A point charge q is placed at a distance d from the centre of a circular disc of radius R. Find electric flux flowing through the disc due to that charge.

Explanation

We know that total flux originated from a point charge q in all directions is `q/(in_0)`. 
This flux is originated in a solid angle `4pi`. In the given case solid angle subtended by the cone subtended by the disc at the point charge is `omega = 2pi (1 - cos theta)`
So, the flux of q which is passing through the surface of the disc is
`phi = q/(in_0) (omega)/(4 pi) = q/(2 in_0) (1 - cos theta)`
From the figure , `cos theta = d/(sqrt(d^2 + R^2))`
so, `phi = q/(2 in_0) {1 - d/(sqrt(d^2 + R^2))}`