendicular to the surface area as shown in the fig



Electric flux for first patch is

CONCLUSION:-

               Total electric flux is directly proportional to charge enclosed by the surface and also on the medium. And it is independent of shape and geometry as from (ix) we see that flux is independent of distance from the surface. This is because "E" is directly proportional to 1/r² where as area is directly proportional to square of distance from the area to the charge r²  so in the end due to this charge closed in the surface is independent of distance of area to the charge so consequently flux is independent of shape or geometry of body enclosing charge. So flux in this spherical like body is same to that of sphere.If the charge is enclosed in a cube then flux would be almost same. This forms the basis of gausses law.