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

Explanation

We know that total flux origianted from a point charge `q` in all direction is `(q)/(epsilon_(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-costheta)`
So the flux of `q` which is passing through the surface of the disc is
`phi=(q)/(epsilon_(0))(Omega)/(4pi)=(q)/(2epsilon_(0))(1-costheta)`
from the figure `costheta=(d)/(sqrt(d^(2)+R^(2)))so`
`phi=(q)/(2pepsilon_(0)){1-(d)/(sqrt(d^(2))+R^(2))}`