4: The electric flux through any closed surface surrounding a point charge q is given by Gauss's law. (a) Enclosed charge is positive. (b) Enclosed charge is negative. The Gaussian surface does not need to correspond to a real, physical object; indeed, it rarely will.
Can Gaussian surface have charge?
It is immediately apparent that for a spherical Gaussian surface of radius r < R the enclosed charge is zero: hence the net flux is zero and the magnitude of the electric field on the Gaussian surface is also 0 (by letting QA = 0 in Gauss's law, where QA is the charge enclosed by the Gaussian surface).
Can flux through a closed Gaussian surface be negative?
The flux out of the closed Gaussian surface is positive. Flux flowing in to the closed Gaussian surface is negative. The net flux through a closed surface (Gaussian surface) is proportional to the net charge inside the surface.
