Find the electric flux due to a point charge 'Q' through the circular region of radius R if the charge is placed on the axis of ring at a distance x.

Explanation

We can divide the circular region into small rings.

Lets take a ring of radius r and width dr. Flux through this small element `dphi=E ds cos theta`
`:. phi_("net")= int E ds cos theta = underset(r=0)overset(r-R)(int) (KQ)/((x^(2)+r^(2)))(2pi r dr) (x/sqrt(x^(2)+r^(2)))=Q/(2 in_(0))[1-x/sqrt(x^(2)+R^(2))]`