Question

One should not let the gaussian surface to pass through any discrete charge. This is because electric field due to a system of discrete charges is not well defined at the location of any charge. Explain this point .

Answer 1

The significance of Gauss law is to calculate electric field at a point. This is easily done by making a gaussian surface to pass through the point at which field is required and simultaneously enclosing the charge due to which the field is required inside the gaussian surface. If the gaussian surface is made to pass through a discrete charge itself then the significance of gauss law is lost as at the point where the discrete charge itself is present the value of electrical field becomes undefined(inverse square law).

The gaussian surface is the one where you compute the product of E.dS

dS→ is the normal unit vector multiplied by the differential area:


^This vector will always exist, BUT the electric field is not defined on the charge itself,so you cannot compute the flux in that point, hence you cannot know the value of the integral so the formula is absurd, as one of the sides is undefined. At the charge point r will become 0 and E->infinity does not define. So we can't draw a gaussGau surface passing through the charge.charge should be inside the surface than only we can calculate the electrical field.