A uniformly charged and infinitely long line having a liner charge density λ is placed at a normal distance y from a point O. Consider a sphere of radius R with O as the center and R > y. Electric flux through the surface of the sphere is

Electric flux ∮  SE→⋅d→s=qin ε0qin, is the charge enclosed by the Gaussian surface, which, in the present case, is the surface of the given sphere. As shown, length AB of line lies inside the sphere. In ΔOO′A, R2=Y2+O′A2∴ O′A=R2−y2 and  AB=2R2−y2 Charge on length AB is 2R2−y2×λTherefore, electric flux is∮  SE→⋅d→s=2λR2−y2ε0